The Error Correction Zoo

Victor V. Albert; Philippe Faist

References

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3rd Generation Partnership Project (3GPP), Technical specification group radio access network, 3GPP TS 38.212 V.15.0.0, 2017.. Appears in: Polar code
M. Aaltonen, “A new upper bound on nonbinary block codes”, Discrete Mathematics 83, 139 (1990) DOI. Appears in: $q$-ary code
S. Aaronson and D. Gottesman, “Improved simulation of stabilizer circuits”, Physical Review A 70, (2004) arXiv:quant-ph/0406196 DOI. Appears in: Qubit stabilizer code, Qubit code
S. Aaronson, D. Grier, and L. Schaeffer, “The Classification of Reversible Bit Operations”, (2015) arXiv:1504.05155. Appears in: Binary code
S. Aaronson, “The Complexity of Quantum States and Transformations: From Quantum Money to Black Holes”, (2016) arXiv:1607.05256. Appears in: Approximate quantum error-correcting code (AQECC)
D. Aasen et al., “Milestones Toward Majorana-Based Quantum Computing”, Physical Review X 6, (2016) arXiv:1511.05153 DOI. Appears in: Majorana box qubit
D. Aasen, D. Bulmash, A. Prem, K. Slagle, and D. J. Williamson, “Topological defect networks for fractons of all types”, Physical Review Research 2, (2020) arXiv:2002.05166 DOI. Appears in: Fracton stabilizer code, Topological code
D. Aasen, Z. Wang, and M. B. Hastings, “Adiabatic paths of Hamiltonians, symmetries of topological order, and automorphism codes”, Physical Review B 106, (2022) arXiv:2203.11137 DOI. Appears in: Honeycomb Floquet code
D. Aasen, J. Haah, P. Bonderson, Z. Wang, and M. Hastings, “Fault-Tolerant Hastings-Haah Codes in the Presence of Dead Qubits”, (2023) arXiv:2307.03715. Appears in: Hastings-Haah Floquet code
D. Aasen, J. Haah, Z. Li, and R. S. K. Mong, “Measurement Quantum Cellular Automata and Anomalies in Floquet Codes”, (2023) arXiv:2304.01277. Appears in: Modular-qudit stabilizer code
A. Abbasfar, D. Divsalar, and K. Yao, “Accumulate-Repeat-Accumulate Codes”, IEEE Transactions on Communications 55, 692 (2007) DOI. Appears in: Accumulate-repeat-accumulate (ARA) code
E. Abbe, A. Shpilka, and A. Wigderson, “Reed-Muller codes for random erasures and errors”, (2014) arXiv:1411.4590. Appears in: Reed-Muller (RM) code
E. Abbe, A. Shpilka, and M. Ye, “Reed-Muller Codes: Theory and Algorithms”, (2020) arXiv:2002.03317. Appears in: Reed-Muller (RM) code
E. Abbe and C. Sandon, “A proof that Reed-Muller codes achieve Shannon capacity on symmetric channels”, (2023) arXiv:2304.02509. Appears in: Reed-Muller (RM) code
K. A. S. Abdel-Ghaffar and H. C. Ferreira, “Systematic encoding of the Varshamov-Tenengol’ts codes and the Constantin-Rao codes”, IEEE Transactions on Information Theory 44, 340 (1998) DOI. Appears in: Constantin-Rao (CR) code
M. H. Abobeih, Y. Wang, J. Randall, S. J. H. Loenen, C. E. Bradley, M. Markham, D. J. Twitchen, B. M. Terhal, and T. H. Taminiau, “Fault-tolerant operation of a logical qubit in a diamond quantum processor”, Nature 606, 884 (2022) arXiv:2108.01646 DOI. Appears in: Five-qubit perfect code
M. Abroshan, R. Venkataramanan, and A. G. i Fabregas, “Efficient Systematic Encoding of Non-binary VT Codes”, (2018) arXiv:1708.04071. Appears in: Varshamov-Tenengolts (VT) code
R. Acharya et al., “Suppressing quantum errors by scaling a surface code logical qubit”, (2022) arXiv:2207.06431. Appears in: Quantum repetition code, XZZX surface code
R. Acharya et al., “Quantum error correction below the surface code threshold”, (2024) arXiv:2408.13687. Appears in: Quantum repetition code, XZZX surface code
J. C. Adcock, S. Morley-Short, A. Dahlberg, and J. W. Silverstone, “Mapping graph state orbits under local complementation”, Quantum 4, 305 (2020) arXiv:1910.03969 DOI. Appears in: Cluster-state code
Addelman, S., & Kempthorne, O. (1961b). Orthogonal Main-Effect Plans. Technical Report ARL 79, Aeronautical Research Lab., Wright-Patterson Air Force Base, Ohio, Nov. 1961.. Appears in: Mixed code, Orthogonal array (OA)
A. Adolphson, “Hypergeometric functions and rings generated by monomials”, Duke Mathematical Journal 73, (1994) DOI. Appears in: Tiger code
“Advances in smart antennas - MIMO-OFDM wireless systems: basics, perspectives, and challenges”, IEEE Wireless Communications 13, 31 (2006) DOI. Appears in: Spacetime block code (STBC)
I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, “Rigorous Results on Valence-Bond Ground States in Antiferromagnets”, Condensed Matter Physics and Exactly Soluble Models 249 (2004) DOI. Appears in: Commuting-projector Hamiltonian code, Frustration-free Hamiltonian code, Valence-bond-solid (VBS) code
A. Agarwal, A. Barg, S. Hu, A. Mazumdar, and I. Tamo, “Combinatorial Alphabet-Dependent Bounds for Locally Recoverable Codes”, IEEE Transactions on Information Theory 64, 3481 (2018) arXiv:1702.02685 DOI. Appears in: Locally recoverable code (LRC)
G. S. Agarwal, “Generation of Pair Coherent States and Squeezing via the Competition of Four-Wave Mixing and Amplified Spontaneous Emission”, Physical Review Letters 57, 827 (1986) DOI. Appears in: Pair-cat code
G. S. Agarwal, “Nonclassical statistics of fields in pair coherent states”, Journal of the Optical Society of America B 5, 1940 (1988) DOI. Appears in: Pair-cat code
V. Aggarwal and A. R. Calderbank, “Boolean Functions, Projection Operators, and Quantum Error Correcting Codes”, IEEE Transactions on Information Theory 54, 1700 (2008) arXiv:cs/0610159 DOI. Appears in: Codeword stabilized (CWS) code, $((5,6,2))$ qubit code, $((5+2r,3\times 2^{2r+1},2))$ Rains code
H. Aghaee Rad et al., “Scaling and networking a modular photonic quantum computer”, Nature (2025) DOI. Appears in: Analog-cluster-state code, GKP CV-cluster-state code
E. Agrell, T. Eriksson, A. Vardy, and K. Zeger, “Closest point search in lattices”, IEEE Transactions on Information Theory 48, 2201 (2002) DOI. Appears in: Gottesman-Kitaev-Preskill (GKP) code
Agrell, E. "Database of sphere packings, 2019." Online: https://codes. se/packings. Accessed (2015).. Appears in: Sphere packing
M. Aguado and G. Vidal, “Entanglement Renormalization and Topological Order”, Physical Review Letters 100, (2008) arXiv:0712.0348 DOI. Appears in: Quantum-double code, String-net code, Kitaev surface code
M. Aguado, “From entanglement renormalisation to the disentanglement of quantum double models”, Annals of Physics 326, 2444 (2011) arXiv:1101.0527 DOI. Appears in: Quantum-double code
D. Aharonov, A. Kitaev, and N. Nisan, “Quantum Circuits with Mixed States”, (1998) arXiv:quant-ph/9806029. Appears in: Approximate operator-algebra QECC
D. Aharonov and M. Ben-Or, “Fault-Tolerant Quantum Computation With Constant Error Rate”, (1999) arXiv:quant-ph/9906129. Appears in: Galois-qudit GRS code, Galois-qudit RS code, Concatenated qubit code, Qubit code
D. Aharonov, “Quantum to classical phase transition in noisy quantum computers”, Physical Review A 62, (2000) arXiv:quant-ph/9910081 DOI. Appears in: Random-circuit code
D. Aharonov, A. Kitaev, and J. Preskill, “Fault-Tolerant Quantum Computation with Long-Range Correlated Noise”, Physical Review Letters 96, (2006) arXiv:quant-ph/0510231 DOI. Appears in: Qubit code
D. Aharonov and L. Eldar, “On the complexity of Commuting Local Hamiltonians, and tight conditions for Topological Order in such systems”, (2011) arXiv:1102.0770. Appears in: 2D lattice stabilizer code, Commuting-projector Hamiltonian code, Topological code
D. Aharonov and L. Eldar, “Quantum Locally Testable Codes”, (2013) arXiv:1310.5664. Appears in: Quantum locally testable code (QLTC)
D. Aharonov, I. Arad, and T. Vidick, “The Quantum PCP Conjecture”, (2013) arXiv:1309.7495. Appears in: Quantum locally testable code (QLTC)
D. Aharonov, O. Kenneth, and I. Vigdorovich, “On the Complexity of Two Dimensional Commuting Local Hamiltonians”, (2018) arXiv:1803.02213 DOI. Appears in: 2D lattice stabilizer code, Commuting-projector Hamiltonian code, Topological code
D. Aharonov and Y. Touati, “Quantum Circuit Depth Lower Bounds For Homological Codes”, (2018) arXiv:1810.03912. Appears in: Kitaev surface code
Y. Aharonov and L. Susskind, “Charge Superselection Rule”, Physical Review 155, 1428 (1967) DOI. Appears in: Bosonic code
Y. Aharonov, H. Pendleton, and A. Petersen, “Modular variables in quantum theory”, International Journal of Theoretical Physics 2, 213 (1969) DOI. Appears in: Square-lattice GKP code
R. Ahlswede and N. Cai, “Codes with the identifiable parent property and the multiple–access channel”, Electronic Notes in Discrete Mathematics 21, 143 (2005) DOI. Appears in: Frameproof (FP) code, Identifiable parent property (IPP) code
C. S. Ahn, Extending Quantum Error Correction: New Continuous Measurement Protocols and Improved Fault-Tolerant Overhead, California Institute of Technology, 2004 DOI. Appears in: Homological code
C. Ahn, A. C. Doherty, and A. J. Landahl, “Continuous quantum error correction via quantum feedback control”, Physical Review A 65, (2002) arXiv:quant-ph/0110111 DOI. Appears in: Finite-dimensional quantum error-correcting code, Quantum repetition code
C. Ahn, H. M. Wiseman, and G. J. Milburn, “Quantum error correction for continuously detected errors”, Physical Review A 67, (2003) arXiv:quant-ph/0302006 DOI. Appears in: Amplitude-damping (AD) code, $[[2m,2m-2,2]]$ error-detecting code
C. Ahn, H. Wiseman, and K. Jacobs, “Quantum error correction for continuously detected errors with any number of error channels per qubit”, Physical Review A 70, (2004) arXiv:quant-ph/0402067 DOI. Appears in: Amplitude-damping (AD) code, $[[2m,2m-2,2]]$ error-detecting code
C. T. Aitchison, D. Bulmash, A. Dua, A. C. Doherty, and D. J. Williamson, “Boundaries and defects in the cubic code”, Physical Review B 109, (2024) arXiv:2308.00138 DOI. Appears in: Haah cubic code (CC)
C. Akers, N. Engelhardt, D. Harlow, G. Penington, and S. Vardhan, “The black hole interior from non-isometric codes and complexity”, (2022) arXiv:2207.06536. Appears in: Holographic tensor-network code
S. Al-Bassam and B. Bose, “On balanced codes”, IEEE Transactions on Information Theory 36, 406 (1990) DOI. Appears in: Balanced code
G. Alagic, Y. Dulek, C. Schaffner, and F. Speelman, “Quantum Fully Homomorphic Encryption with Verification”, Lecture Notes in Computer Science 438 (2017) arXiv:1708.09156 DOI. Appears in: Qubit CSS code
A. Alahmadi, H. Alhazmi, T. Helleseth, R. Hijazi, N. Muthana, and P. Solé, “On the lifted Melas code”, Cryptography and Communications 8, 7 (2015) DOI. Appears in: Melas code, Quaternary linear code over $\mathbb{Z}_4$
M. S. Alam and E. Rieffel, “Dynamical Logical Qubits in the Bacon-Shor Code”, (2024) arXiv:2403.03291. Appears in: Bacon-Shor code, Hastings-Haah Floquet code
S. M. Alamouti, “A simple transmit diversity technique for wireless communications”, IEEE Journal on Selected Areas in Communications 16, 1451 (1998) DOI. Appears in: Alamouti code, Orthogonal Spacetime Block Code (OSTBC)
G. Alber, Th. Beth, Ch. Charnes, A. Delgado, M. Grassl, and M. Mussinger, “Stabilizing Distinguishable Qubits against Spontaneous Decay by Detected-Jump Correcting Quantum Codes”, Physical Review Letters 86, 4402 (2001) arXiv:quant-ph/0103042 DOI. Appears in: Amplitude-damping (AD) code, Dual-rail quantum code, Jump code, Quantum parity code (QPC), Concatenated qubit code, $[[4,2,2]]$ Four-qubit code
G. Alber, Th. Beth, Ch. Charnes, A. Delgado, M. Grassl, and M. Mussinger, “Detected-jump-error-correcting quantum codes, quantum error designs, and quantum computation”, Physical Review A 68, (2003) arXiv:quant-ph/0208140 DOI. Appears in: Combinatorial design, $[[2m,2m-2,2]]$ error-detecting code, Jump code, $[[4,2,2]]$ Four-qubit code
V. V. Albert, G. D. Scholes, and P. Brumer, “Symmetric rotating-wave approximation for the generalized single-mode spin-boson system”, Physical Review A 84, (2011) arXiv:1106.3800 DOI. Appears in: Bosonic $q$-ary expansion
V. V. Albert, C. Shu, S. Krastanov, C. Shen, R.-B. Liu, Z.-B. Yang, R. J. Schoelkopf, M. Mirrahimi, M. H. Devoret, and L. Jiang, “Holonomic Quantum Control with Continuous Variable Systems”, Physical Review Letters 116, (2016) arXiv:1503.00194 DOI. Appears in: Cat code, Two-component cat code
V. V. Albert, S. Pascazio, and M. H. Devoret, “General phase spaces: from discrete variables to rotor and continuum limits”, Journal of Physics A: Mathematical and Theoretical 50, 504002 (2017) arXiv:1709.04460 DOI. Appears in: Analog stabilizer code, Analog surface code, Compactified $\mathbb{R}$ gauge theory code, Homological rotor code, Qudit cubic code, Modular-qudit surface code, Rotor code, Tiger surface code, Abelian topological code
V. V. Albert et al., “Performance and structure of single-mode bosonic codes”, Physical Review A 97, (2018) arXiv:1708.05010 DOI. Appears in: Amplitude-damping (AD) code, Approximate quantum error-correcting code (AQECC), Binomial code, Coherent-state constellation code, Square-lattice GKP code, GNU PI code, Numerically optimized bosonic code, Quantum lattice code, Qudit-into-oscillator code
V. V. Albert, “Lindbladians with multiple steady states: theory and applications”, (2018) arXiv:1802.00010. Appears in: Frustration-free Hamiltonian code
V. V. Albert, S. O. Mundhada, A. Grimm, S. Touzard, M. H. Devoret, and L. Jiang, “Pair-cat codes: autonomous error-correction with low-order nonlinearity”, Quantum Science and Technology 4, 035007 (2019) arXiv:1801.05897 DOI. Appears in: Pair-cat code
V. V. Albert, J. P. Covey, and J. Preskill, “Robust Encoding of a Qubit in a Molecule”, Physical Review X 10, (2020) arXiv:1911.00099 DOI. Appears in: Diatomic molecular code, Group GKP code, Group-based quantum code, Molecular code, Rotor code, Rotor GKP code
V. V. Albert, D. Aasen, W. Xu, W. Ji, J. Alicea, and J. Preskill, “Spin chains, defects, and quantum wires for the quantum-double edge”, (2021) arXiv:2111.12096. Appears in: Generalized 2D color code, Group GKP code, Group-based quantum code, Quantum-double code
V. V. Albert, “Bosonic coding: introduction and use cases”, (2022) arXiv:2211.05714. Appears in: Oscillator-into-oscillator GKP code, Bosonic code
V. V. Albert, Boulder School 2023 Lecture notes. Appears in: $[[4,1,1,2]]$ Four-qubit subsystem code, Ladder Floquet code, $[[4,2,2]]$ Four-qubit code
V. V. Albert, private communication, 2024.. Appears in: Hexacode, Polyphase code, Spherical design
C. D. de Albuquerque, G. G. La Guardia, R. Palazzo Jr., C. R. de O. Q. Queiroz, and V. L. Vieira, “Euclidean and Hyperbolic Asymmetric Topological Quantum Codes”, (2021) arXiv:2105.01144. Appears in: Asymmetric quantum code, Kitaev surface code, 2D hyperbolic surface code
C. D. Albuquerque, R. Palazzo Jr., and E. B. Silva, “Topological quantum codes on compact surfaces with genus g≥2”, Journal of Mathematical Physics 50, (2009) DOI. Appears in: 2D hyperbolic surface code
C. D. Albuquerque, R. Palazzo Jr., and E. B. Silva, “New classes of TQC associated with self-dual, quasi self-dual and denser tessellations”, Quantum Information and Computation 10, 956 (2010) DOI. Appears in: 2D hyperbolic surface code
C. D. Albuquerque et al., On Toric Quantum Codes, Int. J. Pure Appl. Math. 50, 221–-226 (2009).. Appears in: $D$-dimensional twisted toric code
Aleksander Kubica, private communication, 2019. Appears in: Majorana stabilizer code, Five-qubit perfect code
S. P. Alex and L. M. A. Jalloul, “Performance Evaluation of MIMO in IEEE802.16e/WiMAX”, IEEE Journal of Selected Topics in Signal Processing 2, 181 (2008) DOI. Appears in: Spacetime block code (STBC)
K. Alexander et al., “A manufacturable platform for photonic quantum computing”, (2024) arXiv:2404.17570. Appears in: Dual-rail quantum code
Alexei Kitaev, On the Classification of Short-Range Entangled States, talk at Simons Center (2013). Appears in: Hamiltonian-based code
Alexei Kitaev, Toward Topological Classification of Phases with Short-range Entanglement, talk at KITP (2011). Appears in: Hamiltonian-based code
M. G. Algaba, P. V. Sriluckshmy, M. Leib, and F. Šimkovic IV, “Low-depth simulations of fermionic systems on square-grid quantum hardware”, Quantum 8, 1327 (2024) arXiv:2302.01862 DOI. Appears in: Fermion-into-qubit code
J. Alicea, Y. Oreg, G. Refael, F. von Oppen, and M. P. A. Fisher, “Non-Abelian statistics and topological quantum information processing in 1D wire networks”, Nature Physics 7, 412 (2011) arXiv:1006.4395 DOI. Appears in: Majorana box qubit
R. Alicki, M. Fannes, and M. Horodecki, “A statistical mechanics view on Kitaev’s proposal for quantum memories”, Journal of Physics A: Mathematical and Theoretical 40, 6451 (2007) arXiv:quant-ph/0702102 DOI. Appears in: Self-correcting quantum code
R. Alicki, M. Horodecki, P. Horodecki, and R. Horodecki, “On thermal stability of topological qubit in Kitaev’s 4D model”, (2008) arXiv:0811.0033. Appears in: Loop toric code, Self-correcting quantum code
R. Alicki, M. Fannes, and M. Horodecki, “On thermalization in Kitaev’s 2D model”, Journal of Physics A: Mathematical and Theoretical 42, 065303 (2009) arXiv:0810.4584 DOI. Appears in: Self-correcting quantum code
R. Alicki, “Critique of Fault-Tolerant Quantum Information Processing”, (2013) arXiv:1310.8457. Appears in: Quantum error-correcting code (QECC)
P. Aliferis, D. Gottesman, and J. Preskill, “Quantum accuracy threshold for concatenated distance-3 codes”, (2005) arXiv:quant-ph/0504218. Appears in: Concatenated Steane code, Concatenated qubit code, Qubit code
P. Aliferis and B. M. Terhal, “Fault-Tolerant Quantum Computation for Local Leakage Faults”, (2006) arXiv:quant-ph/0511065. Appears in: Qubit code
P. Aliferis and D. W. Leung, “Simple proof of fault tolerance in the graph-state model”, Physical Review A 73, (2006) arXiv:quant-ph/0503130 DOI. Appears in: Cluster-state code
P. Aliferis, D. Gottesman, and J. Preskill, “Accuracy threshold for postselected quantum computation”, (2007) arXiv:quant-ph/0703264. Appears in: Concatenated qubit code, $[[4,2,2]]$ Four-qubit code, $[[6,2,2]]$ $C_6$ code
P. Aliferis and A. W. Cross, “Subsystem Fault Tolerance with the Bacon-Shor Code”, Physical Review Letters 98, (2007) arXiv:quant-ph/0610063 DOI. Appears in: Bacon-Shor code
P. Aliferis and J. Preskill, “Fault-tolerant quantum computation against biased noise”, Physical Review A 78, (2008) arXiv:0710.1301 DOI. Appears in: Asymmetric quantum code
P. Aliferis, F. Brito, D. P. DiVincenzo, J. Preskill, M. Steffen, and B. M. Terhal, “Fault-tolerant computing with biased-noise superconducting qubits: a case study”, New Journal of Physics 11, 013061 (2009) arXiv:0806.0383 DOI. Appears in: Asymmetric quantum code
P. Aliferis and J. Preskill, “Fibonacci scheme for fault-tolerant quantum computation”, Physical Review A 79, (2009) arXiv:0809.5063 DOI. Appears in: Qubit stabilizer code
P. Aliferis, “Level Reduction and the Quantum Threshold Theorem”, (2011) arXiv:quant-ph/0703230. Appears in: Concatenated Steane code, Concatenated qubit code, Qubit code
Allwein, Erin L., Robert E. Schapire, and Yoram Singer. "Reducing multiclass to binary: A unifying approach for margin classifiers." Journal of machine learning research 1.Dec (2000): 113-141.. Appears in: Error-correcting output code (ECOC)
A. Almheiri, X. Dong, and D. Harlow, “Bulk locality and quantum error correction in AdS/CFT”, Journal of High Energy Physics 2015, (2015) arXiv:1411.7041 DOI. Appears in: Approximate operator-algebra QECC, Holographic code, Holographic tensor-network code, Three-qutrit code
N. Alon, J. Edmonds, and M. Luby, “Linear time erasure codes with nearly optimal recovery”, Proceedings of IEEE 36th Annual Foundations of Computer Science DOI. Appears in: Good QLDPC code, Hemicubic code, Quantum locally testable code (QLTC), Quantum locally recoverable code (QLRC), Quantum maximum-distance-separable (MDS) code
N. Alon and M. Luby, “A linear time erasure-resilient code with nearly optimal recovery”, IEEE Transactions on Information Theory 42, 1732 (1996) DOI. Appears in: Good QLDPC code, Hemicubic code, Quantum locally testable code (QLTC), Quantum locally recoverable code (QLRC), Quantum maximum-distance-separable (MDS) code
N. Alon, T. Kaufman, M. Krivelevich, S. Litsyn, and D. Ron, “Testing Reed–Muller Codes”, IEEE Transactions on Information Theory 51, 4032 (2005) DOI. Appears in: Binary linear LTC, Reed-Muller (RM) code
A. B. Aloshious, A. N. Bhagoji, and P. K. Sarvepalli, “On the Local Equivalence of 2D Color Codes and Surface Codes with Applications”, (2018) arXiv:1804.00866. Appears in: 2D color code, 3D color code, 3D surface code, Color code, Homological code, Concatenated qubit code, Kitaev surface code
A. B. Aloshious and P. K. Sarvepalli, “Projecting three-dimensional color codes onto three-dimensional toric codes”, Physical Review A 98, (2018) arXiv:1606.00960 DOI. Appears in: 3D color code
D. Alsina, “PhD thesis: Multipartite entanglement and quantum algorithms”, (2017) arXiv:1706.08318. Appears in: Perfect-tensor code, Maximum distance separable (MDS) code, Modular-qudit cluster-state code
D. Alsina and M. Razavi, “Absolutely maximally entangled states, quantum-maximum-distance-separable codes, and quantum repeaters”, Physical Review A 103, (2021) arXiv:1907.11253 DOI. Appears in: Perfect-tensor code, Galois-qudit RS code, Quantum maximum-distance-separable (MDS) code, $[[4,2,2]]$ Four-qubit code, Five-qubit perfect code
Y. Altug and A. B. Wagner, “Moderate Deviations in Channel Coding”, (2012) arXiv:1208.1924. Appears in: Error-correcting code (ECC)
S. A. Aly, A. Klappenecker, and P. K. Sarvepalli, “Subsystem Codes”, (2006) arXiv:quant-ph/0610153. Appears in: Subsystem Galois-qudit CSS code, Subsystem Galois-qudit stabilizer code, Bose–Chaudhuri–Hocquenghem (BCH) code, Subsystem modular-qudit CSS code, Reed-Solomon (RS) code, Hermitian Galois-qudit code, Subsystem CSS code, Subsystem qubit stabilizer code
S. A. Aly, A. Klappenecker, and P. K. Sarvepalli, “On Quantum and Classical BCH Codes”, (2006) arXiv:quant-ph/0604102. Appears in: Galois-qudit BCH code, Generalized RM (GRM) code, Quantum convolutional code
S. A. Aly, A. Klappenecker, and P. K. Sarvepalli, “Remarkable Degenerate Quantum Stabilizer Codes Derived from Duadic Codes”, (2006) arXiv:quant-ph/0601117. Appears in: Quantum duadic code
S. A. Aly, “A Note on Quantum Hamming Bound”, (2007) arXiv:0711.4603. Appears in: Perfect quantum code
S. A. Aly, A. Klappenecker, and P. K. Sarvepalli, “Quantum Convolutional Codes Derived From Reed-Solomon and Reed-Muller Codes”, (2007) arXiv:quant-ph/0701037. Appears in: Quantum convolutional code, Quantum Reed-Muller code
S. A. Aly, A. Klappenecker, and P. K. Sarvepalli, “On Quantum and Classical BCH Codes”, IEEE Transactions on Information Theory 53, 1183 (2007) DOI. Appears in: Galois-qudit BCH code
S. A. Aly, “On Quantum and Classical Error Control Codes: Constructions and Applications”, (2008) arXiv:0812.5104. Appears in: Algebraic LDPC code, Asymmetric quantum code, Galois-qudit BCH code, Quantum duadic code, Galois-qudit RS code, Galois-qudit quantum RM code, Subsystem Galois-qudit stabilizer code, Generalized RM (GRM) code, Generalized RS (GRS) code, Finite-geometry (FG) QLDPC code, Projective RM (PRM) code, Quantum LDPC (QLDPC) code, Quantum convolutional code, Quasi-cyclic QLDPC (QC-QLDPC) code
S. A. Aly, “A Class of Quantum LDPC Codes Constructed From Finite Geometries”, IEEE GLOBECOM 2008 - 2008 IEEE Global Telecommunications Conference 1 (2008) arXiv:0712.4115 DOI. Appears in: Finite-geometry LDPC (FG-LDPC) code, Finite-geometry (FG) QLDPC code
S. A. Aly, “Asymmetric and Symmetric Subsystem BCH Codes and Beyond”, (2008) arXiv:0803.0764. Appears in: Asymmetric quantum code, Galois-qudit BCH code, Subsystem Galois-qudit stabilizer code
S. A. Aly, “Asymmetric quantum BCH codes”, 2008 International Conference on Computer Engineering & Systems (2008) DOI. Appears in: Asymmetric quantum code, Galois-qudit BCH code, Subsystem Galois-qudit stabilizer code
S. A. Aly and A. Klappenecker, “Subsystem Code Constructions”, (2008) arXiv:0712.4321. Appears in: Subsystem Galois-qudit stabilizer code, Quantum maximum-distance-separable (MDS) code
S. A. Aly, “Families of LDPC Codes Derived from Nonprimitive BCH Codes and Cyclotomic Cosets”, (2008) arXiv:0802.4079. Appears in: Galois-qudit BCH code, Quantum LDPC (QLDPC) code
S. A. Aly and A. Klappenecker, “Constructions of Subsystem Codes over Finite Fields”, (2008) arXiv:0811.1570. Appears in: Subsystem Galois-qudit CSS code, Subsystem CSS code
S. Aly, A. Klappenecker, and P. K. Sarvepalli, “Primitive Quantum BCH Codes over Finite Fields”, (2006) arXiv:quant-ph/0501126. Appears in: Galois-qudit BCH code
A. Ambainis and D. Gottesman, “The minimum distance problem for two-way entanglement purification”, IEEE Transactions on Information Theory 52, 748 (2006) arXiv:quant-ph/0310097 DOI. Appears in: Qubit stabilizer code
A. Ambainis and J. Emerson, “Quantum t-designs: t-wise independence in the quantum world”, (2007) arXiv:quant-ph/0701126. Appears in: $t$-design
M. Amy, D. Maslov, and M. Mosca, “Polynomial-Time T-Depth Optimization of Clifford+T Circuits Via Matroid Partitioning”, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 33, 1476 (2014) arXiv:1303.2042 DOI. Appears in: Qubit code
M. Amy and M. Mosca, “T-Count Optimization and Reed–Muller Codes”, IEEE Transactions on Information Theory 65, 4771 (2019) arXiv:1601.07363 DOI. Appears in: Qubit code, Reed-Muller (RM) code
M. An, J. Byrnes, W. Moran, B. Saffari, H. S. Shapiro, and R. Tolimieri, “Pons, Reed-Muller Codes, and Group Algebras”, NATO Science Series II: Mathematics, Physics and Chemistry 155 DOI. Appears in: $[2^m,m+1,2^{m-1}]$ First-order RM code, Hadamard code, Reed-Muller (RM) code
W. An, M. Medard, and K. R. Duffy, “CRC Codes as Error Correction Codes”, ICC 2021 - IEEE International Conference on Communications (2021) arXiv:2104.13663 DOI. Appears in: Cyclic redundancy check (CRC) code
S. Anders, M. B. Plenio, W. Dür, F. Verstraete, and H.-J. Briegel, “Ground-State Approximation for Strongly Interacting Spin Systems in Arbitrary Spatial Dimension”, Physical Review Letters 97, (2006) arXiv:quant-ph/0602230 DOI. Appears in: Cluster-state code, XP stabilizer code
C. K. Andersen, A. Remm, S. Lazar, S. Krinner, N. Lacroix, G. J. Norris, M. Gabureac, C. Eichler, and A. Wallraff, “Repeated quantum error detection in a surface code”, Nature Physics 16, 875 (2020) arXiv:1912.09410 DOI. Appears in: Rotated surface code, $[[4,2,2]]$ Four-qubit code
T. I. Andersen et al., “Non-Abelian braiding of graph vertices in a superconducting processor”, (2023) arXiv:2210.10255. Appears in: XZZX surface code
U. L. Andersen, J. S. Neergaard-Nielsen, P. van Loock, and A. Furusawa, “Hybrid discrete- and continuous-variable quantum information”, Nature Physics 11, 713 (2015) arXiv:1409.3719 DOI. Appears in: Hybrid cat code, Hybrid qudit-oscillator code
J. B. Anderson and A. Svensson, Coded Modulation Systems (Springer US, 2002) DOI. Appears in: Modulation scheme
J. T. Anderson, “Homological Stabilizer Codes”, (2011) arXiv:1107.3502. Appears in: 2D color code, Rotated surface code, Kitaev surface code
J. T. Anderson, G. Duclos-Cianci, and D. Poulin, “Fault-Tolerant Conversion between the Steane and Reed-Muller Quantum Codes”, Physical Review Letters 113, (2014) arXiv:1403.2734 DOI. Appears in: Quantum Reed-Muller code, $[[15,1,3]]$ quantum Reed-Muller code, $[[7,1,3]]$ Steane code
J. T. Anderson and T. Jochym-O’Connor, “Classification of transversal gates in qubit stabilizer codes”, (2014) arXiv:1409.8320. Appears in: Qubit stabilizer code
J. T. Anderson, “On Groups in the Qubit Clifford Hierarchy”, Quantum 8, 1370 (2024) arXiv:2212.05398 DOI. Appears in: Qubit code
E. Andrade, J. Bolkema, T. Dexter, H. Eggers, V. Luongo, F. Manganiello, and L. Szramowski, “CSS-T Codes from Reed Muller Codes”, (2025) arXiv:2305.06423. Appears in: CSS-T code, Quantum Reed-Muller code
Andreev, N. N. Location of points on a sphere with minimal energy. (Russian) Tr. Mat. Inst. Steklova 219 (1997), Teor. Priblizh. Garmon. Anal., 27–31; translation in Proc. Steklov Inst. Math. 1997, no. 4(219), 20–24. Appears in: $\Lambda_{24}$ Leech lattice-shell code, Spherical sharp configuration
Andreev, Nikolay N. "An extremal property of the icosahedron." East J. Approx 2.4 (1996): 459-462.. Appears in: Icosahedron code, Spherical sharp configuration
Andrew Landahl, private communication, 2023. Appears in: Kitaev surface code
Andries E. Brouwer, Bounds on linear codes, in: Vera S. Pless and W. Cary Huffman (Eds.), Handbook of Coding Theory, pp. 295-461, Elsevier, 1998.. Appears in: Linear binary code, $q$-ary code
R. S. Andrist, H. G. Katzgraber, H. Bombin, and M. A. Martin-Delgado, “Tricolored lattice gauge theory with randomness: fault tolerance in topological color codes”, New Journal of Physics 13, 083006 (2011) arXiv:1005.0777 DOI. Appears in: Honeycomb (6.6.6) color code
R. S. Andrist, H. Bombin, H. G. Katzgraber, and M. A. Martin-Delgado, “Optimal error correction in topological subsystem codes”, Physical Review A 85, (2012) arXiv:1204.1838 DOI. Appears in: 2D subsystem color code
I. Andriyanova, D. Maurice, and J.-P. Tillich, “New constructions of CSS codes obtained by moving to higher alphabets”, (2012) arXiv:1202.3338. Appears in: Galois-qudit surface code
B. Anker and M. Marvian, “Flag Gadgets based on Classical Codes”, (2024) arXiv:2212.10738. Appears in: Qubit stabilizer code
F. Annexstein and M. Baumslag, “A unified approach to off-line permutation routing on parallel networks”, Proceedings of the second annual ACM symposium on Parallel algorithms and architectures - SPAA ’90 398 (1990) DOI. Appears in: Hierarchical code
A. Anshu, N. P. Breuckmann, and C. Nirkhe, “NLTS Hamiltonians from Good Quantum Codes”, Proceedings of the 55th Annual ACM Symposium on Theory of Computing (2023) arXiv:2206.13228 DOI. Appears in: Quantum Tanner code
G. Anthony, H. Gregg, and M. Tshilidzi, “Image Classification Using SVMs: One-against-One Vs One-against-All”, (2007) arXiv:0711.2914. Appears in: Error-correcting output code (ECOC), One-hot code
Anthony Leverrier, Mapping the toric code to the rotated toric code, 2022.. Appears in: Quantum Tanner code, Rotated surface code, Kitaev surface code
A. V. Antipov, E. O. Kiktenko, and A. K. Fedorov, “Realizing a class of stabilizer quantum error correction codes using a single ancilla and circular connectivity”, Physical Review A 107, (2023) arXiv:2207.13356 DOI. Appears in: Five-qubit perfect code
S. Antonini, G. Bentsen, C. Cao, J. Harper, S.-K. Jian, and B. Swingle, “Holographic measurement and bulk teleportation”, Journal of High Energy Physics 2022, (2022) arXiv:2209.12903 DOI. Appears in: Pastawski-Yoshida-Harlow-Preskill (HaPPY) code
Anvin, H. Peter. "The mathematics of RAID-6." (2007).. Appears in: Array code, Reed-Solomon (RS) code
H. Anwar, E. T. Campbell, and D. E. Browne, “Qutrit magic state distillation”, New Journal of Physics 14, 063006 (2012) arXiv:1202.2326 DOI. Appears in: $[[5,1,3]]_{\mathbb{Z}_q}$ modular-qudit code
H. Anwar, B. J. Brown, E. T. Campbell, and D. E. Browne, “Fast decoders for qudit topological codes”, New Journal of Physics 16, 063038 (2014) arXiv:1311.4895 DOI. Appears in: Modular-qudit surface code
Anxiao Jiang, M. Schwartz, and J. Bruck, “Error-correcting codes for rank modulation”, 2008 IEEE International Symposium on Information Theory 1736 (2008) DOI. Appears in: Rank-modulation code
Anxiao Jiang, R. Mateescu, M. Schwartz, and J. Bruck, “Rank Modulation for Flash Memories”, IEEE Transactions on Information Theory 55, 2659 (2009) DOI. Appears in: Gray code, Rank-modulation code
T. Aoki, G. Takahashi, T. Kajiya, J. Yoshikawa, S. L. Braunstein, P. van Loock, and A. Furusawa, “Quantum error correction beyond qubits”, (2008) arXiv:0811.3734. Appears in: $[[9,1,3]]_{\mathbb{R}}$ Lloyd-Slotine code
H. Apel, T. Kohler, and T. Cubitt, “Holographic duality between local Hamiltonians from random tensor networks”, Journal of High Energy Physics 2022, (2022) arXiv:2105.12067 DOI. Appears in: Holographic tensor-network code, Random stabilizer code
H. Apel and N. Baspin, “Simulating LDPC code Hamiltonians on 2D lattices”, (2023) arXiv:2308.13277. Appears in: Hamiltonian-based code, Quantum LDPC (QLDPC) code
H. Apel, T. Cubitt, P. Hayden, T. Kohler, and D. Pérez-García, “Security of quantum position-verification limits Hamiltonian simulation via holography”, Journal of High Energy Physics 2024, (2024) arXiv:2401.09058 DOI. Appears in: Holographic tensor-network code
F. T. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, “Atomic Coherent States in Quantum Optics”, Physical Review A 6, 2211 (1972) DOI. Appears in: Two-mode binomial code
E. Arikan, “Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels”, IEEE Transactions on Information Theory 55, 3051 (2009) DOI. Appears in: Polar code
E. Arikan, “A survey of reed-muller codes from polar coding perspective”, IEEE Information Theory Workshop 2010 (ITW 2010) (2010) DOI. Appears in: $[2^m,m+1,2^{m-1}]$ First-order RM code, Polar code, Reed-Muller (RM) code
S. Arimoto, “On the converse to the coding theorem for discrete memoryless channels (Corresp.)”, IEEE Transactions on Information Theory 19, 357 (1973) DOI. Appears in: Error-correcting code (ECC)
S. Arimoto, "Encoding and decoding of p-ary group codes and the correction system," Information Processing in Japan (in Japanese), vol. 2, pp. 320-325, Nov. 1961.. Appears in: Binary BCH code
E. Arkan, “A performance comparison of polar codes and Reed-Muller codes”, IEEE Communications Letters 12, 447 (2008) DOI. Appears in: Polar code
L. Arnaud and N. J. Cerf, “Exploring pure quantum states with maximally mixed reductions”, Physical Review A 87, (2013) arXiv:1211.4118 DOI. Appears in: Perfect-tensor code
Arnold, V. I. (1999). Symplectization, complexification and mathematical trinities. The Arnoldfest, 23-37.. Appears in: $3_{21}$ polytope code, Hessian polyhedron code, Witting polytope code
S. Arora and M. Sudan, “Improved low-degree testing and its applications”, Proceedings of the twenty-ninth annual ACM symposium on Theory of computing - STOC ’97 485 (1997) DOI. Appears in: Generalized RM (GRM) code, $q$-ary linear LTC
S. Arora and S. Safra, “Probabilistic checking of proofs”, Journal of the ACM 45, 70 (1998) DOI. Appears in: Locally testable code (LTC)
S. Arora, C. Lund, R. Motwani, M. Sudan, and M. Szegedy, “Proof verification and the hardness of approximation problems”, Journal of the ACM 45, 501 (1998) DOI. Appears in: Generalized RM (GRM) code, Locally testable code (LTC), $q$-ary linear LTC
S. Arora and B. Barak, Computational Complexity (Cambridge University Press, 2009) DOI. Appears in: Locally decodable code (LDC)
Arpit Dua, “Subsystem Codes”, (2022) DOI. Appears in: Ladder Floquet code, $[[4,2,2]]$ Four-qubit code
V. Arvind, P. P. Kurur, and K. R. Parthasarathy, “Nonstabilizer Quantum Codes from Abelian Subgroups of the Error Group”, (2002) arXiv:quant-ph/0210097. Appears in: $((n,1+n(q-1),2))_q$ union stabilizer code, Galois-qudit USt code, Union stabilizer (USt) code, $((5,6,2))$ qubit code
F. Arzani, R. I. Booth, and U. Chabaud, “Can effective descriptions of bosonic systems be considered complete?”, (2025) arXiv:2501.13857. Appears in: Bosonic code
A. Ashikhmin and S. Litsyn, “Simple MAP decoding of first order Reed-Muller and Hamming codes”, Proceedings 2003 IEEE Information Theory Workshop (Cat. No.03EX674) 18 DOI. Appears in: $[2^m-1,m,2^{m-1}]$ simplex code
A. Ashikhmin and S. Litsyn, “Upper Bounds on the Size of Quantum Codes”, (1997) arXiv:quant-ph/9709049. Appears in: Block quantum code, Qubit code
A. Ashikhmin and A. Barg, “Binomial moments of the distance distribution: bounds and applications”, IEEE Transactions on Information Theory 45, 438 (1999) DOI. Appears in: Projective two-weight code
A. Ashikhmin, A. Barg, E. Knill, and S. Litsyn, “Quantum Error Detection II: Bounds”, (1999) arXiv:quant-ph/9906131. Appears in: Block quantum code
A. Ashikhmin, A. Barg, E. Knill, and S. Litsyn, “Quantum Error Detection I: Statement of the Problem”, (1999) arXiv:quant-ph/9906126. Appears in: Qubit code
A. Ashikhmin and E. Knill, “Nonbinary Quantum Stabilizer Codes”, (2000) arXiv:quant-ph/0005008. Appears in: Quantum Goppa code, Quantum AG code
A. Ashikhmin and E. Knill, “Nonbinary quantum stabilizer codes”, IEEE Transactions on Information Theory 47, 3065 (2001) DOI. Appears in: Block quantum code, Dual additive code, Galois-qudit color code, Galois-qudit code, Galois-qudit stabilizer code, Galois-qudit surface code, True Galois-qudit stabilizer code, Group-based quantum code, Quantum AG code, Quantum-double code, Abelian quantum-double stabilizer code, Quantum Gabidulin code, Triorthogonal code, Modular-qudit stabilizer code, Modular-qudit code, Hermitian Galois-qudit code
A. Ashikhmin, S. Litsyn, and M. Tsfasman, “Asymptotically good quantum codes”, Physical Review A 63, (2001) arXiv:quant-ph/0006061 DOI. Appears in: Quantum Goppa code
A. Ashikhmin, C.-Y. Lai, and T. A. Brun, “Robust quantum error syndrome extraction by classical coding”, 2014 IEEE International Symposium on Information Theory (2014) DOI. Appears in: Quantum data-syndrome (QDS) code
A. Ashikhmin, C.-Y. Lai, and T. A. Brun, “Correction of data and syndrome errors by stabilizer codes”, 2016 IEEE International Symposium on Information Theory (ISIT) (2016) DOI. Appears in: Quantum data-syndrome (QDS) code
A. Ashikhmin, C.-Y. Lai, and T. A. Brun, “Quantum Data-Syndrome Codes”, IEEE Journal on Selected Areas in Communications 38, 449 (2020) arXiv:1907.01393 DOI. Appears in: Quantum data-syndrome (QDS) code, Quantum quadratic-residue (QR) code, $[[2^r-1, 2^r-2r-1, 3]]$ quantum Hamming code, Quantum maximum-distance-separable (MDS) code, Perfect quantum code, $[[23, 1, 7]]$ Quantum Golay code, $[[7,1,3]]$ Steane code
M. Ashraf and G. Mohammad, “Quantum codes over Fp from cyclic codes over Fp[u, v]/〈u2 − 1, v3 − v, uv − vu〉”, Cryptography and Communications 11, 325 (2018) DOI. Appears in: Skew-cyclic CSS code
H. Asi and E. Yaakobi, “Nearly Optimal Constructions of PIR and Batch Codes”, (2017) arXiv:1701.07206. Appears in: Batch code, Multiplicity code, Private information retrieval (PIR) code
A. Askikhmin, A. Barg, and S. Litsyn, “Estimates of the distance distribution of codes and designs”, IEEE Transactions on Information Theory 47, 1050 (2001) DOI. Appears in: Universally optimal $q$-ary code, Universally optimal spherical code
S. Assiri, B. Cambou, D. D. Booher, D. Ghanai Miandoab, and M. Mohammadinodoushan, “Key Exchange using Ternary system to Enhance Security”, 2019 IEEE 9th Annual Computing and Communication Workshop and Conference (CCWC) (2019) DOI. Appears in: $q$-ary code
E. F. Assmus Jr. and H. F. Mattson Jr., “New 5-designs”, Journal of Combinatorial Theory 6, 122 (1969) DOI. Appears in: Combinatorial design, Dual linear code, Quadratic-residue (QR) code, Self-dual linear code, $[48,24,12]$ self-dual code
E. F. Assmus and J. D. Key, Designs and Their Codes (Cambridge University Press, 1992) DOI. Appears in: Generalized RM (GRM) code, Reed-Muller (RM) code
E. F. Assmus, Jr. and H. F. Mattson, Jr., “Coding and Combinatorics”, SIAM Review 16, 349 (1974) DOI. Appears in: Combinatorial design, Perfect code, Quadratic-residue (QR) code
E. F. Assmus, Jr. and J. D. Key, “Polynomial codes and finite geometries,” in Handbook of Coding Theory, eds. V. S. Pless and W. C. Huffman. Amsterdam: Elsevier, 1998, pp. 1269–1343.. Appears in: Generalized RM (GRM) code
M. Asteris and A. G. Dimakis, “Repairable Fountain Codes”, (2014) arXiv:1401.0734. Appears in: Distributed-storage code, Fountain code
Atri Rudra. List Decoding and Property Testing of Error Correcting Codes. PhD thesis, University of Washington, 8 2007.. Appears in: Folded RS (FRS) code
Y. Aubry, “Reed-Muller codes associated to projective algebraic varieties”, Lecture Notes in Mathematics 4 (1992) DOI. Appears in: Quadric code
K. Audenaert and B. De Moor, “Optimizing completely positive maps using semidefinite programming”, Physical Review A 65, (2002) arXiv:quant-ph/0109155 DOI. Appears in: Approximate quantum error-correcting code (AQECC), Qudit-into-oscillator code
B. Audoux and A. Couvreur, “On tensor products of CSS Codes”, (2018) arXiv:1512.07081. Appears in: Cyclic linear binary code, Homological product code, Finite-geometry LDPC (FG-LDPC) code, Finite-geometry (FG) QLDPC code, Quantum Reed-Muller code, Generalized homological-product qubit CSS code, $[[7,1,3]]$ Steane code
J. M. Auger, H. Anwar, M. Gimeno-Segovia, T. M. Stace, and D. E. Browne, “Fault-tolerance thresholds for the surface code with fabrication errors”, Physical Review A 96, (2017) arXiv:1706.04912 DOI. Appears in: Kitaev surface code
S. V. Avgustinovich and F. I. Solov’eva, “Perfect binary codes with trivial automorphism group”, 1998 Information Theory Workshop (Cat. No.98EX131) DOI. Appears in: Perfect binary code
S. V. Avgustinovich, F. I. Solov’eva, and O. Heden, “On the Structure of Symmetry Groups of Vasil’ev Codes”, Problems of Information Transmission 41, 105 (2005) DOI. Appears in: Vasilyev code
C. J. Axline et al., “On-demand quantum state transfer and entanglement between remote microwave cavity memories”, Nature Physics 14, 705 (2018) arXiv:1712.05832 DOI. Appears in: Binomial code
A. Aydin, M. A. Alekseyev, and A. Barg, “A family of permutationally invariant quantum codes”, Quantum 8, 1321 (2024) arXiv:2310.05358 DOI. Appears in: Binary dihedral PI code, Combinatorial PI code, Four-qubit single-deletion code, GNU PI code, $((7,2,3))$ Pollatsek-Ruskai code
N. Aydin, P. Liu, and B. Yoshino, “Polycyclic Codes Associated with Trinomials: Good Codes and Open Questions”, (2021) arXiv:2106.12065. Appears in: Galois-qudit stabilizer code, Qubit stabilizer code
N. Aydin, P. Liu, and B. Yoshino, “A Database of Quantum Codes”, (2021) arXiv:2108.03567. Appears in: Galois-qudit stabilizer code, Qubit stabilizer code
N. Aydin, Y. Lu, and V. R. Onta, “An Updated Database of $\mathbb{Z}_4$ Codes”, (2022) arXiv:2208.06832. Appears in: Quaternary linear code over $\mathbb{Z}_4$
K. Azuma, K. Tamaki, and H.-K. Lo, “All-photonic quantum repeaters”, Nature Communications 6, (2015) arXiv:1309.7207 DOI. Appears in: Tree cluster-state code
M. Baake and P. A. B. Pleasants, “Algebraic Solution of the Coincidence Problem in Two and Three Dimensions”, Zeitschrift für Naturforschung A 50, 711 (1995) DOI. Appears in: $A_2$ triangular lattice
L. Babai, “On Lovász’ lattice reduction and the nearest lattice point problem”, Combinatorica 6, 1 (1986) DOI. Appears in: Gottesman-Kitaev-Preskill (GKP) code, NTRU-GKP code
L. Babai, L. Fortnow, L. A. Levin, and M. Szegedy, “Checking computations in polylogarithmic time”, Proceedings of the twenty-third annual ACM symposium on Theory of computing - STOC ’91 21 (1991) DOI. Appears in: Generalized RM (GRM) code, Locally testable code (LTC), $q$-ary linear LTC
L. Babai, L. Fortnow, and C. Lund, “Non-deterministic exponential time has two-prover interactive protocols”, Computational Complexity 1, 3 (1991) DOI. Appears in: Locally testable code (LTC)
L. Babai, A. Shpilka, and D. Stefankovic, “Locally Testable Cyclic Codes”, IEEE Transactions on Information Theory 51, 2849 (2005) DOI. Appears in: Cyclic linear binary code, Binary linear LTC, Cyclic linear $q$-ary code, $q$-ary linear LTC
Z. Babar, P. Botsinis, D. Alanis, S. X. Ng, and L. Hanzo, “Fifteen Years of Quantum LDPC Coding and Improved Decoding Strategies”, IEEE Access 3, 2492 (2015) DOI. Appears in: EA QLDPC code, Quantum LDPC (QLDPC) code
Z. Babar, P. Botsinis, D. Alanis, Soon Xin Ng, and L. Hanzo, “The Road From Classical to Quantum Codes: A Hashing Bound Approaching Design Procedure”, IEEE Access 3, 146 (2015) arXiv:1503.02372 DOI. Appears in: Quantum irregular convolutional code (QIRCC)
Z. Babar, S. X. Ng, and L. Hanzo, “EXIT-Chart-Aided Near-Capacity Quantum Turbo Code Design”, IEEE Transactions on Vehicular Technology 64, 866 (2015) arXiv:1502.00910 DOI. Appears in: Quantum turbo code
R. Babbush, N. Wiebe, J. McClean, J. McClain, H. Neven, and G. K.-L. Chan, “Low-Depth Quantum Simulation of Materials”, Physical Review X 8, (2018) arXiv:1706.00023 DOI. Appears in: Fermion code, Fermion-into-qubit code
S. Bachmann, W. De Roeck, B. Donvil, and M. Fraas, “Stability of invertible, frustration-free ground states against large perturbations”, Quantum 6, 793 (2022) arXiv:2110.11194 DOI. Appears in: Frustration-free Hamiltonian code, Hamiltonian-based code, Topological code
C. Bachoc, E. Bannai, and R. Coulangeon, “Codes and designs in Grassmannian spaces”, Discrete Mathematics 277, 15 (2004) DOI. Appears in: $t$-design
C. Bachoc, “Designs, groups and lattices”, (2007) arXiv:0712.1939. Appears in: Barnes-Wall (BW) lattice, $t$-design
C. Bachoc and F. Vallentin, “Optimality and uniqueness of the (4,10,1/6) spherical code”, Journal of Combinatorial Theory, Series A 116, 195 (2009) arXiv:0708.3947 DOI. Appears in: Petersen spherical code, Simplex spherical code, Spherical design
H. Bachor and T. C. Ralph, A Guide to Experiments in Quantum Optics (Wiley, 2019) DOI. Appears in: Two-component cat code
M. Backens, “The ZX-calculus is complete for stabilizer quantum mechanics”, New Journal of Physics 16, 093021 (2014) arXiv:1307.7025 DOI. Appears in: Qubit stabilizer code
D. Bacon, D. A. Lidar, and K. B. Whaley, “Robustness of decoherence-free subspaces for quantum computation”, Physical Review A 60, 1944 (1999) arXiv:quant-ph/9902041 DOI. Appears in: Constant-excitation (CE) code, Dual-rail quantum code, Five-qubit perfect code
D. Bacon, “Decoherence, Control, and Symmetry in Quantum Computers”, (2003) arXiv:quant-ph/0305025. Appears in: Bacon-Shor code
D. Bacon and A. Casaccino, “Quantum Error Correcting Subsystem Codes From Two Classical Linear Codes”, (2006) arXiv:quant-ph/0610088. Appears in: Linear binary code, Generalized Shor code, Qubit stabilizer code, Subsystem hypergraph product (SHP) code
D. Bacon, “Operator quantum error-correcting subsystems for self-correcting quantum memories”, Physical Review A 73, (2006) arXiv:quant-ph/0506023 DOI. Appears in: 3D Bacon-Shor code, Bacon-Shor code, $[[4,1,1,2]]$ Four-qubit subsystem code, $[[9,1,3,3]]$ Nine-qubit Bacon-Shor code, Generalized Shor code, Self-correcting quantum code
D. Bacon, “Stability of quantum concatenated-code Hamiltonians”, Physical Review A 78, (2008) arXiv:0806.2160 DOI. Appears in: Hamiltonian-based code, Concatenated qubit code
D. Bacon, S. T. Flammia, A. W. Harrow, and J. Shi, “Sparse Quantum Codes From Quantum Circuits”, IEEE Transactions on Information Theory 63, 2464 (2017) arXiv:1411.3334 DOI. Appears in: Spacetime circuit code, Sparse subsystem code, Subsystem spacetime circuit code
H. Bacry, A. Grossmann, and J. Zak, “Proof of completeness of lattice states in thekqrepresentation”, Physical Review B 12, 1118 (1975) DOI. Appears in: Bosonic code
J. C. Baez and A. D. Lauda, “Higher-Dimensional Algebra V: 2-Groups”, (2004) arXiv:math/0307200. Appears in: Two-gauge theory code
J. C. Baez and U. Schreiber, “Higher Gauge Theory”, (2006) arXiv:math/0511710. Appears in: Two-gauge theory code
J. C. Baez and J. Huerta, “An invitation to higher gauge theory”, General Relativity and Gravitation 43, 2335 (2010) arXiv:1003.4485 DOI. Appears in: Two-gauge theory code
J. Baez and U. Schreiber, “Higher Gauge Theory: 2-Connections on 2-Bundles”, (2004) arXiv:hep-th/0412325. Appears in: Two-gauge theory code
B. Bagchi and S. P. Inamdar, “Projective Geometric Codes”, Journal of Combinatorial Theory, Series A 99, 128 (2002) DOI. Appears in: Incidence-matrix projective code
L. Bahl and R. Chien, “Single- and multiple-burst-correcting properties of a class of cyclic product codes”, IEEE Transactions on Information Theory 17, 594 (1971) DOI. Appears in: Tensor-product code
L. Bahl, J. Cocke, F. Jelinek, and J. Raviv, “Optimal decoding of linear codes for minimizing symbol error rate (Corresp.)”, IEEE Transactions on Information Theory 20, 284 (1974) DOI. Appears in: Convolutional code
T. Baicheva, I. Bouyukliev, S. Dodunekov, and W. Willems, “On the [10; 5; 6] Reed-Solomon and Glynn codes,” Mathematica Balkanica, New Series, vol. 18, pp. 67–78, 200. Appears in: Glynn code, Reed-Solomon (RS) code
E. Baik, A. Pande, and P. Mohapatra, “Cross-layer coordination for efficient contents delivery in LTE eMBMS traffic”, 2012 IEEE 9th International Conference on Mobile Ad-Hoc and Sensor Systems (MASS 2012) 398 (2012) DOI. Appears in: Fountain code
P. A. Baker, “Phase-modulation data sets for serial transmission at 2,000 and 2,400 bits per second”, Transactions of the American Institute of Electrical Engineers, Part I: Communication and Electronics 81, 166 (1962) DOI. Appears in: Quadrature PSK (QPSK) code
A. Bakshi, A. Liu, A. Moitra, and E. Tang, “High-Temperature Gibbs States are Unentangled and Efficiently Preparable”, (2024) arXiv:2403.16850. Appears in: Topological code
M. S. BALADRAM, “On Explicit Construction of Simplex <i>t</i>-designs”, Interdisciplinary Information Sciences 24, 181 (2018) DOI. Appears in: $t$-design
S. B. Balaji, G. R. Kini, and P. V. Kumar, “A Tight Rate Bound and Matching Construction for Locally Recoverable Codes with Sequential Recovery From Any Number of Multiple Erasures”, (2018) arXiv:1812.02502. Appears in: Sequential-recovery code
S. Balasubramanian, M. Davydova, and E. Lake, “A local automaton for the 2D toric code”, (2024) arXiv:2412.19803. Appears in: Quantum repetition code, Kitaev surface code
V. Balasubramanian, A. Kar, C. Li, and O. Parrikar, “Quantum error correction in the black hole interior”, Journal of High Energy Physics 2023, (2023) arXiv:2203.01961 DOI. Appears in: Kim-Preskill-Tang (KPT) code
M. Baldi, M. Bianchi, F. Chiaraluce, J. Rosenthal, and D. Schipani, “Enhanced public key security for the McEliece cryptosystem”, (2014) arXiv:1108.2462. Appears in: Generalized RS (GRS) code
E. Balevi and J. G. Andrews, “Autoencoder-Based Error Correction Coding for One-Bit Quantization”, (2019) arXiv:1909.12120. Appears in: Turbo code
P. Ball, “Real-Time Error Correction for Quantum Computing”, Physics 14, (2021) DOI. Appears in: $[[7,1,3]]$ Steane code
R. C. Ball, “Fermions without Fermion Fields”, Physical Review Letters 95, (2005) arXiv:cond-mat/0409485 DOI. Appears in: Ball-Verstraete-Cirac (BVC) code
S. Ball, “On sets of vectors of a finite vector space in which every subset of basis size is a basis”, Journal of the European Mathematical Society 14, 733 (2012) DOI. Appears in: Extended GRS code, Maximum distance separable (MDS) code, Narrow-sense RS code, Reed-Solomon (RS) code
S. Ball, Finite Geometry and Combinatorial Applications (Cambridge University Press, 2015) DOI. Appears in: Hirschfeld code
S. Ball, “Some constructions of quantum MDS codes”, (2021) arXiv:1907.04391. Appears in: Glynn code, $[[9,1,5]]_3$ quantum Glynn code
S. Ball and R. Vilar, “The geometry of Hermitian self-orthogonal codes”, (2021) arXiv:2108.08088. Appears in: Glynn code, $[[9,1,5]]_3$ quantum Glynn code
S. Ball, “Grassl–Rötteler cyclic and consta-cyclic MDS codes are generalised Reed–Solomon codes”, Designs, Codes and Cryptography 91, 1685 (2022) DOI. Appears in: Generalized RS (GRS) code, Quantum maximum-distance-separable (MDS) code
B. Ballinger, G. Blekherman, H. Cohn, N. Giansiracusa, E. Kelly, and A. Schürmann, “Experimental Study of Energy-Minimizing Point Configurations on Spheres”, Experimental Mathematics 18, 257 (2009) arXiv:math/0611451 DOI. Appears in: Spherical sharp configuration, Smith $40$-point code
G. Balló and P. Gurin, “Robustness of channel-adapted quantum error correction”, Physical Review A 80, (2009) arXiv:0905.3838 DOI. Appears in: Approximate quantum error-correcting code (AQECC)
B. Balsam and A. Kirillov Jr, “Kitaev’s Lattice Model and Turaev-Viro TQFTs”, (2012) arXiv:1206.2308. Appears in: Hopf-algebra quantum-double code, String-net code
Bambah, R. P., and H. Gupta. "On lattice coverings by spheres." Proceedings of the National Institute of Sciences of India. Vol. 20. Indian National Science Academy, 1954.. Appears in: $A_n^{\perp}$ lattice, Body-centered cubic (bcc) lattice
K. Banaszek, L. Kunz, M. Jachura, and M. Jarzyna, “Quantum Limits in Optical Communications”, Journal of Lightwave Technology 38, 2741 (2020) arXiv:2002.05766 DOI. Appears in: Bosonic c-q code
D. Banfield and A. Kay, “Implementing Logical Operators using Code Rewiring”, (2023) arXiv:2210.14074. Appears in: Triorthogonal code, $[[15,1,3]]$ quantum Reed-Muller code, $[[7,1,3]]$ Steane code, Subsystem qubit stabilizer code
E. Bannai and N. J. A. Sloane, “Uniqueness of Certain Spherical Codes”, Canadian Journal of Mathematics 33, 437 (1981) DOI. Appears in: $E_8$ Gosset lattice-shell code, $3_{21}$ polytope code, $\Lambda_{24}$ Leech lattice-shell code, Spherical sharp configuration, Spherical design, Witting polytope code
E. BANNAI, “Spherical t-designs which are orbits of finite groups”, Journal of the Mathematical Society of Japan 36, (1984) DOI. Appears in: Slepian group-orbit code, Spherical design
E. Bannai, S. T. Dougherty, M. Harada, and M. Oura, “Type II codes, even unimodular lattices, and invariant rings”, IEEE Transactions on Information Theory 45, 1194 (1999) DOI. Appears in: Self-dual additive code, Unimodular lattice
E. Bannai and E. Bannai, “A survey on spherical designs and algebraic combinatorics on spheres”, European Journal of Combinatorics 30, 1392 (2009) DOI. Appears in: Lattice-shell code, Spherical design
E. Bannai, G. Navarro, N. Rizo, and P. H. Tiep, “Unitary t-groups”, (2018) arXiv:1810.02507. Appears in: $t$-design, Twisted $1$-group code
N. Bao and N. Cheng, “Eigenstate thermalization hypothesis and approximate quantum error correction”, Journal of High Energy Physics 2019, (2019) arXiv:1906.03669 DOI. Appears in: Eigenstate thermalization hypothesis (ETH) code
N. Bao and J. Naskar, “Code properties of the holographic Sierpinski triangle”, Physical Review D 106, (2022) arXiv:2203.01379 DOI. Appears in: Approximate operator-algebra QECC, Holographic code
N. Bao, C. Cao, and G. Zhu, “Deconfinement and error thresholds in holography”, Physical Review D 106, (2022) arXiv:2202.04710 DOI. Appears in: Holographic tensor-network code
Y. Bao, R. Fan, A. Vishwanath, and E. Altman, “Mixed-state topological order and the errorfield double formulation of decoherence-induced transitions”, (2023) arXiv:2301.05687. Appears in: 2D lattice stabilizer code
Y. Bao and S. Anand, “Phases of decodability in the surface code with unitary errors”, (2024) arXiv:2411.05785. Appears in: Toric code
B. Q. Baragiola, G. Pantaleoni, R. N. Alexander, A. Karanjai, and N. C. Menicucci, “All-Gaussian Universality and Fault Tolerance with the Gottesman-Kitaev-Preskill Code”, Physical Review Letters 123, (2019) arXiv:1903.00012 DOI. Appears in: Square-lattice GKP code, Gottesman-Kitaev-Preskill (GKP) code
F. Barahona, R. Maynard, R. Rammal, and J. P. Uhry, “Morphology of ground states of two-dimensional frustration model”, Journal of Physics A: Mathematical and General 15, 673 (1982) DOI. Appears in: Kitaev surface code
B. Barak, Z. Dvir, A. Wigderson, and A. Yehudayoff, “Rank Bounds for Design Matrices with Applications to Combinatorial Geometry and Locally Correctable Codes”, (2011) arXiv:1009.4375. Appears in: Analog code, Locally correctable code (LCC)
L. S. Barasch, S. Lakshmivarahan, and S. K. Dhall, “Generalized Gray Codes and Their Properties”, Mathematics for Large Scale Computing 203 (2020) DOI. Appears in: Gray code
B. Barber et al., “A real-time, scalable, fast and resource-efficient decoder for a quantum computer”, Nature Electronics 8, 84 (2025) arXiv:2309.05558 DOI. Appears in: $[[4,2,2]]$ Four-qubit code, Kitaev surface code
M. Bardet, V. Dragoi, A. Otmani, and J.-P. Tillich, “Algebraic properties of polar codes from a new polynomial formalism”, 2016 IEEE International Symposium on Information Theory (ISIT) (2016) arXiv:1601.06215 DOI. Appears in: Polar code
C.-E. Bardyn and T. Karzig, “Exponential lifetime improvement in topological quantum memories”, Physical Review B 94, (2016) arXiv:1512.04528 DOI. Appears in: Self-correcting quantum code, Kitaev surface code
A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter, “Elementary gates for quantum computation”, Physical Review A 52, 3457 (1995) arXiv:quant-ph/9503016 DOI. Appears in: Qubit code
A. Barg, “At the Dawn of the Theory of Codes”, The Mathematical Intelligencer 15, 20 (1993) DOI. Appears in: Finite-dimensional error-correcting code (ECC)
A. Barg, “At the Dawn of the Theory of Codes”, The Mathematical Intelligencer 15, 20 (1993) DOI. Appears in: Covering code, Ternary Golay code
A. Barg, G. Cohen, S. Encheva, G. Kabatiansky, and G. Zémor, “A Hypergraph Approach to the Identifying Parent Property: The Case of Multiple Parents”, SIAM Journal on Discrete Mathematics 14, 423 (2001) DOI. Appears in: Identifiable parent property (IPP) code
A. Barg, J. Justesen, and C. Thommesen, “Concatenated codes with fixed inner code and random outer code”, IEEE Transactions on Information Theory 47, 361 (2001) DOI. Appears in: Concatenated code
A. Barg and G. D. Forney, “Random codes: minimum distances and error exponents”, IEEE Transactions on Information Theory 48, 2568 (2002) DOI. Appears in: Random code
A. Barg and G. Zemor, “Concatenated Codes: Serial and Parallel”, IEEE Transactions on Information Theory 51, 1625 (2005) DOI. Appears in: Concatenated code, Parallel concatenated code, Regular binary Tanner code, Tanner code, Tensor-product code
A. Barg and P. Purkayastha, “Bounds on ordered codes and orthogonal arrays”, (2009) arXiv:cs/0702033. Appears in: $t$-design
A. Barg and A. Mazumdar, “Codes in permutations and error correction for rank modulation”, 2010 IEEE International Symposium on Information Theory 854 (2010) DOI. Appears in: Rank-modulation code
A. Barg, I. Tamo, and S. Vladut, “Locally recoverable codes on algebraic curves”, 2015 IEEE International Symposium on Information Theory (ISIT) (2015) arXiv:1603.08876 DOI. Appears in: Locally recoverable code (LRC), Tamo-Barg-Vladut code
A. Barg, I. Tamo, and S. Vladut, “Locally recoverable codes on algebraic curves”, (2015) arXiv:1501.04904. Appears in: Tamo-Barg-Vladut code
A. Barg, A. Glazyrin, W.-J. Kao, C.-Y. Lai, P.-C. Tseng, and W.-H. Yu, “On the size of maximal binary codes with 2, 3, and 4 distances”, (2022) arXiv:2210.07496. Appears in: Two-weight code
A. Barg, N. J. Coble, D. Hangleiter, and C. Kang, “Geometric structure and transversal logic of quantum Reed-Muller codes”, (2024) arXiv:2410.07595. Appears in: Quantum Reed-Muller code, $[[16,6,4]]$ Tesseract color code
A. M. Barg, G. L. Katsman, M. A. Tsfasman, “Algebraic-Geometric Codes from Curves of Small Genus”, Probl. Peredachi Inf., 23:1 (1987), 42–46; Problems Inform. Transmission, 23:1 (1987), 34–38. Appears in: Klein-quartic code
V. Bargmann, P. Butera, L. Girardello, and J. R. Klauder, “On the completeness of the coherent states”, Reports on Mathematical Physics 2, 221 (1971) DOI. Appears in: Bosonic code
A. Barg and S. Zhou, “A quantum decoding algorithm for the simplex code”, in Proceedings of the 36th Annual Allerton Conference on Communication, Control and Computing, Monticello, IL, 23–25 September 1998 (UIUC 1998) 359–365. Appears in: $[2^m-1,m,2^{m-1}]$ simplex code
M. Barkeshli, C.-M. Jian, and X.-L. Qi, “Theory of defects in Abelian topological states”, Physical Review B 88, (2013) arXiv:1305.7203 DOI. Appears in: Abelian topological code
M. Barkeshli, H.-C. Jiang, R. Thomale, and X.-L. Qi, “Generalized Kitaev Models and Extrinsic Non-Abelian Twist Defects”, Physical Review Letters 114, (2015) arXiv:1405.1780 DOI. Appears in: $\mathbb{Z}_q^{(1)}$ subsystem code
M. Barkeshli, P. Bonderson, M. Cheng, and Z. Wang, “Symmetry fractionalization, defects, and gauging of topological phases”, Physical Review B 100, (2019) arXiv:1410.4540 DOI. Appears in: $G$-enriched Walker-Wang model code
M. Barkeshli, P. Bonderson, M. Cheng, C.-M. Jian, and K. Walker, “Reflection and Time Reversal Symmetry Enriched Topological Phases of Matter: Path Integrals, Non-orientable Manifolds, and Anomalies”, Communications in Mathematical Physics 374, 1021 (2019) arXiv:1612.07792 DOI. Appears in: Topological code
M. Barkeshli, Y.-A. Chen, S.-J. Huang, R. Kobayashi, N. Tantivasadakarn, and G. Zhu, “Codimension-2 defects and higher symmetries in (3+1)D topological phases”, SciPost Physics 14, (2023) arXiv:2208.07367 DOI. Appears in: 3D bosonization code, 3D fermionic surface code, 3D surface code, Kitaev chain code, Kitaev surface code
M. Barkeshli, Y.-A. Chen, P.-S. Hsin, and R. Kobayashi, “Higher-group symmetry in finite gauge theory and stabilizer codes”, SciPost Physics 16, (2024) arXiv:2211.11764 DOI. Appears in: 3D surface code, Lattice stabilizer code
M. Barkeshli, P.-S. Hsin, and R. Kobayashi, “Higher-group symmetry of (3+1)D fermionic $\mathbb{Z}_2$ gauge theory: Logical CCZ, CS, and T gates from higher symmetry”, SciPost Physics 16, (2024) arXiv:2311.05674 DOI. Appears in: 3D fermionic surface code
E. S. Barnes and G. E. Wall, “Some extreme forms defined in terms of Abelian groups”, Journal of the Australian Mathematical Society 1, 47 (1959) DOI. Appears in: Barnes-Wall (BW) lattice, $BW_{32}$ Barnes-Wall lattice, $\Lambda_{16}$ Barnes-Wall lattice
E. S. Barnes and N. J. A. Sloane, “The Optimal Lattice Quantizer in Three Dimensions”, SIAM Journal on Algebraic Discrete Methods 4, 30 (1983) DOI. Appears in: Body-centered cubic (bcc) lattice
J. P. Barnes and W. S. Warren, “Automatic Quantum Error Correction”, Physical Review Letters 85, 856 (2000) arXiv:quant-ph/9912104 DOI. Appears in: Finite-dimensional quantum error-correcting code
R. L. Barnes, “Stabilizer Codes for Continuous-variable Quantum Error Correction”, (2004) arXiv:quant-ph/0405064. Appears in: Analog stabilizer code, $[[8, 3, 3]]$ Eight-qubit Gottesman code
S. M. Barnett and D. T. Pegg, “Phase in quantum optics”, Journal of Physics A: Mathematical and General 19, 3849 (1986) DOI. Appears in: Bosonic rotation code, Homological number-phase code, Number-phase code
H. Barnum, C. Crepeau, D. Gottesman, A. Smith, and A. Tapp, “Authentication of quantum messages”, The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings. arXiv:quant-ph/0205128 DOI. Appears in: EA qubit stabilizer code, Purity-testing stabilizer code, Approximate secret-sharing code
H. Barnum and E. Knill, “Reversing quantum dynamics with near-optimal quantum and classical fidelity”, (2000) arXiv:quant-ph/0004088. Appears in: Approximate quantum error-correcting code (AQECC)
J. A. Barrau, On the combinatory problem of Steiner, Proc. Section of Sciences, Koninklijke Akademie van Wetenschappen te Amsterdam 11 (1908), 352–360.. Appears in: Julin-Golay code
S. D. Barrett and T. M. Stace, “Fault Tolerant Quantum Computation with Very High Threshold for Loss Errors”, Physical Review Letters 105, (2010) arXiv:1005.2456 DOI. Appears in: Raussendorf-Bravyi-Harrington (RBH) cluster-state code
A. Barthe, M. Cerezo, A. T. Sornborger, M. Larocca, and D. García-Martín, “Gate-based quantum simulation of Gaussian bosonic circuits on exponentially many modes”, (2024) arXiv:2407.06290. Appears in: Bosonic code
S. D. Bartlett, H. de Guise, and B. C. Sanders, “Quantum encodings in spin systems and harmonic oscillators”, Physical Review A 65, (2002) arXiv:quant-ph/0109066 DOI. Appears in: Bosonic code
S. D. Bartlett, B. C. Sanders, S. L. Braunstein, and K. Nemoto, “Efficient Classical Simulation of Continuous Variable Quantum Information Processes”, Physical Review Letters 88, (2002) arXiv:quant-ph/0109047 DOI. Appears in: Bosonic code, Stabilizer code
S. D. Bartlett and W. J. Munro, “Quantum Teleportation of Optical Quantum Gates”, Physical Review Letters 90, (2003) arXiv:quant-ph/0208022 DOI. Appears in: Bosonic stabilizer code
S. D. BARTLETT, T. RUDOLPH, and R. W. SPEKKENS, “DIALOGUE CONCERNING TWO VIEWS ON QUANTUM COHERENCE: FACTIST AND FICTIONIST”, International Journal of Quantum Information 04, 17 (2006) arXiv:quant-ph/0507214 DOI. Appears in: Bosonic code
S. Bartolucci et al., “Fusion-based quantum computation”, (2021) arXiv:2101.09310. Appears in: Fusion-based quantum computing (FBQC) code
T. Bartsch, M. Bullimore, and A. Grigoletto, “Representation theory for categorical symmetries”, (2023) arXiv:2305.17165. Appears in: Dijkgraaf-Witten gauge theory code, Two-gauge theory code
A. Bärtschi and S. Eidenbenz, “Deterministic Preparation of Dicke States”, Lecture Notes in Computer Science 126 (2019) arXiv:1904.07358 DOI. Appears in: Permutation-invariant (PI) code
A. O. Barut and L. Girardello, “New “Coherent” States associated with non-compact groups”, Communications in Mathematical Physics 21, 41 (1971) DOI. Appears in: Pair-cat code
N. Baspin and A. Krishna, “Connectivity constrains quantum codes”, Quantum 6, 711 (2022) arXiv:2106.00765 DOI. Appears in: Quantum LDPC (QLDPC) code
N. Baspin and A. Krishna, “Quantifying Nonlocality: How Outperforming Local Quantum Codes Is Expensive”, Physical Review Letters 129, (2022) arXiv:2109.10982 DOI. Appears in: Quantum LDPC (QLDPC) code
N. Baspin, “On combinatorial structures in linear codes”, (2023) arXiv:2309.16411. Appears in: Linear binary code
N. Baspin, V. Guruswami, A. Krishna, and R. Li, “Improved rate-distance trade-offs for quantum codes with restricted connectivity”, (2023) arXiv:2307.03283. Appears in: Quantum LDPC (QLDPC) code
N. Baspin, O. Fawzi, and A. Shayeghi, “A lower bound on the overhead of quantum error correction in low dimensions”, (2023) arXiv:2302.04317. Appears in: Hierarchical code, Qubit code
N. Baspin and D. Williamson, “Wire Codes”, (2024) arXiv:2410.10194. Appears in: Distance-balanced code, Good QLDPC code, Qubit stabilizer code, Subsystem qubit stabilizer code, Lattice subsystem code
A. Bauer, “Disentangling modular Walker-Wang models via fermionic invertible boundaries”, Physical Review B 107, (2023) arXiv:2208.03397 DOI. Appears in: Walker-Wang model code
A. Bauer, “Low-overhead non-Clifford fault-tolerant circuits for all non-chiral abelian topological phases”, (2024) arXiv:2403.12119. Appears in: Abelian TQD stabilizer code
H. Bauer, B. Ganter, and F. Hergert, “Algebraic techniques for nonlinear codes”, Combinatorica 3, 21 (1983) DOI. Appears in: Perfect code
T. Baumbaugh, Y. Diaz, S. Friesenhahn, F. Manganiello, and A. Vetter, “Batch Codes from Hamming and Reed-Müller Codes”, (2017) arXiv:1710.07386. Appears in: Batch code, Generalized RM (GRM) code, $[2^r-1,2^r-r-1,3]$ Hamming code
J. Bausch and F. Leditzky, “Quantum codes from neural networks”, New Journal of Physics 22, 023005 (2020) arXiv:1806.08781 DOI. Appears in: Perfect-tensor code, Neural network quantum code
J. Bausch, T. Cubitt, C. Derby, and J. Klassen, “Mitigating Errors in Local Fermionic Encodings”, (2020) arXiv:2003.07125. Appears in: Ball-Verstraete-Cirac (BVC) code, Derby-Klassen (DK) code
J. Bausch and F. Leditzky, “Error Thresholds for Arbitrary Pauli Noise”, SIAM Journal on Computing 50, 1410 (2021) arXiv:1910.00471 DOI. Appears in: Cluster-state code, Codeword stabilized (CWS) code, Qubit stabilizer code, Tree cluster-state code
J. Bausch et al., “Learning high-accuracy error decoding for quantum processors”, Nature 635, 834 (2024) arXiv:2310.05900 DOI. Appears in: Kitaev surface code
R. J. Baxter, “Eight-Vertex Model in Lattice Statistics”, Physical Review Letters 26, 832 (1971) DOI. Appears in: Quantum-inspired classical block code, X-cube model code
R. J. Baxter, “Partition function of the Eight-Vertex lattice model”, Annals of Physics 70, 193 (1972) DOI. Appears in: Quantum-inspired classical block code, X-cube model code
L. Bazzi, M. Mahdian, and D. A. Spielman, “The Minimum Distance of Turbo-Like Codes”, IEEE Transactions on Information Theory 55, 6 (2009) DOI. Appears in: Repeat-accumulate (RA) code, Repeat-accumulate-accumulate (RAA) code
N. de Beaudrap, X. Bian, and Q. Wang, “Techniques to Reduce π/4-Parity-Phase Circuits, Motivated by the ZX Calculus”, Electronic Proceedings in Theoretical Computer Science 318, 131 (2020) arXiv:1911.09039 DOI. Appears in: Qubit code
N. de Beaudrap, X. Bian, and Q. Wang, “Fast and Effective Techniques for T-Count Reduction via Spider Nest Identities”, (2020) arXiv:2004.05164 DOI. Appears in: Qubit code
N. de Beaudrap and D. Horsman, “The ZX calculus is a language for surface code lattice surgery”, Quantum 4, 218 (2020) arXiv:1704.08670 DOI. Appears in: Kitaev surface code
F. E. Becerra, J. Fan, G. Baumgartner, S. V. Polyakov, J. Goldhar, J. T. Kosloski, and A. Migdall, “M-ary-state phase-shift-keying discrimination below the homodyne limit”, Physical Review A 84, (2011) DOI. Appears in: PSK c-q code
F. E. Becerra, J. Fan, and A. Migdall, “Implementation of generalized quantum measurements for unambiguous discrimination of multiple non-orthogonal coherent states”, Nature Communications 4, (2013) DOI. Appears in: PSK c-q code
F. E. Becerra, J. Fan, G. Baumgartner, J. Goldhar, J. T. Kosloski, and A. Migdall, “Experimental demonstration of a receiver beating the standard quantum limit for multiple nonorthogonal state discrimination”, Nature Photonics 7, 147 (2013) DOI. Appears in: PSK c-q code
F. E. Becerra, J. Fan, and A. Migdall, “Photon number resolution enables quantum receiver for realistic coherent optical communications”, Nature Photonics 9, 48 (2014) DOI. Appears in: PSK c-q code
A. Becker, A. Joux, A. May, and A. Meurer, “Decoding Random Binary Linear Codes in 2 n/20: How 1 + 1 = 0 Improves Information Set Decoding”, Lecture Notes in Computer Science 520 (2012) DOI. Appears in: Random code
D. Beckman, D. Gottesman, A. Kitaev, and J. Preskill, “Measurability of Wilson loop operators”, Physical Review D 65, (2002) arXiv:hep-th/0110205 DOI. Appears in: Topological code
Matt. J. Bedalov et al., “Fault-Tolerant Operation and Materials Science with Neutral Atom Logical Qubits”, (2024) arXiv:2412.07670. Appears in: $[[4,2,2]]$ Four-qubit code
P. Beelen, “The order bound for general algebraic geometric codes”, Finite Fields and Their Applications 13, 665 (2007) DOI. Appears in: Evaluation AG code
P. Beelen and T. Høholdt, “The Decoding of Algebraic Geometry Codes”, Series on Coding Theory and Cryptology 49 (2008) DOI. Appears in: Evaluation AG code
P. Beelen, T. Hoholdt, J. S. R. Nielsen, and Y. Wu, “On Rational Interpolation-Based List-Decoding and List-Decoding Binary Goppa Codes”, IEEE Transactions on Information Theory 59, 3269 (2013) DOI. Appears in: Goppa code
P. Beelen and M. Datta, “Generalized Hamming weights of affine cartesian codes”, (2017) arXiv:1706.02114. Appears in: Hansen toric code
A. Beemer, S. Habib, C. A. Kelley, and J. Kliewer, “A Generalized Algebraic Approach to Optimizing SC-LDPC Codes”, (2017) arXiv:1710.03619. Appears in: Protograph LDPC code, Spatially coupled LDPC (SC-LDPC) code
Beenker, G. J. M. "On double circulant codes." (1980).. Appears in: Binary quadratic-residue (QR) code, Quasi-cyclic code
J. Behrends and B. Béri, “Statistical mechanical mapping and maximum-likelihood thresholds for the surface code under generic single-qubit coherent errors”, (2024) arXiv:2410.22436. Appears in: Toric code
J. Behrends and B. Béri, “The surface code under generic $X$-error channels: Statistical mechanics, error thresholds, and errorfield double phenomenology”, (2024) arXiv:2412.21055. Appears in: Toric code
S. Beigi, P. W. Shor, and D. Whalen, “The Quantum Double Model with Boundary: Condensations and Symmetries”, Communications in Mathematical Physics 306, 663 (2011) arXiv:1006.5479 DOI. Appears in: Quantum-double code
S. Beigi, I. Chuang, M. Grassl, P. Shor, and B. Zeng, “Graph concatenation for quantum codes”, Journal of Mathematical Physics 52, 022201 (2011) arXiv:0910.4129 DOI. Appears in: Codeword stabilized (CWS) code, Concatenated quantum code
S. Beigi, J. Chen, M. Grassl, Z. Ji, Q. Wang, and B. Zeng, “Symmetries of Codeword Stabilized Quantum Codes”, (2013) arXiv:1303.7020 DOI. Appears in: Modular-qudit CWS code, Modular-qudit USt code
S. Beigi and A. Gohari, “Quantum Achievability Proof via Collision Relative Entropy”, IEEE Transactions on Information Theory 60, 7980 (2014) arXiv:1312.3822 DOI. Appears in: Classical-quantum (c-q) code
S. Beigi and M. Tomamichel, “Lower Bounds on Error Exponents via a New Quantum Decoder”, (2023) arXiv:2310.09014. Appears in: Classical-quantum (c-q) code
L. W. Beineke, R. J. Wilson, J. L. Gross, and T. W. Tucker, editors , Topics in Topological Graph Theory (Cambridge University Press, 2009) DOI. Appears in: Algebraic LDPC code, Protograph LDPC code, $q$-ary protograph LDPC code
V. P. Belavkin, “Optimal multiple quantum statistical hypothesis testing”, Stochastics 1, 315 (1975) DOI. Appears in: Coherent-state c-q code
B. A. Bell, D. A. Herrera-Martí, M. S. Tame, D. Markham, W. J. Wadsworth, and J. G. Rarity, “Experimental demonstration of a graph state quantum error-correction code”, Nature Communications 5, (2014) arXiv:1404.5498 DOI. Appears in: $[[4,2,2]]$ Four-qubit code
M. Bellare, O. Goldreich, and M. Sudan, “Free Bits, PCPs, and Nonapproximability---Towards Tight Results”, SIAM Journal on Computing 27, 804 (1998) DOI. Appears in: Long code
B. I. Belov, "A conjecture on the Griesmer bound." Optimization Methods and Their Applications,(Russian), Sibirsk. Energet. Inst. Sibirsk. Otdel. Akad. Nauk SSSR, Irkutsk 182 (1974): 100-106.. Appears in: Anticode, Griesmer code
B. I. Belov, V. N. Logachev, V. P. Sandimirov, “Construction of a Class of Linear Binary Codes Achieving the Varshamov-Griesmer Bound”, Probl. Peredachi Inf., 10:3 (1974), 36–44; Problems Inform. Transmission, 10:3 (1974), 211–217. Appears in: Anticode, Griesmer code
P. Belzig, M. Christandl, and A. Müller-Hermes, “Fault-Tolerant Coding for Entanglement-Assisted Communication”, IEEE Transactions on Information Theory 70, 2655 (2024) arXiv:2210.02939 DOI. Appears in: Entanglement-assisted (EA) QECC
A. Ben-Aroya, O. Regev, and R. de Wolf, “A Hypercontractive Inequality for Matrix-Valued Functions with Applications to Quantum Computing and LDCs”, 2008 49th Annual IEEE Symposium on Foundations of Computer Science (2008) arXiv:0705.3806 DOI. Appears in: Locally decodable code (LDC)
A. Ben-Aroya and A. Ta-Shma, “Approximate quantum error correction for correlated noise”, (2009) arXiv:0909.1466. Appears in: Approximate quantum error-correcting code (AQECC)
M. Ben-Or, C. Crepeau, D. Gottesman, A. Hassidim, and A. Smith, “Secure Multiparty Quantum Computation with (Only) a Strict Honest Majority”, 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS’06) (2006) arXiv:0801.1544 DOI. Appears in: Purity-testing stabilizer code, Approximate secret-sharing code
E. Ben-Sasson, M. Sudan, S. Vadhan, and A. Wigderson, “Randomness-efficient low degree tests and short PCPs via epsilon-biased sets”, Proceedings of the thirty-fifth annual ACM symposium on Theory of computing 612 (2003) DOI. Appears in: Ben-Sasson-Sudan-Vadhan-Wigderson (BSVW) code
E. Ben-Sasson, P. Harsha, and S. Raskhodnikova, “Some 3CNF properties are hard to test”, Proceedings of the thirty-fifth annual ACM symposium on Theory of computing 345 (2003) DOI. Appears in: Expander code, Left-right Cayley complex code
E. Ben-Sasson, O. Goldreich, P. Harsha, M. Sudan, and S. Vadhan, “Robust pcps of proximity, shorter pcps and applications to coding”, Proceedings of the thirty-sixth annual ACM symposium on Theory of computing 1 (2004) DOI. Appears in: Ben-Sasson-Goldreich-Harsha-Sudan-Vadhan (BGHSV) code, Locally decodable code (LDC)
E. Ben-Sasson and M. Sudan, “Robust Locally Testable Codes and Products of Codes”, (2004) arXiv:cs/0408066. Appears in: Dinur code, Tensor-product code
E. Ben-Sasson and M. Sudan, “Simple PCPs with poly-log rate and query complexity”, Proceedings of the thirty-seventh annual ACM symposium on Theory of computing 266 (2005) DOI. Appears in: Ben-Sasson-Sudan code
E. Ben-Sasson and M. Viderman, “Tensor Products of Weakly Smooth Codes Are Robust”, Lecture Notes in Computer Science 290 (2008) DOI. Appears in: Low-density parity-check (LDPC) code, Tensor-product code
E. Ben-Sasson and M. Sudan, “Short PCPs with Polylog Query Complexity”, SIAM Journal on Computing 38, 551 (2008) DOI. Appears in: $q$-ary linear LTC, Reed-Solomon (RS) code
S. Benedetto, D. Divsalar, G. Montorsi, and F. Pollara, “Serial concatenation of interleaved codes: performance analysis, design, and iterative decoding”, IEEE Transactions on Information Theory 44, 909 (1998) DOI. Appears in: Concatenated code, Irregular repeat-accumulate (IRA) code
I. Bengtsson and K. Życzkowski, Geometry of Quantum States (Cambridge University Press, 2017) DOI. Appears in: $t$-design
A. Benhemou, J. K. Pachos, and D. E. Browne, “Non-Abelian statistics with mixed-boundary punctures on the toric code”, Physical Review A 105, (2022) arXiv:2103.08381 DOI. Appears in: Abelian topological code, Twist-defect surface code
A. Benhemou, K. Sahay, L. Lao, and B. J. Brown, “Minimising surface-code failures using a color-code decoder”, (2025) arXiv:2306.16476. Appears in: Kitaev surface code
C. Benito, E. López, B. Peropadre, and A. Bermudez, “Comparative study of quantum error correction strategies for the heavy-hexagonal lattice”, (2025) arXiv:2402.02185. Appears in: Heavy-hexagon code, Kitaev surface code
I. Benjamini, R. Pemantle, and Y. Peres, “Unpredictable paths and percolation”, The Annals of Probability 26, (1998) DOI. Appears in: Repetition code
C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, “Mixed-state entanglement and quantum error correction”, Physical Review A 54, 3824 (1996) arXiv:quant-ph/9604024 DOI. Appears in: EA qubit stabilizer code, Finite-dimensional quantum error-correcting code, Qubit code, Five-qubit perfect code
C. H. Bennett, P. W. Shor, J. A. Smolin, and A. V. Thapliyal, “Entanglement-Assisted Classical Capacity of Noisy Quantum Channels”, Physical Review Letters 83, 3081 (1999) arXiv:quant-ph/9904023 DOI. Appears in: EA qubit code
C. H. Bennett, P. W. Shor, J. A. Smolin, and A. V. Thapliyal, “Entanglement-assisted capacity of a quantum channel and the reverse Shannon theorem”, (2002) arXiv:quant-ph/0106052. Appears in: Entanglement-assisted (EA) QECC
G. Bentsen, P. Nguyen, and B. Swingle, “Approximate Quantum Codes From Long Wormholes”, Quantum 8, 1439 (2024) arXiv:2310.07770 DOI. Appears in: Approximate quantum error-correcting code (AQECC), Holographic code, SYK code
C. Bény, A. Kempf, and D. W. Kribs, “Generalization of Quantum Error Correction via the Heisenberg Picture”, Physical Review Letters 98, (2007) arXiv:quant-ph/0608071 DOI. Appears in: Hybrid QECC, Operator-algebra QECC (OAQECC)
C. Bény, A. Kempf, and D. W. Kribs, “Quantum error correction of observables”, Physical Review A 76, (2007) arXiv:0705.1574 DOI. Appears in: Operator-algebra QECC (OAQECC)
C. BÉNY, D. W. KRIBS, and A. PASIEKA, “ALGEBRAIC FORMULATION OF QUANTUM ERROR CORRECTION”, International Journal of Quantum Information 06, 597 (2008) DOI. Appears in: Operator-algebra QECC (OAQECC)
C. Bény, “Conditions for the approximate correction of algebras”, (2009) arXiv:0907.4207. Appears in: Approximate operator-algebra QECC, Approximate quantum error-correcting code (AQECC)
C. Bény, “Information flow at the quantum-classical boundary”, (2009) arXiv:0901.3629. Appears in: Operator-algebra QECC (OAQECC)
C. Bény, A. Kempf, and D. W. Kribs, “Quantum error correction on infinite-dimensional Hilbert spaces”, Journal of Mathematical Physics 50, (2009) arXiv:0811.0421 DOI. Appears in: Quantum error-correcting code (QECC)
C. Bény and O. Oreshkov, “General Conditions for Approximate Quantum Error Correction and Near-Optimal Recovery Channels”, Physical Review Letters 104, (2010) arXiv:0907.5391 DOI. Appears in: Approximate operator-algebra QECC, Approximate quantum error-correcting code (AQECC), Finite-dimensional quantum error-correcting code
C. Bény, “Perturbative Quantum Error Correction”, Physical Review Letters 107, (2011) arXiv:1102.3809 DOI. Appears in: Approximate quantum error-correcting code (AQECC)
C. Bény and O. Oreshkov, “Approximate simulation of quantum channels”, Physical Review A 84, (2011) arXiv:1103.0649 DOI. Appears in: Approximate quantum error-correcting code (AQECC)
C. Bény, Z. Zimborás, and F. Pastawski, “Approximate recovery with locality and symmetry constraints”, (2019) arXiv:1806.10324. Appears in: Approximate operator-algebra QECC
E. Berardini, R. Dastbasteh, J. E. Martinez, S. Jain, and O. S. Larrarte, “Asymptotically good CSS-T codes exist”, (2024) arXiv:2412.08586. Appears in: CSS-T code
E. Berardini, A. Caminata, and A. Ravagnani, “Structure of CSS and CSS-T quantum codes”, Designs, Codes and Cryptography (2024) arXiv:2310.16504 DOI. Appears in: CSS-T code, Quantum Reed-Muller code
C. Berdou et al., “One Hundred Second Bit-Flip Time in a Two-Photon Dissipative Oscillator”, PRX Quantum 4, (2023) arXiv:2204.09128 DOI. Appears in: Two-component cat code
L. Berent, L. Burgholzer, and R. Wille, “Software Tools for Decoding Quantum Low-Density Parity-Check Codes”, Proceedings of the 28th Asia and South Pacific Design Automation Conference (2023) arXiv:2209.01180 DOI. Appears in: Quantum LDPC (QLDPC) code
L. Berent, T. Hillmann, J. Eisert, R. Wille, and J. Roffe, “Analog Information Decoding of Bosonic Quantum Low-Density Parity-Check Codes”, PRX Quantum 5, (2024) arXiv:2311.01328 DOI. Appears in: 3D surface code, Concatenated bosonic code, Repetition code, XYZ product code
L. Berent, L. Burgholzer, P.-J. H. S. Derks, J. Eisert, and R. Wille, “Decoding quantum color codes with MaxSAT”, Quantum 8, 1506 (2024) arXiv:2303.14237 DOI. Appears in: Honeycomb (6.6.6) color code
T. Bergamaschi, L. Golowich, and S. Gunn, “Approaching the Quantum Singleton Bound with Approximate Error Correction”, (2022) arXiv:2212.09935. Appears in: Folded quantum RS (FQRS) code, Generalized RS (GRS) code, Good QLDPC code, Quantum maximum-distance-separable (MDS) code, Singleton-bound approaching AQECC
J. Berger and T. J. Osborne, “Perfect tangles”, (2018) arXiv:1804.03199. Appears in: Planar-perfect-tensor code, Category-based quantum code
T. P. Berger and P. Loidreau, “How to Mask the Structure of Codes for a Cryptographic Use”, Designs, Codes and Cryptography 35, 63 (2005) DOI. Appears in: Gabidulin code, Generalized RS (GRS) code
T. Berger and P. Charpin, “The automorphism group of Generalized Reed-Muller codes”, Discrete Mathematics 117, 1 (1993) DOI. Appears in: Generalized RM (GRM) code
M. Bergmann and P. van Loock, “Quantum error correction against photon loss using NOON states”, Physical Review A 94, (2016) arXiv:1512.07605 DOI. Appears in: Concatenated bosonic code, Quantum parity code (QPC), Two-mode binomial code
J. Bergou and B.-G. Englert, “Operators of the phase. Fundamentals”, Annals of Physics 209, 479 (1991) DOI. Appears in: Bosonic code
E. R. Berlekamp, “Coding theory and the Mathieu groups”, Information and Control 18, 40 (1971) DOI. Appears in: Nordstrom-Robinson (NR) code
E. R. Berlekamp, Algebraic Coding Theory (WORLD SCIENTIFIC, 2014) DOI. Appears in: Berlekamp code, Constacyclic code, Srivastava code
E. Berlekamp, “Nonbinary BCH decoding (Abstr.)”, IEEE Transactions on Information Theory 14, 242 (1968) DOI. Appears in: Generalized RS (GRS) code, Bose–Chaudhuri–Hocquenghem (BCH) code
E. Berlekamp and L. Welch, “Weight distributions of the cosets of the (32,6) Reed-Muller code”, IEEE Transactions on Information Theory 18, 203 (1972) DOI. Appears in: $[2^m,m+1,2^{m-1}]$ First-order RM code
E. Berlekamp, “Goppa codes”, IEEE Transactions on Information Theory 19, 590 (1973) DOI. Appears in: Goppa code
E. Berlekamp, R. McEliece, and H. van Tilborg, “On the inherent intractability of certain coding problems (Corresp.)”, IEEE Transactions on Information Theory 24, 384 (1978) DOI. Appears in: Linear binary code
E. Berlekamp, “Bit-serial Reed - Solomon encoders”, IEEE Transactions on Information Theory 28, 869 (1982) DOI. Appears in: Reed-Solomon (RS) code
E. R. Berlekamp, Algebraic Coding Theory, McGraw-Hill, 1968. Appears in: Binary BCH code, Generalized RS (GRS) code, Bose–Chaudhuri–Hocquenghem (BCH) code, Reed-Solomon (RS) code
E. R. Berlekamp and L. Welch, Error Correction of Algebraic Block Codes. U.S. Patent, Number 4,633,470 1986.. Appears in: Reed-Solomon (RS) code
S. D. Berman, “On the theory of group codes”, Cybernetics 3, 25 (1969) DOI. Appears in: Generalized RM (GRM) code, Group-algebra code, Reed-Muller (RM) code
S. D. Berman, “Semisimple cyclic and Abelian codes. II”, Cybernetics 3, 17 (1970) DOI. Appears in: Group-algebra code
Berman, A., Dor, A., Shany, Y., Shapir, I., and Doubchak, A. (2023). U.S. Patent No. 11,855,658. Washington, DC: U.S. Patent and Trademark Office.. Appears in: Generalized RS (GRS) code
J. Bermejo-Vega and M. V. den Nest, “Classical simulations of Abelian-group normalizer circuits with intermediate measurements”, (2013) arXiv:1210.3637. Appears in: Stabilizer code
J. Bermejo-Vega, C. Y.-Y. Lin, and M. V. den Nest, “The computational power of normalizer circuits over black-box groups”, (2014) arXiv:1409.4800. Appears in: Stabilizer code
J. Bermejo-Vega, C. Y.-Y. Lin, and M. V. den Nest, “Normalizer circuits and a Gottesman-Knill theorem for infinite-dimensional systems”, (2015) arXiv:1409.3208. Appears in: Rotor code, Rotor stabilizer code
J. J. Bernal, Á. del Río, and J. J. Simón, “An intrinsical description of group codes”, Designs, Codes and Cryptography 51, 289 (2009) DOI. Appears in: Group-algebra code
F. Bernhardt, P. Landrock, and O. Manz, “The extended golay codes considered as ideals”, Journal of Combinatorial Theory, Series A 55, 235 (1990) DOI. Appears in: $[24, 12, 8]$ Extended Golay code, Group-algebra code
D. J. Bernstein, T. Lange, and C. Peters, “Smaller Decoding Exponents: Ball-Collision Decoding”, Lecture Notes in Computer Science 743 (2011) DOI. Appears in: Random code
M. Bernstein, N. J. A. Sloane, and P. E. Wright, “On sublattices of the hexagonal lattice”, Discrete Mathematics 170, 29 (1997) DOI. Appears in: $A_2$ triangular lattice
C. Berrou, A. Glavieux, and P. Thitimajshima, “Near Shannon limit error-correcting coding and decoding: Turbo-codes. 1”, Proceedings of ICC ’93 - IEEE International Conference on Communications DOI. Appears in: Turbo code
C. Berrou and A. Glavieux, “Near optimum error correcting coding and decoding: turbo-codes”, IEEE Transactions on Communications 44, 1261 (1996) DOI. Appears in: Turbo code
D. W. Berry, A. M. Childs, R. Cleve, R. Kothari, and R. D. Somma, “Simulating Hamiltonian Dynamics with a Truncated Taylor Series”, Physical Review Letters 114, (2015) arXiv:1412.4687 DOI. Appears in: Spin GKP code
N. Berthusen et al., “Experiments with the four-dimensional surface code on a quantum charge-coupled device quantum computer”, Physical Review A 110, (2024) arXiv:2408.08865 DOI. Appears in: Loop toric code, Single-shot code
N. Berthusen, D. Devulapalli, E. Schoute, A. M. Childs, M. J. Gullans, A. V. Gorshkov, and D. Gottesman, “Toward a 2D Local Implementation of Quantum Low-Density Parity-Check Codes”, PRX Quantum 6, (2025) arXiv:2404.17676 DOI. Appears in: Bivariate bicycle (BB) code
I. Besedin et al., “Realizing Lattice Surgery on Two Distance-Three Repetition Codes with Superconducting Qubits”, (2025) arXiv:2501.04612. Appears in: Quantum repetition code, $[[9,1,3]]$ Surface-17 code
M. Best, “Binary codes with a minimum distance of four (Corresp.)”, IEEE Transactions on Information Theory 26, 738 (1980) DOI. Appears in: Best $(10,40,4)$ code
Best, M.R. 1978. Binary codes with minimum distance four. Report ZW 112/78, Math Centrum, Amsterdam.. Appears in: Best $(10,40,4)$ code, Julin-Golay code
T. Beth, D. Jungnickel, and H. Lenz, Design Theory (Cambridge University Press, 1999) DOI. Appears in: Combinatorial design
T. Beth, C. Charnes, M. Grassl, G. Alber, A. Delgado, and M. Mussinger, Designs, Codes and Cryptography 29, 51 (2003) DOI. Appears in: Combinatorial design, $[[2m,2m-2,2]]$ error-detecting code, Jump code, Self-dual linear code
K. Betsumiya and A. Munemasa, “On triply even binary codes”, Journal of the London Mathematical Society 86, 1 (2012) arXiv:1012.4134 DOI. Appears in: Divisible code, Doubled color code, Quantum divisible code, $[[49,1,5]]$ triorthogonal code
K. Betsumiya and A. Munemasa, “On triply even binary codes”, Journal of the London Mathematical Society 86, 1 (2012) DOI. Appears in: Divisible code, $[[49,1,5]]$ triorthogonal code
V. Bettaque and B. Swingle, “The Structure of the Majorana Clifford Group”, (2024) arXiv:2407.11319. Appears in: Fermion code
Beutelspacher, Albrecht, and Ute Rosenbaum. Projective geometry: from foundations to applications. Cambridge University Press, 1998.. Appears in: Maximum distance separable (MDS) code, Projective geometry code
M. E. Beverland, S. Huang, and V. Kliuchnikov, “Fault tolerance of stabilizer channels”, (2024) arXiv:2401.12017. Appears in: Modular-qudit stabilizer code
M. Beverland, E. Campbell, M. Howard, and V. Kliuchnikov, “Lower bounds on the non-Clifford resources for quantum computations”, Quantum Science and Technology 5, 035009 (2020) arXiv:1904.01124 DOI. Appears in: Qubit stabilizer code
S. Bhandari, P. Harsha, M. Kumar, and M. Sudan, “Decoding multivariate multiplicity codes on product sets”, Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing (2021) arXiv:2012.01530 DOI. Appears in: Multiplicity code
S. Bhandari, P. Harsha, M. Kumar, and M. Sudan, “Ideal-Theoretic Explanation of Capacity-Achieving Decoding”, (2021) arXiv:2103.07930 DOI. Appears in: Folded RS (FRS) code, Group-algebra code, Multiplicity code
L. Bhardwaj, D. Gaiotto, and A. Kapustin, “State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter”, Journal of High Energy Physics 2017, (2017) arXiv:1605.01640 DOI. Appears in: 2D color code, 3D color code, 3D subsystem color code, 3D surface code, Color code, Cubic theory code, Double-semion stabilizer code, Homological code, Abelian quantum-double stabilizer code, Dihedral $G=D_m$ quantum-double code, Concatenated qubit code, Subsystem modular-qudit stabilizer code, Modular-qudit surface code, Kitaev surface code, Abelian TQD stabilizer code, Two-foliated fracton code, Two-gauge theory code
D. Bhatnagar, M. Steinberg, D. Elkouss, C. G. Almudever, and S. Feld, “Low-Depth Flag-Style Syndrome Extraction for Small Quantum Error-Correction Codes”, 2023 IEEE International Conference on Quantum Computing and Engineering (QCE) 63 (2023) arXiv:2305.00784 DOI. Appears in: Five-qubit perfect code, $[[7,1,3]]$ Steane code
S. Bhatnagar and P. V. Kumar, “A Tighter Distance Upper-Bound for Gottesman-Kitaev-Preskill Codes”, 2024 IEEE Information Theory Workshop (ITW) 615 (2024) DOI. Appears in: Gottesman-Kitaev-Preskill (GKP) code
A. Bhattacharyya, S. Kopparty, G. Schoenebeck, M. Sudan, and D. Zuckerman, “Optimal Testing of Reed-Muller Codes”, (2010) arXiv:0910.0641. Appears in: Binary linear LTC, Reed-Muller (RM) code
A. Bhattacharyya, S. Gopi, and A. Tal, “Lower bounds for 2-query LCCs over large alphabet”, (2017) arXiv:1611.06980. Appears in: Locally correctable code (LCC), Locally decodable code (LDC)
D. Bhaumik, K. Bhaumik, and B. Dutta-Roy, “Charged bosons and the coherent state”, Journal of Physics A: Mathematical and General 9, 1507 (1976) DOI. Appears in: Pair-cat code
D. Bhoumik, R. Majumdar, D. Madan, D. Vinayagamurthy, S. Raghunathan, and S. Sur-Kolay, “Efficient Syndrome Decoder for Heavy Hexagonal QECC via Machine Learning”, ACM Transactions on Quantum Computing 5, 1 (2024) arXiv:2210.09730 DOI. Appears in: Heavy-hexagon code
I. Białynicki-Birula and J. Mycielski, “Uncertainty relations for information entropy in wave mechanics”, Communications in Mathematical Physics 44, 129 (1975) DOI. Appears in: Qubit CSS code
L. Biedenharn, E. Lieb, B. Simon, and F. Wilczek, “The Ancestry of the ‘Anyon’”, Physics Today 43, 90 (1990) DOI. Appears in: Topological code
J. Bierbrauer and Y. Edel, “New code parameters from Reed-Solomon subfield codes”, IEEE Transactions on Information Theory 43, 953 (1997) DOI. Appears in: Twisted BCH code
J. Bierbrauer and Y. Edel, “Extending and LengtheningBCHCodes”, Finite Fields and Their Applications 3, 314 (1997) DOI. Appears in: Twisted BCH code
J. Bierbrauer and Y. Edel, “Quantum twisted codes”, Journal of Combinatorial Designs 8, 174 (2000) DOI. Appears in: Perfect quantum code, Quantum twisted code, Hermitian Galois-qudit code
J. Bierbrauer, Introduction to Coding Theory (Chapman and Hall/CRC, 2016) DOI. Appears in: Anticode, Binary BCH code, Ovoid code, Denniston code, Divisible code, Extended GRS code, Griesmer code, $[7,4,3]$ Hamming code, Hexacode, Hyperoval code, Projective geometry code, $q$-ary simplex code, Ternary Golay code, $(u|u+v)$-construction code
Biggs, Norman. Finite groups of automorphisms: course given at the University of Southampton, October-December 1969. Vol. 6. CUP Archive, 1971.. Appears in: Slepian group-orbit code
E. Biglieri, J. Proakis, and S. Shamai, “Fading channels: information-theoretic and communications aspects”, IEEE Transactions on Information Theory 44, 2619 (1998) DOI. Appears in: Spacetime block code (STBC)
M. Bilokur, S. Gopalakrishnan, and S. Majidy, “Thermodynamic limitations on fault-tolerant quantum computing”, (2024) arXiv:2411.12805. Appears in: Qubit code
J. R. Bitner, G. Ehrlich, and E. M. Reingold, “Efficient generation of the binary reflected gray code and its applications”, Communications of the ACM 19, 517 (1976) DOI. Appears in: Gray code
S. R. Blackburn, “Frameproof Codes”, SIAM Journal on Discrete Mathematics 16, 499 (2003) DOI. Appears in: Frameproof (FP) code
T. Blackmore and G. H. Norton, “Matrix-Product Codes over ? q”, Applicable Algebra in Engineering, Communication and Computing 12, 477 (2001) DOI. Appears in: Generalized RM (GRM) code, Matrix-product code
R. E. Blahut, “The Gleason-Prange theorem”, IEEE Transactions on Information Theory 37, 1269 (1991) DOI. Appears in: Binary quadratic-residue (QR) code
R. E. Blahut, Algebraic Codes on Lines, Planes, and Curves (Cambridge University Press, 2001) DOI. Appears in: Evaluation AG code, Hermitian code, Norm-trace code
R. E. Blahut, Algebraic Codes for Data Transmission (Cambridge University Press, 2003) DOI. Appears in: Generalized RM (GRM) code, Finite-geometry LDPC (FG-LDPC) code
R. E. Blahut, Modem Theory (Cambridge University Press, 2009) DOI. Appears in: Phase-shift keying (PSK) code, Quadrature-amplitude modulation (QAM) code
R.E. Blahut, Theory and practice of error-control codes, Addison-Wesley 1983.. Appears in: Binary BCH code, Bose–Chaudhuri–Hocquenghem (BCH) code, Reed-Solomon (RS) code
I. F. Blake, G. Cohen, and M. Deza, “Coding with permutations”, Information and Control 43, 1 (1979) DOI. Appears in: Code in permutations
I. F. Blake, Essays on Coding Theory (Cambridge University Press, 2024) DOI. Appears in: Batch code, Distributed-storage code, Fountain code, Hamiltonian-based code, $[2^r-1,2^r-r-1,3]$ Hamming code, Locally decodable code (LDC), Low-density parity-check (LDPC) code, Locally recoverable code (LRC), Private information retrieval (PIR) code, Polar code, Rank-metric code
I. F. Blake, "Coding for Erasures and Fountain Codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI. Appears in: Tornado code
M. Blaum and R. M. Roth, “New array codes for multiple phased burst correction”, IEEE Transactions on Information Theory 39, 66 (1993) DOI. Appears in: B-code, Reed-Solomon (RS) code
M. Blaum, J. Brady, J. Bruck, and Jai Menon, “EVENODD: an efficient scheme for tolerating double disk failures in RAID architectures”, IEEE Transactions on Computers 44, 192 (1995) DOI. Appears in: EVENODD code
M. Blaum, J. Bruck, and A. Vardy, “MDS array codes with independent parity symbols”, IEEE Transactions on Information Theory 42, 529 (1996) DOI. Appears in: Generalized EVENODD code
M. Blaum, J. L. Hafner, and S. Hetzler, “Partial-MDS Codes and their Application to RAID Type of Architectures”, (2014) arXiv:1205.0997. Appears in: Maximally recoverable (MR) code
M. Blaum, P. G. Farrell, H. C. A. van Tilborg, 1998. Array codes. Handbook of coding theory, 2 (Part 2), pp. 1855-1909.. Appears in: Array code, B-code, Generalized EVENODD code, Cross-interleaved RS (CIRS) code, EVENODD code, MDS array code, Rank-metric code, Reed-Solomon (RS) code
D. Bleichenbacher, A. Kiayias, and M. Yung, “Decoding interleaved Reed–Solomon codes over noisy channels”, Theoretical Computer Science 379, 348 (2007) DOI. Appears in: Interleaved RS (IRS) code
H. F. Blichfeldt, “The minimum value of quadratic forms, and the closest packing of spheres”, Mathematische Annalen 101, 605 (1929) DOI. Appears in: $E_8$ Gosset lattice, $E_7$ root lattice, $E_6$ root lattice
H. F. Blichfeldt, “The minimum values of positive quadratic forms in six, seven and eight variables”, Mathematische Zeitschrift 39, 1 (1935) DOI. Appears in: $E_8$ Gosset lattice, $E_7$ root lattice, $E_6$ root lattice
Blichfeldt, H. F. "On the minimum value of positive real quadratic forms in 6 variables." Bulletin of American Math. Soc 31 (1925): 386.. Appears in: $E_8$ Gosset lattice, $E_7$ root lattice, $E_6$ root lattice
È. L. Blokh, V. V. Zyablov, “Coding of Generalized Concatenated Codes”, Probl. Peredachi Inf., 10:3 (1974), 45–50; Problems Inform. Transmission, 10:3 (1974), 218–222. Appears in: Generalized concatenated code (GCC)
M. Blum, M. Luby, and R. Rubinfeld, “Self-testing/correcting with applications to numerical problems”, Proceedings of the twenty-second annual ACM symposium on Theory of computing - STOC ’90 (1990) DOI. Appears in: Binary linear LTC, Hadamard code
M. Blum, M. Luby, and R. Rubinfeld, “Self-testing/correcting with applications to numerical problems”, Journal of Computer and System Sciences 47, 549 (1993) DOI. Appears in: Binary linear LTC, Hadamard code, Locally testable code (LTC)
R. Blume-Kohout, H. K. Ng, D. Poulin, and L. Viola, “Characterizing the Structure of Preserved Information in Quantum Processes”, Physical Review Letters 100, (2008) arXiv:0705.4282 DOI. Appears in: Operator-algebra QECC (OAQECC)
R. Blume-Kohout, H. K. Ng, D. Poulin, and L. Viola, “Information-preserving structures: A general framework for quantum zero-error information”, Physical Review A 82, (2010) arXiv:1006.1358 DOI. Appears in: Operator-algebra QECC (OAQECC)
R. Blume-Kohout and P. S. Turner, “The Curious Nonexistence of Gaussian 2-Designs”, Communications in Mathematical Physics 326, 755 (2014) arXiv:1110.1042 DOI. Appears in: Bosonic code, $t$-design
D. Bluvstein et al., “A quantum processor based on coherent transport of entangled atom arrays”, Nature 604, 451 (2022) arXiv:2112.03923 DOI. Appears in: $[[7,1,3]]$ Steane code, Toric code
D. Bluvstein et al., “Logical quantum processor based on reconfigurable atom arrays”, Nature 626, 58 (2023) arXiv:2312.03982 DOI. Appears in: $[[8,3,2]]$ Smallest interesting color code, $[[7,1,3]]$ Steane code, XZZX surface code
A. Bocharov, X. Cui, V. Kliuchnikov, and Z. Wang, “Efficient topological compilation for a weakly integral anyonic model”, Physical Review A 93, (2016) arXiv:1504.03383 DOI. Appears in: Modular-qudit code
I. E. Bocharova, F. Hug, R. Johannesson, B. D. Kudryashov, and R. V. Satyukov, “Searching for Voltage Graph-Based LDPC Tailbiting Codes With Large Girth”, IEEE Transactions on Information Theory 58, 2265 (2012) arXiv:1108.0840 DOI. Appears in: Quasi-cyclic LDPC (QC-LDPC) code
T. C. Bohdanowicz, E. Crosson, C. Nirkhe, and H. Yuen, “Good approximate quantum LDPC codes from spacetime circuit Hamiltonians”, Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing (2019) arXiv:1811.00277 DOI. Appears in: Circuit-to-Hamiltonian approximate code, Quantum low-weight check (QLWC) code
A. Bols and S. Vadnerkar, “Classification of the anyon sectors of Kitaev’s quantum double model”, (2023) arXiv:2310.19661. Appears in: Quantum-double code
A. Bolt, G. Duclos-Cianci, D. Poulin, and T. M. Stace, “Foliated Quantum Error-Correcting Codes”, Physical Review Letters 117, (2016) arXiv:1607.02579 DOI. Appears in: Cluster-state code, Qubit CSS code
H. Bombin and M. A. Martin-Delgado, “Topological Quantum Distillation”, Physical Review Letters 97, (2006) arXiv:quant-ph/0605138 DOI. Appears in: 2D color code, Truncated trihexagonal (4.6.12) color code, Square-octagon (4.8.8) color code, Color code, Honeycomb (6.6.6) color code
H. Bombin and M. A. Martin-Delgado, “Topological quantum error correction with optimal encoding rate”, Physical Review A 73, (2006) arXiv:quant-ph/0602063 DOI. Appears in: $D$-dimensional twisted toric code
H. Bombin and M. A. Martin-Delgado, “Exact topological quantum order inD=3and beyond: Branyons and brane-net condensates”, Physical Review B 75, (2007) arXiv:cond-mat/0607736 DOI. Appears in: 2D color code, 3D color code, 3D surface code, Truncated trihexagonal (4.6.12) color code, Square-octagon (4.8.8) color code, Color code, Cubic honeycomb color code, Honeycomb tiling, Hyperbolic color code, $\mathbb{Z}^n$ hypercubic lattice, Stellated color code, Triangular surface code
H. Bombin and M. A. Martin-Delgado, “Homological error correction: Classical and quantum codes”, Journal of Mathematical Physics 48, (2007) arXiv:quant-ph/0605094 DOI. Appears in: $D$-dimensional twisted toric code, Cycle code, Perfect binary code, Qubit CSS code, Classical topological code
H. Bombin and M. A. Martin-Delgado, “Optimal resources for topological two-dimensional stabilizer codes: Comparative study”, Physical Review A 76, (2007) arXiv:quant-ph/0703272 DOI. Appears in: Rotated surface code, Kitaev surface code
H. Bombin and M. A. Martin-Delgado, “Family of non-Abelian Kitaev models on a lattice: Topological condensation and confinement”, Physical Review B 78, (2008) arXiv:0712.0190 DOI. Appears in: Quantum-double code
H. Bombin and M. A. Martin-Delgado, “Quantum measurements and gates by code deformation”, Journal of Physics A: Mathematical and Theoretical 42, 095302 (2009) arXiv:0704.2540 DOI. Appears in: Twist-defect surface code
H. Bombin, M. Kargarian, and M. A. Martin-Delgado, “Interacting anyonic fermions in a two-body color code model”, Physical Review B 80, (2009) arXiv:0811.0911 DOI. Appears in: Three-fermion (3F) subsystem code
H. Bombin, “Topological Order with a Twist: Ising Anyons from an Abelian Model”, Physical Review Letters 105, (2010) arXiv:1004.1838 DOI. Appears in: $[[14,3,3]]$ Rhombic dodecahedron surface code, Abelian topological code, Twist-defect color code, Twist-defect surface code
H. Bombin, “Topological subsystem codes”, Physical Review A 81, (2010) arXiv:0908.4246 DOI. Appears in: 2D subsystem color code, Bacon-Shor code, Subsystem color code, Three-fermion (3F) subsystem code, Lattice subsystem code
H. Bombin, “Clifford gates by code deformation”, New Journal of Physics 13, 043005 (2011) arXiv:1006.5260 DOI. Appears in: 2D subsystem color code, 3D color code, Twist-defect color code
H. Bombin, R. W. Chhajlany, M. Horodecki, and M. A. Martin-Delgado, “Self-Correcting Quantum Computers”, (2012) arXiv:0907.5228. Appears in: Color code, Self-correcting quantum code
H. Bombin, G. Duclos-Cianci, and D. Poulin, “Universal topological phase of two-dimensional stabilizer codes”, New Journal of Physics 14, 073048 (2012) arXiv:1103.4606 DOI. Appears in: 2D lattice stabilizer code, Three-fermion (3F) subsystem code, Kitaev surface code
H. Bombin, R. S. Andrist, M. Ohzeki, H. G. Katzgraber, and M. A. Martin-Delgado, “Strong Resilience of Topological Codes to Depolarization”, Physical Review X 2, (2012) arXiv:1202.1852 DOI. Appears in: Toric code
H. Bombin, “An Introduction to Topological Quantum Codes”, (2013) arXiv:1311.0277. Appears in: Color code
H. Bombín, “Structure of 2D Topological Stabilizer Codes”, Communications in Mathematical Physics 327, 387 (2014) arXiv:1107.2707 DOI. Appears in: 2D lattice stabilizer code, Kitaev surface code
H. Bombin, “Gauge Color Codes: Optimal Transversal Gates and Gauge Fixing in Topological Stabilizer Codes”, (2015) arXiv:1311.0879. Appears in: 2D color code, 3D subsystem color code, Color code, $[[2^r-1,1,3]]$ simplex code, Modular-qudit color code, Simplex spherical code, Subsystem color code, Tetrahedral color code
H. Bombín, “Single-Shot Fault-Tolerant Quantum Error Correction”, Physical Review X 5, (2015) arXiv:1404.5504 DOI. Appears in: 3D subsystem color code, Single-shot code
H. Bombin, “Dimensional Jump in Quantum Error Correction”, (2016) arXiv:1412.5079. Appears in: 2D color code, 3D color code
H. Bombin, “2D quantum computation with 3D topological codes”, (2018) arXiv:1810.09571. Appears in: Tetrahedral color code
H. Bombin, C. Dawson, T. Farrelly, Y. Liu, N. Nickerson, M. Pant, F. Pastawski, and S. Roberts, “Fault-tolerant complexes”, (2023) arXiv:2308.07844. Appears in: Fusion-based quantum computing (FBQC) code
H. Bombín, C. Dawson, N. Nickerson, M. Pant, and J. Sullivan, “Increasing error tolerance in quantum computers with dynamic bias arrangement”, (2023) arXiv:2303.16122. Appears in: Asymmetric quantum code, Cluster-state code, XZZX surface code
H. Bombín, C. Dawson, Y.-H. Liu, N. Nickerson, F. Pastawski, and S. Roberts, “Modular decoding: parallelizable real-time decoding for quantum computers”, (2023) arXiv:2303.04846. Appears in: Abelian topological code
H. Bombín, C. Dawson, R. V. Mishmash, N. Nickerson, F. Pastawski, and S. Roberts, “Logical Blocks for Fault-Tolerant Topological Quantum Computation”, PRX Quantum 4, (2023) arXiv:2112.12160 DOI. Appears in: Fusion-based quantum computing (FBQC) code, Twist-defect surface code
H. Bombin, D. Litinski, N. Nickerson, F. Pastawski, and S. Roberts, “Unifying flavors of fault tolerance with the ZX calculus”, Quantum 8, 1379 (2024) arXiv:2303.08829 DOI. Appears in: Kitaev surface code
H. Bombín, M. Pant, S. Roberts, and K. I. Seetharam, “Fault-Tolerant Postselection for Low-Overhead Magic State Preparation”, PRX Quantum 5, (2024) arXiv:2212.00813 DOI. Appears in: Kitaev surface code
A. Bondarenko, D. Radchenko, and M. Viazovska, “Optimal asymptotic bounds for spherical designs”, (2011) arXiv:1009.4407. Appears in: Spherical design
P. H. Bonderson, Non-Abelian Anyons and Interferometry, California Institute of Technology, 2007 DOI. Appears in: $\mathbb{Z}_q^{(1)}$ subsystem code, Topological code, Abelian topological code
R. S. Bondurant, “Near-quantum optimum receivers for the phase-quadrature coherent-state channel”, Optics Letters 18, 1896 (1993) DOI. Appears in: Coherent FSK (CFSK) c-q code
D. Boneh and J. Shaw, “Collusion-Secure Fingerprinting for Digital Data”, Advances in Cryptology — CRYPT0’ 95 452 (1995) DOI. Appears in: Frameproof (FP) code
D. Boneh and J. Shaw, “Collusion-secure fingerprinting for digital data”, IEEE Transactions on Information Theory 44, 1897 (1998) DOI. Appears in: Frameproof (FP) code
N. E. Bonesteel, “Chiral spin liquids and quantum error-correcting codes”, Physical Review A 62, (2000) arXiv:quant-ph/0006092 DOI. Appears in: Valence-bond-solid (VBS) code
N. E. Bonesteel and D. P. DiVincenzo, “Quantum circuits for measuring Levin-Wen operators”, Physical Review B 86, (2012) arXiv:1206.6048 DOI. Appears in: String-net code
J. P. Bonilla Ataides, D. K. Tuckett, S. D. Bartlett, S. T. Flammia, and B. J. Brown, “The XZZX surface code”, Nature Communications 12, (2021) arXiv:2009.07851 DOI. Appears in: Asymmetric quantum code, Twisted XZZX toric code, XZZX surface code
A. Bonnecaze and P. Solé, “Quaternary constructions of formally self-dual binary codes and unimodular lattices”, Lecture Notes in Computer Science 194 (1994) DOI. Appears in: $E_8$ Gosset lattice, $[23, 12, 7]$ Golay code, $\Lambda_{24}$ Leech lattice, Octacode
A. Bonnecaze, P. Sole, and A. R. Calderbank, “Quaternary quadratic residue codes and unimodular lattices”, IEEE Transactions on Information Theory 41, 366 (1995) DOI. Appears in: $E_8$ Gosset lattice, Octacode
A. Bonnecaze, P. Gaborit, M. Harada, M. Kitazume, and P. Solé, “Niemeier lattices and Type II codes over Z4”, Discrete Mathematics 205, 1 (1999) DOI. Appears in: Niemeier lattice, Octacode, Quaternary linear code over $\mathbb{Z}_4$
M. Boon and J. Zak, “Discrete coherent states on the von Neumann lattice”, Physical Review B 18, 6744 (1978) DOI. Appears in: Bosonic code
M. Borello and W. Willems, “On the algebraic structure of quasi group codes”, (2021) arXiv:1912.09167. Appears in: Linear $q$-ary code, Quasi group-algebra code
J. Borges, J. Rifà, and V. A. Zinoviev, “On Completely Regular Codes”, (2017) arXiv:1703.08684. Appears in: Completely regular code, Perfect code, Quasi-perfect code, Uniformly packed code
N. Borisov, I. Petrov, and A. Tayduganov, “Asymmetric Adaptive LDPC-Based Information Reconciliation for Industrial Quantum Key Distribution”, Entropy 25, 31 (2022) arXiv:2212.01121 DOI. Appears in: Low-density parity-check (LDPC) code
K. Boroczky, Packing of spheres in spaces of constant curvature, Acta Math. Acad. Sci. Hung. 32 (1978), 243–261.. Appears in: 600-cell code, Biorthogonal spherical code, Simplex spherical code
S. Borodachov, P. Boyvalenkov, P. Dragnev, D. Hardin, E. Saff, and M. Stoyanova, “Energy bounds for weighted spherical codes and designs via linear programming”, (2024) arXiv:2403.07457. Appears in: 24-cell code, Biorthogonal spherical code, Hypercube code, Pentakis dodecahedron code, Spherical design
Borrelli, Chris. "IEEE 802.3 cyclic redundancy check." application note: Virtex Series and Virtex-II Family, XAPP209 (v1. 0) (2001).. Appears in: Cyclic redundancy check (CRC) code
R. C. Bose and D. K. Ray-Chaudhuri, “On a class of error correcting binary group codes”, Information and Control 3, 68 (1960) DOI. Appears in: Binary BCH code
R. C. Bose and D. K. Ray-Chaudhuri, “Further results on error correcting binary group codes”, Information and Control 3, 279 (1960) DOI. Appears in: Binary BCH code
R. C. Bose (1947). Mathematical theory of the symmetrical factorial design. Sankhyā: The Indian Journal of Statistics, 107-166.. Appears in: Ovoid code, Hyperoval code, Maximum distance separable (MDS) code, Projective geometry code
W. Bosma, J. Cannon, and G. Matthews, “Programming with algebraic structures”, Proceedings of the international symposium on Symbolic and algebraic computation - ISSAC ’94 52 (1994) DOI. Appears in: Lattice-based code
W. BOSMA, J. CANNON, and C. PLAYOUST, “The Magma Algebra System I: The User Language”, Journal of Symbolic Computation 24, 235 (1997) DOI. Appears in: Lattice-based code
D. Boucher, W. Geiselmann, and F. Ulmer, “Skew-cyclic codes”, (2006) arXiv:math/0604603. Appears in: Skew-cyclic code
D. Boucher and F. Ulmer, “Linear codes using skew polynomials with automorphisms and derivations”, Designs, Codes and Cryptography 70, 405 (2012) DOI. Appears in: Linearized RS code
J. E. Bourassa et al., “Blueprint for a Scalable Photonic Fault-Tolerant Quantum Computer”, Quantum 5, 392 (2021) arXiv:2010.02905 DOI. Appears in: GKP CV-cluster-state code
M. F. Bourque and B. Petri, “Linear programming bounds for hyperbolic surfaces”, (2023) arXiv:2302.02540. Appears in: Hyperbolic sphere packing
P. A. H. Bours, “On the construction of perfect deletion-correcting codes using design theory”, Designs, Codes and Cryptography 6, 5 (1995) DOI. Appears in: Combinatorial design, Editing code, Perfect code
J. Boutros, O. Pothier, and G. Zemor, “Generalized low density (Tanner) codes”, 1999 IEEE International Conference on Communications (Cat. No. 99CH36311) DOI. Appears in: Generalized Gallager code
I. Bouyukliev, M. Dzhumalieva-Stoeva, and V. Monev, “Classification of Binary Self-Dual Codes of Length 40”, IEEE Transactions on Information Theory 61, 4253 (2015) DOI. Appears in: Two-weight code
S. Bouyuklieva, “Some optimal self-orthogonal and self-dual codes”, Discrete Mathematics 287, 1 (2004) DOI. Appears in: Self-dual linear code
S. Bouyuklieva, "Self-dual codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI. Appears in: Divisible code, Self-dual linear code
G. Bowen, “Entanglement required in achieving entanglement-assisted channel capacities”, Physical Review A 66, (2002) arXiv:quant-ph/0205117 DOI. Appears in: $[[3, 1, 3;2]]$ EA code, EA qubit code, Entanglement-assisted (EA) QECC
P. G. Boyvalenkov, P. D. Dragnev, D. P. Hardin, E. B. Saff, and M. M. Stoyanova, “Universal upper and lower bounds on energy of spherical designs”, (2015) arXiv:1509.07837. Appears in: Kerdock spherical code, Universally optimal spherical code
P. G. Boyvalenkov, P. D. Dragnev, D. P. Hardin, E. B. Saff, and M. M. Stoyanova, “Energy bounds for codes and designs in Hamming spaces”, Designs, Codes and Cryptography 82, 411 (2016) DOI. Appears in: Universally optimal $q$-ary code
P. G. Boyvalenkov, K. V. Delchev, D. V. Zinoviev, and V. A. Zinoviev, “On two-weight codes”, (2020) arXiv:2005.13623. Appears in: Two-weight code
P. Boyvalenkov and D. Danev, “Uniqueness of the 120-point spherical 11-design in four dimensions”, Archiv der Mathematik 77, 360 (2001) DOI. Appears in: 600-cell code, Spherical design
P. Boyvalenkov, D. Danev, "Linear programming bounds." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI. Appears in: 24-cell code, Ovoid code, $q$-ary sharp configuration, Denniston code, $[23, 12, 7]$ Golay code, Hadamard code, Hill projective-cap code, Hyperoval code, Single parity-check (SPC) code, $q$-ary repetition code, $ED_m$ code, Semakov-Zinoviev-Zaitsev (SZZ) equidistant code, Ternary Golay code, Universally optimal $q$-ary code, Universally optimal spherical code
T. Brack, M. Alles, F. Kienle, and N. Wehn, “A Synthesizable IP Core for WIMAX 802.16E LDPC Code Decoding”, 2006 IEEE 17th International Symposium on Personal, Indoor and Mobile Radio Communications (2006) DOI. Appears in: Quasi-cyclic LDPC (QC-LDPC) code
A. J. Brady, A. Eickbusch, S. Singh, J. Wu, and Q. Zhuang, “Advances in bosonic quantum error correction with Gottesman–Kitaev–Preskill Codes: Theory, engineering and applications”, Progress in Quantum Electronics 93, 100496 (2024) arXiv:2308.02913 DOI. Appears in: Gottesman-Kitaev-Preskill (GKP) code
J. Brakensiek, S. Gopi, and V. Makam, “Generic Reed-Solomon Codes Achieve List-decoding Capacity”, (2024) arXiv:2206.05256. Appears in: Reed-Solomon (RS) code
F. G. S. L. Brandão, A. W. Harrow, and M. Horodecki, “Local Random Quantum Circuits are Approximate Polynomial-Designs”, Communications in Mathematical Physics 346, 397 (2016) arXiv:1208.0692 DOI. Appears in: Local Haar-random circuit qubit code, $t$-design
F. G. S. L. Brandão, A. W. Harrow, and M. Horodecki, “Local Random Quantum Circuits are Approximate Polynomial-Designs”, Communications in Mathematical Physics 346, 397 (2016) DOI. Appears in: Local Haar-random circuit qubit code, Topological code
F. G. S. L. Brandão, E. Crosson, M. B. Şahinoğlu, and J. Bowen, “Quantum Error Correcting Codes in Eigenstates of Translation-Invariant Spin Chains”, Physical Review Letters 123, (2019) arXiv:1710.04631 DOI. Appears in: Eigenstate thermalization hypothesis (ETH) code
S. Brandsen, A. Mandal, and H. D. Pfister, “Belief Propagation with Quantum Messages for Symmetric Classical-Quantum Channels”, (2022) arXiv:2207.04984. Appears in: Qubit c-q code
O. Bratteli and D. W. Robinson, Operator Algebras and Quantum Statistical Mechanics 1 (Springer Berlin Heidelberg, 1987) DOI. Appears in: Hamiltonian-based code
J. S. Brauchart and P. J. Grabner, “Distributing many points on spheres: Minimal energy and designs”, Journal of Complexity 31, 293 (2015) arXiv:1407.8282 DOI. Appears in: Universally optimal spherical code
M. Braun, M. Kiermaier, and A. Wassermann, “q-Analogs of Designs: Subspace Designs”, Network Coding and Subspace Designs 171 (2018) DOI. Appears in: Subspace design
S. L. Braunstein, “Error Correction for Continuous Quantum Variables”, Physical Review Letters 80, 4084 (1998) arXiv:quant-ph/9711049 DOI. Appears in: $[[5,1,3]]_{\mathbb{R}}$ Braunstein five-mode code, $[[9,1,3]]_{\mathbb{R}}$ Lloyd-Slotine code, Oscillator-into-oscillator code
S. L. Braunstein, “Quantum error correction for communication with linear optics”, Nature 394, 47 (1998) DOI. Appears in: $[[5,1,3]]_{\mathbb{R}}$ Braunstein five-mode code, $[[9,1,3]]_{\mathbb{R}}$ Lloyd-Slotine code
S. L. Braunstein and P. van Loock, “Quantum information with continuous variables”, Reviews of Modern Physics 77, 513 (2005) arXiv:quant-ph/0410100 DOI. Appears in: Bosonic code
S. B. Bravyi and A. Yu. Kitaev, “Quantum codes on a lattice with boundary”, (1998) arXiv:quant-ph/9811052. Appears in: Kitaev surface code
S. B. Bravyi and A. Yu. Kitaev, “Fermionic Quantum Computation”, Annals of Physics 298, 210 (2002) arXiv:quant-ph/0003137 DOI. Appears in: Bravyi-Kitaev superfast (BKSF) code, Bravyi-Kitaev transformation (BKT) code, Fermion code, Majorana stabilizer code, Quantum parity code (QPC)
S. Bravyi and M. Vyalyi, “Commutative version of the k-local Hamiltonian problem and common eigenspace problem”, (2004) arXiv:quant-ph/0308021. Appears in: 2D lattice stabilizer code, Commuting-projector Hamiltonian code, Topological code
S. Bravyi, “Lagrangian representation for fermionic linear optics”, (2004) arXiv:quant-ph/0404180. Appears in: Fermion code
S. Bravyi and A. Kitaev, “Universal quantum computation with ideal Clifford gates and noisy ancillas”, Physical Review A 71, (2005) arXiv:quant-ph/0403025 DOI. Appears in: $[[2^r-1,1,3]]$ simplex code, Qubit stabilizer code, Modular-qudit stabilizer code, $[[15,1,3]]$ quantum Reed-Muller code, Five-qubit perfect code
S. Bravyi, M. B. Hastings, and F. Verstraete, “Lieb-Robinson Bounds and the Generation of Correlations and Topological Quantum Order”, Physical Review Letters 97, (2006) arXiv:quant-ph/0603121 DOI. Appears in: Kitaev surface code, Topological code
S. Bravyi, “Universal quantum computation with theν=5∕2fractional quantum Hall state”, Physical Review A 73, (2006) arXiv:quant-ph/0511178 DOI. Appears in: Kitaev honeycomb code
S. Bravyi and B. Terhal, “A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes”, New Journal of Physics 11, 043029 (2009) arXiv:0810.1983 DOI. Appears in: 2D lattice stabilizer code, Crystalline-circuit qubit code, Qubit stabilizer code, Random-circuit code, Self-correcting quantum code, Lattice stabilizer code, Lattice subsystem code
S. Bravyi, D. Poulin, and B. Terhal, “Tradeoffs for Reliable Quantum Information Storage in 2D Systems”, Physical Review Letters 104, (2010) arXiv:0909.5200 DOI. Appears in: Linear binary code, Homological code, Newman-Moore code, Lattice stabilizer code
S. Bravyi, B. M. Terhal, and B. Leemhuis, “Majorana fermion codes”, New Journal of Physics 12, 083039 (2010) arXiv:1004.3791 DOI. Appears in: Linear binary code, Majorana color code, Majorana stabilizer code, Qubit CSS code, Qubit stabilizer code, Subsystem modular-qudit CSS code
S. Bravyi, M. B. Hastings, and S. Michalakis, “Topological quantum order: Stability under local perturbations”, Journal of Mathematical Physics 51, (2010) arXiv:1001.0344 DOI. Appears in: Commuting-projector Hamiltonian code, Hamiltonian-based code, Quantum LDPC (QLDPC) code, Topological code
S. Bravyi and M. B. Hastings, “A Short Proof of Stability of Topological Order under Local Perturbations”, Communications in Mathematical Physics 307, 609 (2011) arXiv:1001.4363 DOI. Appears in: Commuting-projector Hamiltonian code, Hamiltonian-based code, Quantum LDPC (QLDPC) code, Topological code
S. Bravyi and J. Haah, “Energy Landscape of 3D Spin Hamiltonians with Topological Order”, Physical Review Letters 107, (2011) arXiv:1105.4159 DOI. Appears in: Self-correcting quantum code
S. Bravyi, “Subsystem codes with spatially local generators”, Physical Review A 83, (2011) arXiv:1008.1029 DOI. Appears in: Bravyi-Bacon-Shor (BBS) code, $[[6,2,3,2]]$ BBS code, Subsystem hypergraph product (SHP) code, Lattice stabilizer code, Lattice subsystem code
S. Bravyi, B. Leemhuis, and B. M. Terhal, “Topological order in an exactly solvable 3D spin model”, Annals of Physics 326, 839 (2011) arXiv:1006.4871 DOI. Appears in: Chamon model code
S. Bravyi and J. Haah, “Magic-state distillation with low overhead”, Physical Review A 86, (2012) arXiv:1209.2426 DOI. Appears in: $[[6k+2,3k,2]]$ Campbell-Howard code, Divisible code, $[[k+4,k,2]]$ H code, Quantum Reed-Muller code, Triorthogonal code, Modular-qudit stabilizer code, $[[3k + 8, k, 2]]$ triorthogonal code, $[[49,1,5]]$ triorthogonal code
S. Bravyi and R. König, “Disorder-Assisted Error Correction in Majorana Chains”, Communications in Mathematical Physics 316, 641 (2012) arXiv:1108.3845 DOI. Appears in: Kitaev chain code
S. Bravyi and J. Haah, “Quantum Self-Correction in the 3D Cubic Code Model”, Physical Review Letters 111, (2013) arXiv:1112.3252 DOI. Appears in: Haah cubic code (CC), Self-correcting quantum code, Lattice stabilizer code
S. Bravyi and R. König, “Classification of Topologically Protected Gates for Local Stabilizer Codes”, Physical Review Letters 110, (2013) arXiv:1206.1609 DOI. Appears in: Lattice stabilizer code
S. Bravyi and M. B. Hastings, “Homological Product Codes”, (2013) arXiv:1311.0885. Appears in: Homological product code, Qubit CSS code
S. Bravyi, G. Duclos-Cianci, D. Poulin, and M. Suchara, “Subsystem surface codes with three-qubit check operators”, (2013) arXiv:1207.1443. Appears in: Subsystem surface code
S. Bravyi, M. Suchara, and A. Vargo, “Efficient algorithms for maximum likelihood decoding in the surface code”, Physical Review A 90, (2014) arXiv:1405.4883 DOI. Appears in: Kitaev surface code, Toric code
S. Bravyi and A. Cross, “Doubled Color Codes”, (2015) arXiv:1509.03239. Appears in: Square-octagon (4.8.8) color code, Doubled color code, Quantum quadratic-residue (QR) code, Quantum divisible code, $[[15,1,3]]$ quantum Reed-Muller code, $[[49,1,5]]$ triorthogonal code, $[[7,1,3]]$ Steane code
S. Bravyi, M. Englbrecht, R. König, and N. Peard, “Correcting coherent errors with surface codes”, npj Quantum Information 4, (2018) arXiv:1710.02270 DOI. Appears in: Majorana stabilizer code, Kitaev surface code, Toric code
S. Bravyi, A. Kliesch, R. Koenig, and E. Tang, “Obstacles to Variational Quantum Optimization from Symmetry Protection”, Physical Review Letters 125, (2020) arXiv:1910.08980 DOI. Appears in: Quantum repetition code
S. Bravyi, D. Gosset, R. König, and M. Tomamichel, “Quantum advantage with noisy shallow circuits”, Nature Physics 16, 1040 (2020) arXiv:1904.01502 DOI. Appears in: Kitaev surface code
S. Bravyi and D. Maslov, “Hadamard-Free Circuits Expose the Structure of the Clifford Group”, IEEE Transactions on Information Theory 67, 4546 (2021) arXiv:2003.09412 DOI. Appears in: Qubit code
S. Bravyi, I. Kim, A. Kliesch, and R. Koenig, “Adaptive constant-depth circuits for manipulating non-abelian anyons”, (2022) arXiv:2205.01933. Appears in: Quantum-double code
S. Bravyi, D. Lee, Z. Li, and B. Yoshida, “How much entanglement is needed for quantum error correction?”, (2024) arXiv:2405.01332. Appears in: GNU PI code, Movassagh-Ouyang Hamiltonian code, Quantum LDPC (QLDPC) code, Concatenated qubit code, Qubit stabilizer code, Qubit code, $((n,1,2))$ Bravyi-Lee-Li-Yoshida PI code
S. Bravyi, A. W. Cross, J. M. Gambetta, D. Maslov, P. Rall, and T. J. Yoder, “High-threshold and low-overhead fault-tolerant quantum memory”, Nature 627, 778 (2024) arXiv:2308.07915 DOI. Appears in: $[[144,12,12]]$ gross code, Bivariate bicycle (BB) code, Qubit CSS code
A. Breger, M. Ehler, M. Gräf, and T. Peter, “Cubatures on Grassmannians: Moments, Dimension Reduction, and Related Topics”, Compressed Sensing and its Applications 235 (2017) arXiv:1705.02978 DOI. Appears in: $t$-design
C. G. Brell, S. T. Flammia, S. D. Bartlett, and A. C. Doherty, “Toric codes and quantum doubles from two-body Hamiltonians”, New Journal of Physics 13, 053039 (2011) arXiv:1011.1942 DOI. Appears in: $[[4,1,1,2]]$ Four-qubit subsystem code, Hamiltonian-based code, Quantum-double code
C. G. Brell, S. Burton, G. Dauphinais, S. T. Flammia, and D. Poulin, “Thermalization, Error Correction, and Memory Lifetime for Ising Anyon Systems”, Physical Review X 4, (2014) arXiv:1311.0019 DOI. Appears in: Topological code
C. G. Brell, “Generalized cluster states based on finite groups”, New Journal of Physics 17, 023029 (2015) arXiv:1408.6237 DOI. Appears in: Group-based cluster-state code, Group GKP code, Group-based quantum code
C. G. Brell, “Generalized color codes supporting non-Abelian anyons”, Physical Review A 91, (2015) arXiv:1408.6238 DOI. Appears in: Generalized 2D color code
C. G. Brell, “A proposal for self-correcting stabilizer quantum memories in 3 dimensions (or slightly less)”, New Journal of Physics 18, 013050 (2016) arXiv:1411.7046 DOI. Appears in: Linear binary code, Fractal surface code, Hypergraph product (HGP) code, Self-correcting quantum code
M. J. Bremner, A. Montanaro, and D. J. Shepherd, “Average-Case Complexity Versus Approximate Simulation of Commuting Quantum Computations”, Physical Review Letters 117, (2016) arXiv:1504.07999 DOI. Appears in: $[[2^D,D,2]]$ hypercube quantum code
Brendan J. Frey. Graphical models for machine learning and digital communication. MIT press, 1998.. Appears in: Tanner code
G. K. Brennen, M. Aguado, and J. I. Cirac, “Simulations of quantum double models”, New Journal of Physics 11, 053009 (2009) arXiv:0901.1345 DOI. Appears in: Quantum-double code, Dihedral $G=D_m$ quantum-double code
L. Brenner, L. Caha, X. Coiteux-Roy, and R. Koenig, “The complexity of Gottesman-Kitaev-Preskill states”, (2024) arXiv:2410.19610. Appears in: Square-lattice GKP code
N. P. Breuckmann and B. M. Terhal, “Space-time circuit-to-Hamiltonian construction and its applications”, Journal of Physics A: Mathematical and Theoretical 47, 195304 (2014) arXiv:1311.6101 DOI. Appears in: Circuit-to-Hamiltonian approximate code, Brown-Fawzi random Clifford-circuit code
N. P. Breuckmann, K. Duivenvoorden, D. Michels, and B. M. Terhal, “Local Decoders for the 2D and 4D Toric Code”, (2016) arXiv:1609.00510. Appears in: Loop toric code, Toric code
N. P. Breuckmann and B. M. Terhal, “Constructions and Noise Threshold of Hyperbolic Surface Codes”, IEEE Transactions on Information Theory 62, 3731 (2016) arXiv:1506.04029 DOI. Appears in: 2D hyperbolic surface code
N. P. Breuckmann, C. Vuillot, E. Campbell, A. Krishna, and B. M. Terhal, “Hyperbolic and semi-hyperbolic surface codes for quantum storage”, Quantum Science and Technology 2, 035007 (2017) arXiv:1703.00590 DOI. Appears in: Kitaev surface code, 2D hyperbolic surface code
N. P. Breuckmann, “PhD thesis: Homological Quantum Codes Beyond the Toric Code”, (2018) arXiv:1802.01520. Appears in: Qubit CSS code
N. P. Breuckmann and J. N. Eberhardt, “Quantum Low-Density Parity-Check Codes”, PRX Quantum 2, (2021) arXiv:2103.06309 DOI. Appears in: Hypergraph product (HGP) code, Quantum LDPC (QLDPC) code, High-dimensional expander (HDX) code, 2D hyperbolic surface code
N. P. Breuckmann and J. N. Eberhardt, “Balanced Product Quantum Codes”, IEEE Transactions on Information Theory 67, 6653 (2021) arXiv:2012.09271 DOI. Appears in: Abelian LP code, Balanced product (BP) code, Distance-balanced code, Expander LP code, Fiber-bundle code, Lifted-product (LP) code, Subsystem qubit stabilizer code, Toric code
N. P. Breuckmann and J. N. Eberhardt, “Quantum Low-Density Parity-Check Codes”, PRX Quantum 2, (2021) DOI. Appears in: Lifted-product (LP) code
N. P. Breuckmann and V. Londe, “Single-Shot Decoding of Linear Rate LDPC Quantum Codes With High Performance”, IEEE Transactions on Information Theory 68, 272 (2022) arXiv:2001.03568 DOI. Appears in: Guth-Lubotzky code
N. P. Breuckmann and S. Burton, “Fold-Transversal Clifford Gates for Quantum Codes”, Quantum 8, 1372 (2024) arXiv:2202.06647 DOI. Appears in: $[23, 12, 7]$ Golay code, Qubit CSS code, $[[30,8,3]]$ Bring code
N. P. Breuckmann, M. Davydova, J. N. Eberhardt, and N. Tantivasadakarn, “Cups and Gates I: Cohomology invariants and logical quantum operations”, (2024) arXiv:2410.16250. Appears in: Two-block group-algebra (2BGA) codes, 3D surface code, Expander LP code, $D$-dimensional twisted toric code, Hyperbolic surface code, Hypergraph product (HGP) code, Plaquette Ising code, Qubit CSS code, Repetition code, Kitaev surface code, Two-foliated fracton code
J. C. Bridgeman, A. Kubica, and M. Vasmer, “Lifting Topological Codes: Three-Dimensional Subsystem Codes from Two-Dimensional Anyon Models”, PRX Quantum 5, (2024) arXiv:2305.06365 DOI. Appears in: 3D subsystem surface code, Single-shot code
H. J. Briegel and R. Raussendorf, “Persistent Entanglement in Arrays of Interacting Particles”, Physical Review Letters 86, 910 (2001) arXiv:quant-ph/0004051 DOI. Appears in: Cluster-state code, Square-lattice cluster-state code
J. Briët and R. de Wolf, “Locally Decodable Quantum Codes”, (2008) arXiv:0806.2101. Appears in: Locally decodable code (LDC), Quantum locally recoverable code (QLRC)
S. ten Brink, G. Kramer, and A. Ashikhmin, “Design of Low-Density Parity-Check Codes for Modulation and Detection”, IEEE Transactions on Communications 52, 670 (2004) DOI. Appears in: Irregular LDPC code
B. L. Brock, S. Singh, A. Eickbusch, V. V. Sivak, A. Z. Ding, L. Frunzio, S. M. Girvin, and M. H. Devoret, “Quantum Error Correction of Qudits Beyond Break-even”, (2024) arXiv:2409.15065. Appears in: Square-lattice GKP code
D. J. Brod, “Efficient classical simulation of matchgate circuits with generalized inputs and measurements”, Physical Review A 93, (2016) arXiv:1602.03539 DOI. Appears in: Fermion code
P. Brooks, A. Kitaev, and J. Preskill, “Protected gates for superconducting qubits”, Physical Review A 87, (2013) arXiv:1302.4122 DOI. Appears in: Kitaev current-mirror qubit code, Square-lattice GKP code, Zero-pi qubit code
P. Brooks and J. Preskill, “Fault-tolerant quantum computation with asymmetric Bacon-Shor codes”, Physical Review A 87, (2013) arXiv:1211.1400 DOI. Appears in: Asymmetric quantum code, Bacon-Shor code
M. Broué and M. Enguehard, “Une famille infinie de formes quadratiques entières; leurs groupes d’automorphismes”, Annales scientifiques de l’École normale supérieure 6, 17 (1973) DOI. Appears in: Barnes-Wall (BW) lattice
A. E. Brouwer, J. B. Shearer, N. J. A. Sloane, and W. D. Smith, “A new table of constant weight codes”, IEEE Transactions on Information Theory 36, 1334 (1990) DOI. Appears in: Constant-weight code
A. E. Brouwer and M. van Eupen, Designs, Codes and Cryptography 11, 261 (1997) DOI. Appears in: Projective geometry code, Two-weight code
A. E. Brouwer, H. O. Hamalainen, P. R. J. Ostergard, and N. J. A. Sloane, “Bounds on mixed binary/ternary codes”, IEEE Transactions on Information Theory 44, 140 (1998) DOI. Appears in: Binary-ternary mixed code
A. E. Brouwer and H. Van Maldeghem, Strongly Regular Graphs (Cambridge University Press, 2022) DOI. Appears in: Ovoid code, Hyperoval code, Projective two-weight code, Ternary Golay code
A. E. Brouwer, "Two-weight Codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI. Appears in: Denniston code, Hexacode, $[56,6,36]_3$ Hill-cap code, Hill projective-cap code, Hyperoval code, Projective two-weight code, Ternary Golay code, Two-weight code, Weight-two code
B. J. Brown, W. Son, C. V. Kraus, R. Fazio, and V. Vedral, “Generating topological order from a two-dimensional cluster state using a duality mapping”, New Journal of Physics 13, 065010 (2011) arXiv:1105.2111 DOI. Appears in: Kitaev surface code
B. J. Brown, D. Loss, J. K. Pachos, C. N. Self, and J. R. Wootton, “Quantum memories at finite temperature”, Reviews of Modern Physics 88, (2016) arXiv:1411.6643 DOI. Appears in: 3D Bacon-Shor code, Quantum repetition code, Repetition code, Self-correcting quantum code
B. J. Brown, N. H. Nickerson, and D. E. Browne, “Fault-tolerant error correction with the gauge color code”, Nature Communications 7, (2016) arXiv:1503.08217 DOI. Appears in: 3D subsystem color code, Color code, $[[2^r-1,1,3]]$ simplex code, Simplex spherical code, Single-shot code, Subsystem color code
B. J. Brown, K. Laubscher, M. S. Kesselring, and J. R. Wootton, “Poking Holes and Cutting Corners to Achieve Clifford Gates with the Surface Code”, Physical Review X 7, (2017) arXiv:1609.04673 DOI. Appears in: Abelian topological code, Twist-defect surface code
B. J. Brown and D. J. Williamson, “Parallelized quantum error correction with fracton topological codes”, Physical Review Research 2, (2020) arXiv:1901.08061 DOI. Appears in: Checkerboard model code, Fracton stabilizer code, X-cube model code, XZZX surface code
B. J. Brown and S. Roberts, “Universal fault-tolerant measurement-based quantum computation”, Physical Review Research 2, (2020) arXiv:1811.11780 DOI. Appears in: Cluster-state code, Qubit stabilizer code
B. J. Brown, “A fault-tolerant non-Clifford gate for the surface code in two dimensions”, Science Advances 6, (2020) arXiv:1903.11634 DOI. Appears in: Kitaev surface code
B. J. Brown, “Conservation Laws and Quantum Error Correction: Toward a Generalized Matching Decoder”, IEEE BITS the Information Theory Magazine 2, 5 (2022) arXiv:2207.06428 DOI. Appears in: Quantum LDPC (QLDPC) code
B. J. Brown, “Color code with a logical control-$S$ gate using transversal $T$ rotations”, (2024) arXiv:2411.15035. Appears in: Cubic honeycomb color code
B. Brown, “Anyon condensation and the color code”, (2022) DOI. Appears in: Floquet color code
N. C. Brown, M. Newman, and K. R. Brown, “Handling leakage with subsystem codes”, New Journal of Physics 21, 073055 (2019) arXiv:1903.03937 DOI. Appears in: Bacon-Shor code, Subsystem rotated surface code
N. C. Brown et al., “Advances in compilation for quantum hardware -- A demonstration of magic state distillation and repeat-until-success protocols”, (2023) arXiv:2310.12106. Appears in: Five-qubit perfect code
R. Brown, “From Groups to Groupoids: a Brief Survey”, Bulletin of the London Mathematical Society 19, 113 (1987) DOI. Appears in: Groupoid toric code
W. Brown and O. Fawzi, “Short random circuits define good quantum error correcting codes”, 2013 IEEE International Symposium on Information Theory (2013) arXiv:1312.7646 DOI. Appears in: Brown-Fawzi random Clifford-circuit code
D. E. Browne and T. Rudolph, “Resource-Efficient Linear Optical Quantum Computation”, Physical Review Letters 95, (2005) arXiv:quant-ph/0405157 DOI. Appears in: Cluster-state code, Dual-rail quantum code
D. Browne, Lecture notes. Appears in: Homological code, Qubit CSS code
R. A. Brualdi, J. S. Graves, and K. M. Lawrence, “Codes with a poset metric”, Discrete Mathematics 147, 57 (1995) DOI. Appears in: Poset code
T. A. Brun, I. Devetak, and M.-H. Hsieh, “General entanglement-assisted quantum error-correcting codes”, 2007 IEEE International Symposium on Information Theory 2101 (2007) DOI. Appears in: Entanglement-assisted (EA) subsystem QECC
T. A. Brun and M.-H. Hsieh, “Entanglement-assisted quantum error-correcting codes”, Quantum Error Correction 181 (2013) DOI. Appears in: Entanglement-assisted (EA) QECC
T. A. Brun, I. Devetak, and M.-H. Hsieh, “Catalytic Quantum Error Correction”, IEEE Transactions on Information Theory 60, 3073 (2014) arXiv:quant-ph/0608027 DOI. Appears in: Linear binary code, EA MDS code, Entanglement-assisted (EA) QECC, EA qubit stabilizer code
T. A. Brun, “Quantum Error Correction”, Oxford Research Encyclopedia of Physics (2020) arXiv:1910.03672 DOI. Appears in: Quantum error-correcting code (QECC)
T. Brun, I. Devetak, and M.-H. Hsieh, “Correcting Quantum Errors with Entanglement”, Science 314, 436 (2006) arXiv:quant-ph/0610092 DOI. Appears in: Linear binary code, $[[3, 1, 3;2]]$ EA code, EA MDS code, Entanglement-assisted (EA) QECC, EA qubit stabilizer code, Linear $q$-ary code, Five-qubit perfect code
T. Brun and M.-H. Hsieh, “Entanglement-Assisted Quantum Error-Correcting Codes”, (2016) arXiv:1610.04013. Appears in: Entanglement-assisted (EA) QECC
S. Bseiso, J. Pommerening, R. R. Allen, S. H. Simon, and L. Hormozi, “Minimal Quantum Circuits for Simulating Fibonacci Anyons”, (2024) arXiv:2407.21761. Appears in: Fibonacci string-net code
K. Bu, “Extremality of stabilizer states”, (2024) arXiv:2403.13632. Appears in: Modular-qudit stabilizer code
K. Bu, W. Gu, and X. Li, “Quantum locally recoverable code with intersecting recovery sets”, (2025) arXiv:2501.10354. Appears in: Hypergraph product (HGP) code, Quantum locally recoverable code (QLRC)
F. Buchali, F. Steiner, G. Bocherer, L. Schmalen, P. Schulte, and W. Idler, “Rate Adaptation and Reach Increase by Probabilistically Shaped 64-QAM: An Experimental Demonstration”, Journal of Lightwave Technology 34, 1599 (2016) DOI. Appears in: Quadrature-amplitude modulation (QAM) code
S. D. Buchbinder, C. L. Huang, and Y. S. Weinstein, “Encoding an Arbitrary State in a [7,1,3] Quantum Error Correction Code”, (2011) arXiv:1109.1714. Appears in: $[[7,1,3]]$ Steane code
J. R. Buck, S. J. van Enk, and C. A. Fuchs, “Experimental proposal for achieving superadditive communication capacities with a binary quantum alphabet”, Physical Review A 61, (2000) DOI. Appears in: BPSK c-q code
R. de Buda, “The upper error bound of a new near-optimal code”, IEEE Transactions on Information Theory 21, 441 (1975) DOI. Appears in: Lattice-based code
O. Buerschaper and M. Aguado, “Mapping Kitaev’s quantum double lattice models to Levin and Wen’s string-net models”, Physical Review B 80, (2009) arXiv:0907.2670 DOI. Appears in: Hopf-algebra quantum-double code, Quantum-double code
O. Buerschaper, J. M. Mombelli, M. Christandl, and M. Aguado, “A hierarchy of topological tensor network states”, Journal of Mathematical Physics 54, (2013) arXiv:1007.5283 DOI. Appears in: Hopf-algebra quantum-double code
O. Buerschaper, M. Christandl, L. Kong, and M. Aguado, “Electric–magnetic duality of lattice systems with topological order”, Nuclear Physics B 876, 619 (2013) arXiv:1006.5823 DOI. Appears in: Multi-fusion string-net code, Hopf-algebra quantum-double code, Quantum-double code
H. Buhrman, M. Folkertsma, B. Loff, and N. M. P. Neumann, “State preparation by shallow circuits using feed forward”, Quantum 8, 1552 (2024) arXiv:2307.14840 DOI. Appears in: PI qubit code
A. Bullivant, M. Calçada, Z. Kádár, P. Martin, and J. F. Martins, “Topological phases from higher gauge symmetry in3+1dimensions”, Physical Review B 95, (2017) arXiv:1606.06639 DOI. Appears in: Quantum-double code, Walker-Wang model code, Two-gauge theory code
A. Bullivant, Y. Hu, and Y. Wan, “Twisted quantum double model of topological order with boundaries”, Physical Review B 96, (2017) arXiv:1706.03611 DOI. Appears in: Quantum-double code, Twisted quantum double (TQD) code
A. Bullivant and C. Delcamp, “Tube algebras, excitations statistics and compactification in gauge models of topological phases”, Journal of High Energy Physics 2019, (2019) arXiv:1905.08673 DOI. Appears in: Dijkgraaf-Witten gauge theory code, Twisted quantum double (TQD) code
A. Bullivant, M. Calçada, Z. Kádár, J. F. Martins, and P. Martin, “Higher lattices, discrete two-dimensional holonomy and topological phases in (3 + 1)D with higher gauge symmetry”, Reviews in Mathematical Physics 32, 2050011 (2019) arXiv:1702.00868 DOI. Appears in: Two-gauge theory code
A. Bullivant and C. Delcamp, “Excitations in strict 2-group higher gauge models of topological phases”, Journal of High Energy Physics 2020, (2020) arXiv:1909.07937 DOI. Appears in: Dijkgraaf-Witten gauge theory code, Two-gauge theory code
A. Bullivant and C. Delcamp, “Gapped boundaries and string-like excitations in (3+1)d gauge models of topological phases”, Journal of High Energy Physics 2021, (2021) arXiv:2006.06536 DOI. Appears in: Dijkgraaf-Witten gauge theory code
S. S. Bullock and G. K. Brennen, “Qudit surface codes and gauge theory with finite cyclic groups”, Journal of Physics A: Mathematical and Theoretical 40, 3481 (2007) arXiv:quant-ph/0609070 DOI. Appears in: Galois-qudit surface code, Abelian quantum-double stabilizer code, Modular-qudit surface code
D. Bulmash and M. Barkeshli, “Absolute anomalies in (2+1)D symmetry-enriched topological states and exact (3+1)D constructions”, Physical Review Research 2, (2020) arXiv:2003.11553 DOI. Appears in: $G$-enriched Walker-Wang model code
A. Burchardt and Z. Raissi, “Stochastic local operations with classical communication of absolutely maximally entangled states”, Physical Review A 102, (2020) arXiv:2003.13639 DOI. Appears in: Perfect-tensor code
I. A. Burenkov, O. V. Tikhonova, and S. V. Polyakov, “Quantum receiver for large alphabet communication”, Optica 5, 227 (2018) arXiv:1802.08287 DOI. Appears in: Coherent FSK (CFSK) c-q code, PSK c-q code
I. A. Burenkov, M. V. Jabir, N. F. R. Annafianto, A. Battou, and S. V. Polyakov, “Experimental demonstration of time resolving quantum receiver for bandwidth and power efficient communications”, Conference on Lasers and Electro-Optics FF1D.1 (2020) DOI. Appears in: PSK c-q code
I. A. Burenkov, M. V. Jabir, A. Battou, and S. V. Polyakov, “Time-Resolving Quantum Measurement Enables Energy-Efficient, Large-Alphabet Communication”, PRX Quantum 1, (2020) DOI. Appears in: Coherent FSK (CFSK) c-q code
I. A. Burenkov, M. V. Jabir, and S. V. Polyakov, “Practical quantum-enhanced receivers for classical communication”, AVS Quantum Science 3, (2021) DOI. Appears in: Coherent-state c-q code
M. V. Burnashev and A. S. Holevo, “On Reliability Function of Quantum Communication Channel”, (1998) arXiv:quant-ph/9703013. Appears in: Classical-quantum (c-q) code
F. J. Burnell and C. Nayak, “SU(2) slave fermion solution of the Kitaev honeycomb lattice model”, Physical Review B 84, (2011) arXiv:1104.5485 DOI. Appears in: Kitaev honeycomb code, Topological code
F. J. Burnell, X. Chen, L. Fidkowski, and A. Vishwanath, “Exactly soluble model of a three-dimensional symmetry-protected topological phase of bosons with surface topological order”, Physical Review B 90, (2014) arXiv:1302.7072 DOI. Appears in: Symmetry-protected topological (SPT) code, Three-fermion (3F) Walker-Wang model code, Abelian topological code, Walker-Wang model code
H. Burton and E. Weldon, “Cyclic product codes”, IEEE Transactions on Information Theory 11, 433 (1965) DOI. Appears in: Tensor-product code
H. Burton, “Inversionless decoding of binary BCH codes”, IEEE Transactions on Information Theory 17, 464 (1971) DOI. Appears in: Binary BCH code, Bose–Chaudhuri–Hocquenghem (BCH) code
S. Burton, C. G. Brell, and S. T. Flammia, “Classical simulation of quantum error correction in a Fibonacci anyon code”, Physical Review A 95, (2017) arXiv:1506.03815 DOI. Appears in: Fibonacci string-net code
S. Burton, E. Durso-Sabina, and N. C. Brown, “Genons, Double Covers and Fault-tolerant Clifford Gates”, (2024) arXiv:2406.09951. Appears in: 2D color code, Qubit code, Subsystem modular-qudit CSS code, $[[4,2,2]]$ Four-qubit code, Twist-defect surface code
K. A. Bush, “Orthogonal Arrays of Index Unity”, The Annals of Mathematical Statistics 23, 426 (1952) DOI. Appears in: Hexacode, Narrow-sense RS code, Reed-Solomon (RS) code
Bush, K. A. “Orthogonal Arrays of Index Unity.” The Annals of Mathematical Statistics 23, no. 3 (1952): 426–34.. Appears in: Narrow-sense RS code, Reed-Solomon (RS) code
Butman, Deutsch, and Miller. Performance of concatenated codes for deep space missions. 1981.. Appears in: Convolutional code
F. Butt, S. Heußen, M. Rispler, and M. Müller, “Fault-Tolerant Code-Switching Protocols for Near-Term Quantum Processors”, PRX Quantum 5, (2024) arXiv:2306.17686 DOI. Appears in: $[[15,1,3]]$ quantum Reed-Muller code, $[[7,1,3]]$ Steane code
F. Butt, D. F. Locher, K. Brechtelsbauer, H. P. Büchler, and M. Müller, “Measurement-free, scalable and fault-tolerant universal quantum computing”, (2024) arXiv:2410.13568. Appears in: 2D color code, 3D color code
J. W. Byers, M. Luby, M. Mitzenmacher, and A. Rege, “A digital fountain approach to reliable distribution of bulk data”, ACM SIGCOMM Computer Communication Review 28, 56 (1998) DOI. Appears in: Fountain code, Tornado code
M. S. Byrd and D. A. Lidar, “Combined error correction techniques for quantum computing architectures”, Journal of Modern Optics 50, 1285 (2003) arXiv:quant-ph/0210072 DOI. Appears in: Dual-rail quantum code
A. Cabello, A. J. López-Tarrida, P. Moreno, and J. R. Portillo, “Entanglement in eight-qubit graph states”, Physics Letters A 373, 2219 (2009) arXiv:0812.4625 DOI. Appears in: Cluster-state code
V. R. Cadambe and A. Mazumdar, “Bounds on the Size of Locally Recoverable Codes”, IEEE Transactions on Information Theory 61, 5787 (2015) DOI. Appears in: Locally recoverable code (LRC), Optimal LRC
C. Cafaro, D. Markham, and P. van Loock, “Scheme for constructing graphs associated with stabilizer quantum codes”, (2014) arXiv:1407.2777. Appears in: Codeword stabilized (CWS) code, Graph quantum code, Qubit stabilizer code, $[[4,2,2]]$ Four-qubit code
C. Cafaro and P. van Loock, “Approximate quantum error correction for generalized amplitude-damping errors”, Physical Review A 89, (2014) arXiv:1308.4582 DOI. Appears in: Approximate quantum error-correcting code (AQECC)
K. E. Cahill and R. J. Glauber, “Ordered Expansions in Boson Amplitude Operators”, Physical Review 177, 1857 (1969) DOI. Appears in: Bosonic code
W. Cai, Y. Ma, W. Wang, C.-L. Zou, and L. Sun, “Bosonic quantum error correction codes in superconducting quantum circuits”, Fundamental Research 1, 50 (2021) arXiv:2010.08699 DOI. Appears in: Bosonic code
M. Cain, C. Zhao, H. Zhou, N. Meister, J. P. B. Ataides, A. Jaffe, D. Bluvstein, and M. D. Lukin, “Correlated decoding of logical algorithms with transversal gates”, (2024) arXiv:2403.03272. Appears in: Qubit stabilizer code
C. Calcluth, N. Reichel, A. Ferraro, and G. Ferrini, “Sufficient Condition for Universal Quantum Computation Using Bosonic Circuits”, PRX Quantum 5, (2024) arXiv:2309.07820 DOI. Appears in: Gottesman-Kitaev-Preskill (GKP) code
C. Calcluth, O. Hahn, J. Bermejo-Vega, A. Ferraro, and G. Ferrini, “Classical simulation of circuits with realistic Gottesman-Kitaev-Preskill states”, (2024) arXiv:2412.13136. Appears in: Gottesman-Kitaev-Preskill (GKP) code
A. R. Calderbank, P. IDelsarte, and N. J. A. Sloane, “A strengthening of the Assmus-Mattson theorem”, IEEE Transactions on Information Theory 37, 1261 (1991) DOI. Appears in: Combinatorial design, Dual linear code
A. R. Calderbank, A. R. Hammons Jr., P. V. Kumar, N. J. A. Sloane, and P. Solé, “A linear construction for certain Kerdock and Preparata codes”, (1993) arXiv:math/9310227. Appears in: Kerdock code, Nordstrom-Robinson (NR) code, Preparata code, Self-dual linear code
A. R. Calderbank and P. W. Shor, “Good quantum error-correcting codes exist”, Physical Review A 54, 1098 (1996) arXiv:quant-ph/9512032 DOI. Appears in: Galois-qudit CSS code, Generalized quantum divisible code, Qubit CSS code, Modular-qudit CSS code, Random stabilizer code, $[[15, 7, 3]]$ quantum Hamming code
A. R. Calderbank, E. M. Rains, P. W. Shor, and N. J. A. Sloane, “Quantum Error Correction via Codes over GF(4)”, (1997) arXiv:quant-ph/9608006. Appears in: Dodecacode, $[[2m,2m-2,2]]$ error-detecting code, Qubit BCH code, Perfect quantum code, $((9,12,3))$ qubit code, Qubit CSS code, Qubit code, $[[11,1,5]]$ quantum dodecacode, Five-qubit perfect code, $[[6,1,3]]$ Six-qubit stabilizer code, $[[6,4,2]]$ error-detecting code, Hermitian qubit code
A. R. Calderbank, E. M. Rains, P. W. Shor, and N. J. A. Sloane, “Quantum Error Correction and Orthogonal Geometry”, Physical Review Letters 78, 405 (1997) arXiv:quant-ph/9605005 DOI. Appears in: Qubit stabilizer code, Random stabilizer code, $[[8, 3, 3]]$ Eight-qubit Gottesman code
A. R. Calderbank, “The art of signaling: fifty years of coding theory”, IEEE Transactions on Information Theory 44, 2561 (1998) DOI. Appears in: Error-correcting code (ECC), $[23, 12, 7]$ Golay code, Sphere packing
A. R. Calderbank, S. N. Diggavi, and N. Al-Dhahir, “Space-time signaling based on Kerdock and Delsafte-Goethals codes”, 2004 IEEE International Conference on Communications (IEEE Cat. No.04CH37577) (2004) DOI. Appears in: Delsarte-Goethals (DG) code
A. Calderbank, P. Cameron, W. Kantor, and J. Seidel, “Z${}_{\text{4}}$ -Kerdock Codes, Orthogonal Spreads, and Extremal Euclidean Line-Sets”, Proceedings of the London Mathematical Society 75, 436 (1997) DOI. Appears in: Cluster-state code, Kerdock code, $t$-design
R. Calderbank and W. M. Kantor, “The Geometry of Two-Weight Codes”, Bulletin of the London Mathematical Society 18, 97 (1986) DOI. Appears in: Ovoid code, Projective geometry code, Two-weight code
M. Calixto, A. Mayorgas, and J. Guerrero, “Entanglement and U(D)-spin squeezing in symmetric multi-quDit systems and applications to quantum phase transitions in Lipkin–Meshkov–Glick D-level atom models”, Quantum Information Processing 20, (2021) arXiv:2104.10581 DOI. Appears in: Two-mode binomial code
T. Camara, H. Ollivier, and J.-P. Tillich, “Constructions and performance of classes of quantum LDPC codes”, (2005) arXiv:quant-ph/0502086. Appears in: Camara-Ollivier-Tillich code, Quantum LDPC (QLDPC) code
B. Cambou and D. Telesca, “Ternary Computing to Strengthen Cybersecurity”, Advances in Intelligent Systems and Computing 898 (2018) DOI. Appears in: $q$-ary code
P. J. Cameron, J. M. Goethals, and J. J. Seidel, “Strongly regular graphs having strongly regular subconstituents”, Journal of Algebra 55, 257 (1978) DOI. Appears in: Cameron-Goethals-Seidel (CGS) isotropic subspace code
P. J. Cameron and J. H. van Lint, Designs, Graphs, Codes and Their Links (Cambridge University Press, 1991) DOI. Appears in: Combinatorial design
P. J. CAMERON and J. J. SEIDEL, “QUADRATIC FORMS OVER GF(2)”, Geometry and Combinatorics 290 (1991) DOI. Appears in: Kerdock spherical code
P. J. Cameron, “Permutation codes”, European Journal of Combinatorics 31, 482 (2010) DOI. Appears in: Code in permutations
Cameron, Peter J. "Generalisation of Fisher’s inequality to fields with more than one element." Combinatorics, London Math. Soc. Lecture Note Ser 13 (1973): 9-13.. Appears in: Subspace design, $t$-design
Cameron, Peter J. "Some bridges between codes and designs." Unpublished manuscript, Queen Mary and Westfield College, London (1998).. Appears in: Mixed code
P. Campagne-Ibarcq et al., “Quantum error correction of a qubit encoded in grid states of an oscillator”, Nature 584, 368 (2020) DOI. Appears in: Square-lattice GKP code
P. Campagne-Ibarcq et al., “Quantum error correction of a qubit encoded in grid states of an oscillator”, Nature 584, 368 (2020) arXiv:1907.12487 DOI. Appears in: Square-lattice GKP code, Hexagonal GKP code
R. Campari and D. Cassi, “Generalization of the Peierls-Griffiths theorem for the Ising model on graphs”, Physical Review E 81, (2010) arXiv:1002.1227 DOI. Appears in: Fractal surface code, Self-correcting quantum code
E. T. Campbell and D. E. Browne, “On the Structure of Protocols for Magic State Distillation”, (2009) arXiv:0908.0838. Appears in: Qubit stabilizer code
E. T. Campbell and D. E. Browne, “Bound States for Magic State Distillation in Fault-Tolerant Quantum Computation”, Physical Review Letters 104, (2010) arXiv:0908.0836 DOI. Appears in: Qubit stabilizer code
E. T. Campbell, H. Anwar, and D. E. Browne, “Magic-State Distillation in All Prime Dimensions Using Quantum Reed-Muller Codes”, Physical Review X 2, (2012) arXiv:1205.3104 DOI. Appears in: Prime-qudit RM code
E. T. Campbell and M. Howard, “Unified framework for magic state distillation and multiqubit gate synthesis with reduced resource cost”, Physical Review A 95, (2017) arXiv:1606.01904 DOI. Appears in: $[[6k+2,3k,2]]$ Campbell-Howard code, $[[2^D,D,2]]$ hypercube quantum code, Quantum divisible code, Quantum Reed-Muller code, Triorthogonal code, Qubit code, Reed-Muller (RM) code
E. T. Campbell and M. Howard, “Unifying Gate Synthesis and Magic State Distillation”, Physical Review Letters 118, (2017) arXiv:1606.01906 DOI. Appears in: $[[2^D,D,2]]$ hypercube quantum code, Quantum Reed-Muller code
E. T. Campbell, B. M. Terhal, and C. Vuillot, “Roads towards fault-tolerant universal quantum computation”, Nature 549, 172 (2017) arXiv:1612.07330 DOI. Appears in: $[[k+4,k,2]]$ H code, $[[3k + 8, k, 2]]$ triorthogonal code, $[[15,1,3]]$ quantum Reed-Muller code, $[[4,2,2]]$ Four-qubit code, $[[6,2,2]]$ $C_6$ code
E. T. Campbell, “A theory of single-shot error correction for adversarial noise”, Quantum Science and Technology 4, 025006 (2019) arXiv:1805.09271 DOI. Appears in: Hypergraph product (HGP) code, Qubit stabilizer code, Single-shot code
E. Campbell, “The smallest interesting colour code,” Online available at https://earltcampbell.com/2016/09/26/the-smallest-interesting-colour-code/ (2016), accessed on 2019-12-09.. Appears in: Ball color code, $[[2^D,D,2]]$ hypercube quantum code, $[[8,3,2]]$ Smallest interesting color code
C. Campopiano and B. Glazer, “A Coherent Digital Amplitude and Phase Modulation Scheme”, IEEE Transactions on Communications 10, 90 (1962) DOI. Appears in: $A_2$ triangular lattice
J. A. Campos and K. R. Brown, “Clifford-Deformed Compass Codes”, (2024) arXiv:2412.03808. Appears in: Asymmetric quantum code, Clifford-deformed surface code (CDSC), Compass code
M. Campos, M. Jenssen, M. Michelen, and J. Sahasrabudhe, “A new lower bound for sphere packing”, (2023) arXiv:2312.10026. Appears in: Sphere packing
E. Camps-Moreno, H. H. López, G. L. Matthews, D. Ruano, R. San-José, and I. Soprunov, “An algebraic characterization of binary CSS-T codes and cyclic CSS-T codes for quantum fault tolerance”, Quantum Information Processing 23, (2024) arXiv:2312.17518 DOI. Appears in: Cyclic linear binary code, Linear binary code, CSS-T code, Quantum Reed-Muller code, Triorthogonal code
E. Camps-Moreno, H. H. López, G. L. Matthews, and E. McMillon, “Toward Quantum CSS-T Codes from Sparse Matrices”, (2024) arXiv:2406.00425. Appears in: Qubit CSS code
T. Can, N. Rengaswamy, R. Calderbank, and H. D. Pfister, “Kerdock Codes Determine Unitary 2-Designs”, IEEE Transactions on Information Theory 66, 6104 (2020) arXiv:1904.07842 DOI. Appears in: Cluster-state code, Kerdock code, $t$-design
Cannon, J., Bosma, W., Fieker, C., & Steel, A. (2008). HANDBOOK OF MAGMA FUNCTIONS.. Appears in: Lattice-based code
D. G. Cantor, “On arithmetical algorithms over finite fields”, Journal of Combinatorial Theory, Series A 50, 285 (1989) DOI. Appears in: Reed-Solomon (RS) code
C. Cao and B. Lackey, “Approximate Bacon-Shor code and holography”, Journal of High Energy Physics 2021, (2021) arXiv:2010.05960 DOI. Appears in: Holographic hybrid code
C. Cao, G. Cheng, and B. Swingle, “Large $N$ Matrix Quantum Mechanics as a Quantum Memory”, (2022) arXiv:2211.08448. Appears in: Holographic code, Matrix-model code
C. Cao, C. Zhang, Z. Wu, M. Grassl, and B. Zeng, “Quantum variational learning for quantum error-correcting codes”, Quantum 6, 828 (2022) arXiv:2204.03560 DOI. Appears in: Approximate quantum error-correcting code (AQECC)
C. Cao and B. Lackey, “Quantum Lego: Building Quantum Error Correction Codes from Tensor Networks”, PRX Quantum 3, (2022) arXiv:2109.08158 DOI. Appears in: Tensor-network code, $[[4,2,2]]$ Four-qubit code, $[[6,4,2]]$ error-detecting code, $[[7,1,3]]$ Steane code
C. Cao and B. Lackey, “Quantum weight enumerators and tensor networks”, (2023) arXiv:2211.02756. Appears in: Qubit code
C. Cao, M. J. Gullans, B. Lackey, and Z. Wang, “Quantum Lego Expansion Pack: Enumerators from Tensor Networks”, (2024) arXiv:2308.05152. Appears in: Tensor-network code, Qubit code
H. Cao et al., “Exact Decoding of Repetition Code under Circuit Level Noise”, (2025) arXiv:2501.03582. Appears in: Quantum repetition code
M. Cao and J. Cui, “Construction of new quantum codes via Hermitian dual-containing matrix-product codes”, Quantum Information Processing 19, (2020) DOI. Appears in: Matrix-product code, Hermitian Galois-qudit code
Y. Cao, S. Liu, H. Deng, Z. Xia, X. Wu, and Y.-X. Wang, “Robust analog quantum simulators by quantum error-detecting codes”, (2024) arXiv:2412.07764. Appears in: Bravyi-Bacon-Shor (BBS) code, Commuting-projector Hamiltonian code, $[[4,2,2]]$ Four-qubit code, Subsystem qubit stabilizer code
M. Capalbo, O. Reingold, S. Vadhan, and A. Wigderson, “Randomness conductors and constant-degree lossless expanders”, Proceedings of the thiry-fourth annual ACM symposium on Theory of computing 659 (2002) DOI. Appears in: Expander code, Lossless expander balanced-product code
G. Cariolaro, R. Corvaja, and G. Pierobon, “Gaussian states and geometrically uniform symmetry”, Physical Review A 90, (2014) arXiv:1410.5282 DOI. Appears in: PSK c-q code
C. Carlet, “The Automorphism Groups of the Kerdock Codes”, Journal of Information and Optimization Sciences 12, 387 (1991) DOI. Appears in: Kerdock code
C. Carlet, “The automorphism groups of the Delsarte-Goethals codes”, Designs, Codes and Cryptography 3, 237 (1993) DOI. Appears in: Delsarte-Goethals (DG) code
Carl W. Helstrom. Quantum Detection and Estimation Theory. Elsevier, 1976.. Appears in: Number-phase code, PPM c-q code, PSK c-q code
E. K. Carlson, “Protecting Molecular Qubits from Noise”, Physics 13, (2020) DOI. Appears in: Molecular code
S. Carrozza, A. Chatwin-Davies, P. A. Hoehn, and F. M. Mele, “A correspondence between quantum error correcting codes and quantum reference frames”, (2024) arXiv:2412.15317. Appears in: Gauss' law code, Stabilizer code, Kitaev surface code, Abelian topological code
Cartier, Pierre. "Quantum mechanical commutation relations and theta functions." Proc. Sympos. Pure Math. Vol. 9. 1966.. Appears in: Square-lattice GKP code
F. Caruso, J. Eisert, V. Giovannetti, and A. S. Holevo, “Multi-mode bosonic Gaussian channels”, New Journal of Physics 10, 083030 (2008) arXiv:0804.0511 DOI. Appears in: Bosonic code
F. Caruso, J. Eisert, V. Giovannetti, and A. S. Holevo, “Optimal unitary dilation for bosonic Gaussian channels”, Physical Review A 84, (2011) arXiv:1009.1108 DOI. Appears in: Bosonic code
W. Cary Huffman, “On the classification and enumeration of self-dual codes”, Finite Fields and Their Applications 11, 451 (2005) DOI. Appears in: Self-dual linear code
M. Casanova, K. Ohki, and F. Ticozzi, “Finding Quantum Codes via Riemannian Optimization”, (2024) arXiv:2407.08423. Appears in: Approximate quantum error-correcting code (AQECC)
A. Cassagne et al., “AFF3CT: A Fast Forward Error Correction Toolbox!”, SoftwareX 10, 100345 (2019) DOI. Appears in: Low-density parity-check (LDPC) code, Polar code, Turbo code
O. Castaños, R. López-Peña, and V. I. Man’ko, “Crystallized schrödinger cat states”, Journal of Russian Laser Research 16, 477 (1995) DOI. Appears in: Cat code
C. Castelnovo and C. Chamon, “Topological quantum glassiness”, Philosophical Magazine 92, 304 (2012) arXiv:1108.2051 DOI. Appears in: Sierpinsky fractal spin-liquid (SFSL) code
L. Caune et al., “Demonstrating real-time and low-latency quantum error correction with superconducting qubits”, (2024) arXiv:2410.05202. Appears in: $[[4,2,2]]$ Four-qubit code
C. M. Caves and P. D. Drummond, “Quantum limits on bosonic communication rates”, Reviews of Modern Physics 66, 481 (1994) DOI. Appears in: Bosonic c-q code
R. Ceccarelli, G. Vallone, F. De Martini, P. Mataloni, and A. Cabello, “Experimental Entanglement and Nonlocality of a Two-Photon Six-Qubit Cluster State”, Physical Review Letters 103, (2009) arXiv:0906.2233 DOI. Appears in: Cluster-state code
N. J. Cerf and R. Cleve, “Information-theoretic interpretation of quantum error-correcting codes”, Physical Review A 56, 1721 (1997) arXiv:quant-ph/9702031 DOI. Appears in: Finite-dimensional quantum error-correcting code, Quantum maximum-distance-separable (MDS) code
N. J. Cerf, “Entropic bounds on coding for noisy quantum channels”, Physical Review A 57, 3330 (1998) arXiv:quant-ph/9707023 DOI. Appears in: Finite-dimensional quantum error-correcting code
N. J. Cerf, G. Leuchs, and E. S. Polzik, “Quantum Information with Continuous Variables of Atoms and Light”, (2007) DOI. Appears in: Bosonic code
C. Cesare, A. J. Landahl, D. Bacon, S. T. Flammia, and A. Neels, “Adiabatic topological quantum computing”, Physical Review A 92, (2015) arXiv:1406.2690 DOI. Appears in: Honeycomb Floquet code, Kitaev surface code
M. Cha, P. Naaijkens, and B. Nachtergaele, “On the Stability of Charges in Infinite Quantum Spin Systems”, Communications in Mathematical Physics 373, 219 (2019) arXiv:1804.03203 DOI. Appears in: Abelian quantum-double stabilizer code, Topological code
U. Chabaud, G. Ferrini, F. Grosshans, and D. Markham, “Classical simulation of Gaussian quantum circuits with non-Gaussian input states”, Physical Review Research 3, (2021) arXiv:2010.14363 DOI. Appears in: Bosonic code
U. Chabaud, M. Joseph, S. Mehraban, and A. Motamedi, “Bosonic Quantum Computational Complexity”, (2024) arXiv:2410.04274. Appears in: Bosonic code
H. Chadwick and L. Kurz, “Rank permutation group codes based on Kendall’s correlation statistic”, IEEE Transactions on Information Theory 15, 306 (1969) DOI. Appears in: Code in permutations
P. Chaichanavong and P. H. Siegel, “Tensor-product parity code for magnetic recording”, IEEE Transactions on Magnetics 42, 350 (2006) DOI. Appears in: Tensor-product code
A. Chailloux and J.-P. Tillich, “Quantum advantage from soft decoders”, (2024) arXiv:2411.12553. Appears in: Reed-Solomon (RS) code
I. M. Chakravarti, “Families of Codes with Few Distinct Weights from Singular and Non-Singular Hermitian Varieties and Quadrics in Projective Geometries and Hadamard Difference Sets and Designs Associated with Two-Weight Codes”, The IMA Volumes in Mathematics and Its Applications 35 (1990) DOI. Appears in: Hermitian-hypersurface code
C. Chamberland and M. E. Beverland, “Flag fault-tolerant error correction with arbitrary distance codes”, Quantum 2, 53 (2018) arXiv:1708.02246 DOI. Appears in: $[[2^r-1,1,3]]$ simplex code, Qubit CSS code, Qubit stabilizer code, Kitaev surface code, Honeycomb (6.6.6) color code
C. Chamberland and P. Ronagh, “Deep neural decoders for near term fault-tolerant experiments”, Quantum Science and Technology 3, 044002 (2018) arXiv:1802.06441 DOI. Appears in: Kitaev surface code
C. Chamberland, A. Kubica, T. J. Yoder, and G. Zhu, “Triangular color codes on trivalent graphs with flag qubits”, New Journal of Physics 22, 023019 (2020) arXiv:1911.00355 DOI. Appears in: Honeycomb (6.6.6) color code
C. Chamberland and K. Noh, “Very low overhead fault-tolerant magic state preparation using redundant ancilla encoding and flag qubits”, npj Quantum Information 6, (2020) arXiv:2003.03049 DOI. Appears in: Honeycomb (6.6.6) color code
C. Chamberland, G. Zhu, T. J. Yoder, J. B. Hertzberg, and A. W. Cross, “Topological and Subsystem Codes on Low-Degree Graphs with Flag Qubits”, Physical Review X 10, (2020) arXiv:1907.09528 DOI. Appears in: Compass code, Heavy-hexagon code, Rotated surface code
C. Chamberland et al., “Building a Fault-Tolerant Quantum Computer Using Concatenated Cat Codes”, PRX Quantum 3, (2022) arXiv:2012.04108 DOI. Appears in: Concatenated cat code, Cat-repetition code, Quantum repetition code, Rotated surface code, Two-component cat code
C. Chamberland and E. T. Campbell, “Universal Quantum Computing with Twist-Free and Temporally Encoded Lattice Surgery”, PRX Quantum 3, (2022) arXiv:2109.02746 DOI. Appears in: Kitaev surface code
C. Chamberland and E. T. Campbell, “Circuit-level protocol and analysis for twist-based lattice surgery”, Physical Review Research 4, (2022) arXiv:2201.05678 DOI. Appears in: Twist-defect surface code
C. Chamberland, L. Goncalves, P. Sivarajah, E. Peterson, and S. Grimberg, “Techniques for combining fast local decoders with global decoders under circuit-level noise”, Quantum Science and Technology 8, 045011 (2023) arXiv:2208.01178 DOI. Appears in: Rotated surface code, Kitaev surface code
C. Chamon, “Quantum Glassiness in Strongly Correlated Clean Systems: An Example of Topological Overprotection”, Physical Review Letters 94, (2005) arXiv:cond-mat/0404182 DOI. Appears in: Chamon model code
A. Chan, R. M. Nandkishore, M. Pretko, and G. Smith, “Unitary-projective entanglement dynamics”, Physical Review B 99, (2019) arXiv:1808.05949 DOI. Appears in: Monitored random-circuit code
T. Chan and S. C. Benjamin, “Actis: A Strictly Local Union–Find Decoder”, Quantum 7, 1183 (2023) arXiv:2305.18534 DOI. Appears in: Kitaev surface code
N. Chancellor, “Domain wall encoding of discrete variables for quantum annealing and QAOA”, Quantum Science and Technology 4, 045004 (2019) arXiv:1903.05068 DOI. Appears in: One-hot quantum code
N. Chancellor, A. Kissinger, S. Zohren, J. Roffe, and D. Horsman, “Graphical structures for design and verification of quantum error correction”, Quantum Science and Technology 8, 045028 (2023) arXiv:1611.08012 DOI. Appears in: Coherent-parity-check (CPC) code, $[2^r-1,2^r-r-1,3]$ Hamming code, Qubit CSS code, $[[2^r+r, 2^r-r-2, 3]]$ Ring CPC code
D. Chandra, Z. Babar, H. V. Nguyen, D. Alanis, P. Botsinis, S. X. Ng, and L. Hanzo, “Quantum Topological Error Correction Codes: The Classical-to-Quantum Isomorphism Perspective”, IEEE Access 6, 13729 (2018) DOI. Appears in: Classical topological code
O. Chandra, G. Muraleedharan, and G. K. Brennen, “Non-local resources for error correction in quantum LDPC codes”, (2024) arXiv:2409.05818. Appears in: Hypergraph product (HGP) code
V. Chandrasekaran and A. Levine, “Quantum error correction in SYK and bulk emergence”, Journal of High Energy Physics 2022, (2022) arXiv:2203.05058 DOI. Appears in: SYK code
E.-J. Chang and C.-Y. Lai, “High-Rate Amplitude-Damping Shor Codes with Immunity to Collective Coherent Errors”, (2024) arXiv:2412.16450. Appears in: Amplitude-damping CWS code, Concatenated qubit code
L. Chang, “Kitaev models based on unitary quantum groupoids”, Journal of Mathematical Physics 55, (2014) arXiv:1309.4181 DOI. Appears in: Multi-fusion string-net code, Hopf-algebra quantum-double code
L. Chang, M. Cheng, S. X. Cui, Y. Hu, W. Jin, R. Movassagh, P. Naaijkens, Z. Wang, and A. Young, “On enriching the Levin–Wen model with symmetry”, Journal of Physics A: Mathematical and Theoretical 48, 12FT01 (2015) arXiv:1412.6589 DOI. Appears in: Multi-fusion string-net code, Groupoid toric code
Changyan Di, D. Proietti, I. E. Telatar, T. J. Richardson, and R. L. Urbanke, “Finite-length analysis of low-density parity-check codes on the binary erasure channel”, IEEE Transactions on Information Theory 48, 1570 (2002) DOI. Appears in: Low-density parity-check (LDPC) code
R. Chao and B. W. Reichardt, “Fault-tolerant quantum computation with few qubits”, npj Quantum Information 4, (2018) arXiv:1705.05365 DOI. Appears in: $[[2m,2m-2,2]]$ error-detecting code, Perfect quantum code, $[[15, 7, 3]]$ quantum Hamming code
R. Chao and B. W. Reichardt, “Quantum Error Correction with Only Two Extra Qubits”, Physical Review Letters 121, (2018) arXiv:1705.02329 DOI. Appears in: $[[2m,2m-2,2]]$ error-detecting code, $[[2^r-1, 2^r-2r-1, 3]]$ quantum Hamming code, Five-qubit perfect code, $[[7,1,3]]$ Steane code
R. Chao, M. E. Beverland, N. Delfosse, and J. Haah, “Optimization of the surface code design for Majorana-based qubits”, Quantum 4, 352 (2020) arXiv:2007.00307 DOI. Appears in: Honeycomb Floquet code, Kitaev surface code
Chaoping Xing, “Asymptotic bounds on frameproof codes”, IEEE Transactions on Information Theory 48, 2991 (2002) DOI. Appears in: Evaluation AG code, Frameproof (FP) code
Chaoping Xing, “Nonlinear codes from algebraic curves improving the Tsfasman-Vladut-Zink bound”, IEEE Transactions on Information Theory 49, 1653 (2003) DOI. Appears in: Nonlinear AG code
A. Chapman and S. T. Flammia, “Characterization of solvable spin models via graph invariants”, Quantum 4, 278 (2020) arXiv:2003.05465 DOI. Appears in: Fermion code, Fermion-into-qubit code
A. Chapman, S. T. Flammia, and A. J. Kollár, “Free-Fermion Subsystem Codes”, (2022) arXiv:2201.07254. Appears in: Bacon-Shor code, Majorana stabilizer code, Majorana subsystem stabilizer code, Subsystem qubit stabilizer code, Lattice subsystem code
M. Chapman, T. Vidick, and H. Yuen, “Efficiently stable presentations from error-correcting codes”, (2023) arXiv:2311.04681. Appears in: Generalized RM (GRM) code, $q$-ary linear LTC
R. J. Chapman, A. Karim, Z. Huang, S. T. Flammia, M. Tomamichel, and A. Peruzzo, “Beating the classical limits of information transmission using a quantum decoder”, Physical Review A 97, (2018) arXiv:1704.07036 DOI. Appears in: Qubit c-q code
Charpin, Pascale. Codes idéaux de certaines algèbres modulaires. Diss. 1982.. Appears in: Generalized RM (GRM) code, Group-algebra code, Reed-Muller (RM) code
D. Chase, “Class of algorithms for decoding block codes with channel measurement information”, IEEE Transactions on Information Theory 18, 170 (1972) DOI. Appears in: Linear binary code
H. F. Chau, “Five quantum register error correction code for higher spin systems”, Physical Review A 56, R1 (1997) arXiv:quant-ph/9702033 DOI. Appears in: $[[5,1,3]]_{\mathbb{Z}_q}$ modular-qudit code
H. F. Chau, “Correcting quantum errors in higher spin systems”, Physical Review A 55, R839 (1997) arXiv:quant-ph/9610023 DOI. Appears in: $[[9,1,3]]_{\mathbb{Z}_q}$ modular-qudit code
H. F. Chau, “Quantum convolutional error-correcting codes”, Physical Review A 58, 905 (1998) arXiv:quant-ph/9712029 DOI. Appears in: Quantum convolutional code
H. F. Chau, “Good quantum-convolutional error-correction codes and their decoding algorithm exist”, Physical Review A 60, 1966 (1999) arXiv:quant-ph/9806032 DOI. Appears in: Quantum convolutional code
B. Chen, S. Ling, and G. Zhang, “Application of Constacyclic Codes to Quantum MDS Codes”, IEEE Transactions on Information Theory 61, 1474 (2015) DOI. Appears in: Constacyclic code, Quantum maximum-distance-separable (MDS) code, Hermitian Galois-qudit code
E. H. Chen, T. J. Yoder, Y. Kim, N. Sundaresan, S. Srinivasan, M. Li, A. D. Córcoles, A. W. Cross, and M. Takita, “Calibrated Decoders for Experimental Quantum Error Correction”, Physical Review Letters 128, (2022) arXiv:2110.04285 DOI. Appears in: Heavy-hexagon code, $[[4,2,2]]$ Four-qubit code
E. H. Chen et al., “Nishimori transition across the error threshold for constant-depth quantum circuits”, Nature Physics 21, 161 (2024) arXiv:2309.02863 DOI. Appears in: Quantum repetition code
H. Chen, “Some Good Error-Correcting Codes from Algebraic-Geometric Codes”, (2001) arXiv:quant-ph/0107102. Appears in: Quantum AG code
H. Chen and R. Cramer, “Algebraic Geometric Secret Sharing Schemes and Secure Multi-Party Computations over Small Fields”, Lecture Notes in Computer Science 521 (2006) DOI. Appears in: Residue AG code
H. Chen, R. Cramer, S. Goldwasser, R. de Haan, and V. Vaikuntanathan, “Secure Computation from Random Error Correcting Codes”, Advances in Cryptology - EUROCRYPT 2007 291 (2007) DOI. Appears in: Random code
H. Chen, M. Vasmer, N. P. Breuckmann, and E. Grant, “Automated discovery of logical gates for quantum error correction (with Supplementary (153 pages))”, Quantum Information and Computation 22, 947 (2022) arXiv:1912.10063 DOI. Appears in: $[[4,2,2]]$ Four-qubit code, $[[6,4,2]]$ error-detecting code, $[[8,2,2]]$ hyperbolic color code, $[[8,3,2]]$ Smallest interesting color code, $[[8, 3, 3]]$ Eight-qubit Gottesman code, $[[7,1,3]]$ twist-defect surface code
J. Chen, A. Dholakia, E. Eleftheriou, M. P. C. Fossorier, and X.-Y. Hu, “Reduced-Complexity Decoding of LDPC Codes”, IEEE Transactions on Communications 53, 1288 (2005) DOI. Appears in: Low-density parity-check (LDPC) code
J. Chen, R. M. Tanner, J. Zhang, and M. P. C. Fossorier, “Construction of Irregular LDPC Codes by Quasi-Cyclic Extension”, IEEE Transactions on Information Theory 53, 1479 (2007) DOI. Appears in: Repeat-accumulate (RA) code
J. Chen, J. L. Habif, Z. Dutton, R. Lazarus, and S. Guha, “Optical codeword demodulation with error rates below the standard quantum limit using a conditional nulling receiver”, Nature Photonics 6, 374 (2012) arXiv:1111.4017 DOI. Appears in: PPM c-q code
J. Chen, Z. Yi, Z. Liang, and X. Wang, “Improved Belief Propagation Decoding Algorithms for Surface Codes”, (2024) arXiv:2407.11523. Appears in: Kitaev surface code
K. Chen, Y. Liu, W. Fang, J. Paykin, X. R. Wu, A. Schmitz, S. Zdancewic, and G. Li, “Verifying Fault-Tolerance of Quantum Error Correction Codes”, (2025) arXiv:2501.14380. Appears in: Qubit stabilizer code
L. Chen, Y. Ren, R. Fan, and A. Jaffe, “A Universal Circuit Set Using the $S_3$ Quantum Double”, (2024) arXiv:2411.09697. Appears in: Dihedral $G=D_m$ quantum-double code
M. Chen, N. C. Menicucci, and O. Pfister, “Experimental Realization of Multipartite Entanglement of 60 Modes of a Quantum Optical Frequency Comb”, Physical Review Letters 112, (2014) arXiv:1311.2957 DOI. Appears in: Analog-cluster-state code
X. Chen, B. Zeng, and I. L. Chuang, “Nonbinary codeword-stabilized quantum codes”, Physical Review A 78, (2008) arXiv:0808.3086 DOI. Appears in: Modular-qudit CWS code
X. Chen, R. Duan, Z. Ji, and B. Zeng, “Quantum State Reduction for Universal Measurement Based Computation”, Physical Review Letters 105, (2010) arXiv:1002.1567 DOI. Appears in: Cluster-state code, Symmetry-protected topological (SPT) code, Lattice stabilizer code
X. Chen, Z.-C. Gu, and X.-G. Wen, “Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order”, Physical Review B 82, (2010) arXiv:1004.3835 DOI. Appears in: Hamiltonian-based code
X. Chen, Z.-C. Gu, and X.-G. Wen, “Classification of gapped symmetric phases in one-dimensional spin systems”, Physical Review B 83, (2011) arXiv:1008.3745 DOI. Appears in: Magnon code, Symmetry-protected topological (SPT) code, Valence-bond-solid (VBS) code
X. Chen, Z.-C. Gu, and X.-G. Wen, “Complete classification of one-dimensional gapped quantum phases in interacting spin systems”, Physical Review B 84, (2011) arXiv:1103.3323 DOI. Appears in: Magnon code, Symmetry-protected topological (SPT) code, Valence-bond-solid (VBS) code
X. Chen, Z.-C. Gu, Z.-X. Liu, and X.-G. Wen, “Symmetry protected topological orders in interacting bosonic systems”, (2013) arXiv:1301.0861. Appears in: Cluster-state code, Symmetry-protected topological (SPT) code, Twisted quantum double (TQD) code, Lattice stabilizer code
X. Chen, Z.-C. Gu, Z.-X. Liu, and X.-G. Wen, “Symmetry protected topological orders and the group cohomology of their symmetry group”, Physical Review B 87, (2013) arXiv:1106.4772 DOI. Appears in: Cubic theory code, Magnon code, Symmetry-protected topological (SPT) code, Valence-bond-solid (VBS) code
X. Chen, A. Dua, P.-S. Hsin, C.-M. Jian, W. Shirley, and C. Xu, “Loops in 4+1d topological phases”, SciPost Physics 15, (2023) arXiv:2112.02137 DOI. Appears in: Loop toric code, Homological code, Abelian topological code
Y.-A. Chen, A. Kapustin, and Đ. Radičević, “Exact bosonization in two spatial dimensions and a new class of lattice gauge theories”, Annals of Physics 393, 234 (2018) arXiv:1711.00515 DOI. Appears in: 2D bosonization code, Kitaev honeycomb code
Y.-A. Chen and A. Kapustin, “Bosonization in three spatial dimensions and a 2-form gauge theory”, Physical Review B 100, (2019) arXiv:1807.07081 DOI. Appears in: 3D bosonization code, 3D fermionic surface code
Y.-A. Chen, “Exact bosonization in arbitrary dimensions”, Physical Review Research 2, (2020) arXiv:1911.00017 DOI. Appears in: Bosonization code
Y.-A. Chen and P.-S. Hsin, “Exactly solvable lattice Hamiltonians and gravitational anomalies”, SciPost Physics 14, (2023) arXiv:2110.14644 DOI. Appears in: Chen-Hsin invertible-order code, Symmetry-protected topological (SPT) code, Topological code, Two-gauge theory code
Y.-A. Chen and Y. Xu, “Equivalence between Fermion-to-Qubit Mappings in two Spatial Dimensions”, PRX Quantum 4, (2023) arXiv:2201.05153 DOI. Appears in: 2D bosonization code, Bravyi-Kitaev superfast (BKSF) code, Ball-Verstraete-Cirac (BVC) code, Fermion-into-qubit code, Jordan-Wigner transformation code, Kitaev honeycomb code
Y.-A. Chen and S. Tata, “Higher cup products on hypercubic lattices: Application to lattice models of topological phases”, Journal of Mathematical Physics 64, (2023) arXiv:2106.05274 DOI. Appears in: 3D surface code
Y.-A. Chen, A. V. Gorshkov, and Y. Xu, “Error-correcting codes for fermionic quantum simulation”, SciPost Physics 16, (2024) arXiv:2210.08411 DOI. Appears in: 2D bosonization code
Y.-H. Chen and T. Grover, “Separability Transitions in Topological States Induced by Local Decoherence”, Physical Review Letters 132, (2024) arXiv:2309.11879 DOI. Appears in: 2D lattice stabilizer code
Z.-H. Chen, M.-C. Chen, C.-Y. Lu, and J.-W. Pan, “Transversal Logical Clifford gates on rotated surface codes with reconfigurable neutral atom arrays”, (2024) arXiv:2412.01391. Appears in: Rotated surface code
“Exponential suppression of bit or phase errors with cyclic error correction”, Nature 595, 383 (2021) arXiv:2102.06132 DOI. Appears in: Quantum repetition code, Rotated surface code, $[[4,2,2]]$ Four-qubit code
Z. Chen and N. Rengaswamy, “Tailoring Fault-Tolerance to Quantum Algorithms”, (2024) arXiv:2404.11953. Appears in: $[[2m,2m-2,2]]$ error-detecting code
H.-C. Cheng, “Simple and Tighter Derivation of Achievability for Classical Communication Over Quantum Channels”, PRX Quantum 4, (2023) arXiv:2208.02132 DOI. Appears in: Classical-quantum (c-q) code
K. Cheng, M. Ouyang, C. Shangguan, and Y. Shen, “When can an expander code correct $Ω(n)$ errors in $O(n)$ time?”, (2024) arXiv:2312.16087. Appears in: Expander code
Y. C. Cheng and R. J. Silbey, “Microscopic quantum dynamics study on the noise threshold of fault-tolerant quantum error correction”, Physical Review A 72, (2005) arXiv:quant-ph/0412168 DOI. Appears in: Quantum repetition code
Z. Cheng, E. Huang, V. Khemani, M. J. Gullans, and M. Ippoliti, “Emergent unitary designs for encoded qubits from coherent errors and syndrome measurements”, (2024) arXiv:2412.04414. Appears in: Kitaev surface code, $t$-design
Chen, Y. H., Truong, T. K., Chang, Y., Lee, C. D., & Chen, S. H. (2007). Algebraic decoding of quadratic residue codes using Berlekamp-Massey algorithm. Journal of information science and engineering, 23(1), 127-145.. Appears in: Binary quadratic-residue (QR) code
S. Chesi, D. Loss, S. Bravyi, and B. M. Terhal, “Thermodynamic stability criteria for a quantum memory based on stabilizer and subsystem codes”, New Journal of Physics 12, 025013 (2010) arXiv:0907.2807 DOI. Appears in: Self-correcting quantum code
S. Chesi, B. Röthlisberger, and D. Loss, “Self-correcting quantum memory in a thermal environment”, Physical Review A 82, (2010) arXiv:0908.4264 DOI. Appears in: Self-correcting quantum code, Kitaev surface code
S. Chessa and V. Giovannetti, “Quantum capacity analysis of multi-level amplitude damping channels”, Communications Physics 4, (2021) arXiv:2008.00477 DOI. Appears in: Amplitude-damping (AD) code
Cheung, K-M., and F. Pollara. "Phobos lander coding system: Software and analysis." The Telecommunications and Data Acquisition Report (1988).. Appears in: Binary BCH code
J. Chiaverini et al., “Realization of quantum error correction”, Nature 432, 602 (2004) DOI. Appears in: Quantum repetition code
R. W. Chien and J. D. Whitfield, “Custom fermionic codes for quantum simulation”, (2020) arXiv:2009.11860. Appears in: Derby-Klassen (DK) code, Fermion-into-qubit code, XZZX surface code
R. Chien and S. Ng, “Dual product codes for correction of multiple low-density burst errors”, IEEE Transactions on Information Theory 19, 672 (1973) DOI. Appears in: Tensor-product code
R. Chien and D. Choy, “Algebraic generalization of BCH-Goppa-Helgert codes”, IEEE Transactions on Information Theory 21, 70 (1975) DOI. Appears in: Chien-Choy generalized BCH (GBCH) code
M. Chiew and S. Strelchuk, “Discovering optimal fermion-qubit mappings through algorithmic enumeration”, Quantum 7, 1145 (2023) arXiv:2110.12792 DOI. Appears in: Jordan-Wigner transformation code
S. K. Chilappagari, Dung Viet Nguyen, B. Vasic, and M. W. Marcellin, “On Trapping Sets and Guaranteed Error Correction Capability of LDPC Codes and GLDPC Codes”, IEEE Transactions on Information Theory 56, 1600 (2010) arXiv:0805.2427 DOI. Appears in: Expander code
G. Chiribella, M. Dall’Arno, G. M. D’Ariano, C. Macchiavello, and P. Perinotti, “Quantum error correction with degenerate codes for correlated noise”, Physical Review A 83, (2011) arXiv:1007.3655 DOI. Appears in: Block quantum code, Finite-dimensional quantum error-correcting code
J. Cho, “Fault-tolerant linear optics quantum computation by error-detecting quantum state transfer”, Physical Review A 76, (2007) arXiv:quant-ph/0612073 DOI. Appears in: Concatenated qubit code, $[[4,2,2]]$ Four-qubit code, $[[6,2,2]]$ $C_6$ code
S. H. Choe and R. Koenig, “Long-range data transmission in a fault-tolerant quantum bus architecture”, (2022) arXiv:2209.09774. Appears in: Kitaev surface code
S. H. Choe and R. Koenig, “How to fault-tolerantly realize any quantum circuit with local operations”, (2024) arXiv:2402.13863. Appears in: Qubit code
H. Choi, F. T. Chong, D. Englund, and Y. Ding, “Fault Tolerant Non-Clifford State Preparation for Arbitrary Rotations”, (2023) arXiv:2303.17380. Appears in: Qubit stabilizer code
M.-D. Choi and D. W. Kribs, “Method to Find Quantum Noiseless Subsystems”, Physical Review Letters 96, (2006) arXiv:quant-ph/0507213 DOI. Appears in: Operator-algebra QECC (OAQECC)
M.-D. Choi, D. W. Kribs, and K. Życzkowski, “Quantum error correcting codes from the compression formalism”, Reports on Mathematical Physics 58, 77 (2006) arXiv:quant-ph/0511101 DOI. Appears in: Finite-dimensional quantum error-correcting code
M.-D. Choi, D. W. Kribs, and K. Zyczkowski, “Higher-Rank Numerical Ranges and Compression Problems”, (2006) arXiv:math/0511278. Appears in: Finite-dimensional quantum error-correcting code
M.-D. Choi, N. Johnston, and D. W. Kribs, “The multiplicative domain in quantum error correction”, Journal of Physics A: Mathematical and Theoretical 42, 245303 (2009) arXiv:0811.0947 DOI. Appears in: Subsystem QECC
S. Choi, J. Y. Hyun, H. K. Kim, and D. Y. Oh, “MacWilliams-type equivalence relations”, (2013) arXiv:1205.1090. Appears in: Poset code
S. Choi, Y. Bao, X.-L. Qi, and E. Altman, “Quantum Error Correction in Scrambling Dynamics and Measurement-Induced Phase Transition”, Physical Review Letters 125, (2020) arXiv:1903.05124 DOI. Appears in: Monitored random-circuit code
B. Chor, O. Goldreich, E. Kushilevitz, and M. Sudan, “Private information retrieval”, Proceedings of IEEE 36th Annual Foundations of Computer Science DOI. Appears in: Private information retrieval (PIR) code
B. Chor, E. Kushilevitz, O. Goldreich, and M. Sudan, “Private information retrieval”, Journal of the ACM 45, 965 (1998) DOI. Appears in: Private information retrieval (PIR) code
B. Chor, A. Fiat, M. Naor, and B. Pinkas, “Tracing traitors”, IEEE Transactions on Information Theory 46, 893 (2000) DOI. Appears in: Traceability code
K. S. Chou et al., “Demonstrating a superconducting dual-rail cavity qubit with erasure-detected logical measurements”, (2023) arXiv:2307.03169. Appears in: Dual-rail quantum code
Y. Choukroun and L. Wolf, “Error Correction Code Transformer”, (2022) arXiv:2203.14966. Appears in: Linear binary code
Y. Choukroun and L. Wolf, “Deep Quantum Error Correction”, (2023) arXiv:2301.11930. Appears in: Qubit CSS code
D. R. Chowdhury, S. Basu, I. S. Gupta, and P. P. Chaudhuri, “Design of CAECC - cellular automata based error correcting code”, IEEE Transactions on Computers 43, 759 (1994) DOI. Appears in: Newman-Moore code
M. Christandl and A. Müller-Hermes, “Fault-Tolerant Coding for Quantum Communication”, IEEE Transactions on Information Theory 70, 282 (2024) arXiv:2009.07161 DOI. Appears in: Error-correcting code (ECC), Quantum error-correcting code (QECC)
M. Christandl, O. Fawzi, and A. Goswami, “Fault-tolerant quantum input/output”, (2024) arXiv:2408.05260. Appears in: Concatenated qubit code
J. Christian, D. Green, P. Huston, and D. Penneys, “A lattice model for condensation in Levin-Wen systems”, (2023) arXiv:2303.04711. Appears in: String-net code
I. L. Chuang and Y. Yamamoto, “Simple quantum computer”, Physical Review A 52, 3489 (1995) arXiv:quant-ph/9505011 DOI. Appears in: Dual-rail quantum code
I. L. Chuang and Y. Yamamoto, “Simple quantum computer”, Physical Review A 52, 3489 (1995) DOI. Appears in: Dual-rail quantum code
I. L. Chuang and Y. Yamamoto, “Quantum Bit Regeneration”, Physical Review Letters 76, 4281 (1996) arXiv:quant-ph/9604031 DOI. Appears in: Dual-rail quantum code
I. L. Chuang, D. W. Leung, and Y. Yamamoto, “Bosonic quantum codes for amplitude damping”, Physical Review A 56, 1114 (1997) DOI. Appears in: Amplitude-damping (AD) code, Approximate quantum error-correcting code (AQECC), Chuang-Leung-Yamamoto (CLY) code, Constant-excitation (CE) code, Two-mode binomial code
I. Chuang, A. Cross, G. Smith, J. Smolin, and B. Zeng, “Codeword stabilized quantum codes: Algorithm and structure”, Journal of Mathematical Physics 50, (2009) arXiv:0803.3232 DOI. Appears in: Qubit stabilizer code
C. T. Chubb, V. Y. F. Tan, and M. Tomamichel, “Moderate Deviation Analysis for Classical Communication over Quantum Channels”, Communications in Mathematical Physics 355, 1283 (2017) arXiv:1701.03114 DOI. Appears in: Classical-quantum (c-q) code, Error-correcting code (ECC)
C. T. Chubb and S. T. Flammia, “Statistical mechanical models for quantum codes with correlated noise”, Annales de l’Institut Henri Poincaré D, Combinatorics, Physics and their Interactions 8, 269 (2021) arXiv:1809.10704 DOI. Appears in: 2D lattice stabilizer code, Qubit stabilizer code, Subsystem qubit stabilizer code, Toric code
B. S. Cirel’son, “Reliable storage of information in a system of unreliable components with local interactions”, Lecture Notes in Mathematics 15 (1978) DOI. Appears in: Repetition code
J. Claes, J. E. Bourassa, and S. Puri, “Tailored cluster states with high threshold under biased noise”, npj Quantum Information 9, (2023) arXiv:2201.10566 DOI. Appears in: Asymmetric quantum code, Cluster-state code, XZZX surface code
S. Clark, “Valence bond solid formalism ford-level one-way quantum computation”, Journal of Physics A: Mathematical and General 39, 2701 (2006) arXiv:quant-ph/0512155 DOI. Appears in: Modular-qudit cluster-state code, Modular-qudit code
A. Cleland, “An introduction to the surface code”, SciPost Physics Lecture Notes (2022) DOI. Appears in: Kitaev surface code
B. Clerckx and C. Oestges, “From Multi-Dimensional Propagation to Multi-Link MIMO Channels”, Mimo Wireless Networks 29 (2013) DOI. Appears in: Spacetime code (STC)
R. Cleve and D. Gottesman, “Efficient computations of encodings for quantum error correction”, Physical Review A 56, 76 (1997) arXiv:quant-ph/9607030 DOI. Appears in: Qubit stabilizer code
R. Cleve, D. Gottesman, and H.-K. Lo, “How to Share a Quantum Secret”, Physical Review Letters 83, 648 (1999) arXiv:quant-ph/9901025 DOI. Appears in: Prime-qudit RS code, Approximate secret-sharing code, Three-qutrit code
L. Clinton, T. Cubitt, B. Flynn, F. M. Gambetta, J. Klassen, A. Montanaro, S. Piddock, R. A. Santos, and E. Sheridan, “Towards near-term quantum simulation of materials”, Nature Communications 15, (2024) arXiv:2205.15256 DOI. Appears in: Derby-Klassen (DK) code
P. T. Cochrane, G. J. Milburn, and W. J. Munro, “Macroscopically distinct quantum-superposition states as a bosonic code for amplitude damping”, Physical Review A 59, 2631 (1999) arXiv:quant-ph/9809037 DOI. Appears in: Two-component cat code
B. Coecke and R. Duncan, “Interacting Quantum Observables”, Automata, Languages and Programming 298 DOI. Appears in: Coherent-parity-check (CPC) code, Qubit stabilizer code, Kitaev surface code
B. Coecke and R. Duncan, “Interacting quantum observables: categorical algebra and diagrammatics”, New Journal of Physics 13, 043016 (2011) arXiv:0906.4725 DOI. Appears in: Coherent-parity-check (CPC) code, Qubit stabilizer code, Kitaev surface code
L. Coffman, G. Smith, and X. Gao, “Measuring Non-Gaussian Magic in Fermions: Convolution, Entropy, and the Violation of Wick’s Theorem and the Matchgate Identity”, (2025) arXiv:2501.06179. Appears in: Fermion code
J. Cohen and M. Mirrahimi, “Dissipation-induced continuous quantum error correction for superconducting circuits”, Physical Review A 90, (2014) arXiv:1409.6759 DOI. Appears in: Concatenated cat code
L. Z. Cohen, I. H. Kim, S. D. Bartlett, and B. J. Brown, “Low-overhead fault-tolerant quantum computing using long-range connectivity”, Science Advances 8, (2022) arXiv:2110.10794 DOI. Appears in: Distance-balanced code, Bivariate bicycle (BB) code, Quantum LDPC (QLDPC) code
G. Cohen, I. Honkala, S. Litsyn, A. Lobstein, Covering codes. Elsevier, 1997.. Appears in: Covering code, Quasi-perfect code, Weighted-covering code
G. Cohen, I. Honkala, S. Litsyn, A. Lobstein, Covering Codes, Elsevier (1997).. Appears in: Covering code
H. Cohn and N. Elkies, “New upper bounds on sphere packings I”, Annals of Mathematics 157, 689 (2003) arXiv:math/0110009 DOI. Appears in: Sphere packing
H. Cohn and A. Kumar, “Universally optimal distribution of points on spheres”, Journal of the American Mathematical Society 20, 99 (2006) arXiv:math/0607446 DOI. Appears in: 24-cell code, 600-cell code, Cameron-Goethals-Seidel (CGS) isotropic subspace code, Sharp configuration, $E_8$ Gosset lattice, $E_7$ lattice-shell code, $E_6$ lattice-shell code, $3_{21}$ polytope code, Hessian polyhedron code, Icosahedron code, $\Lambda_{24}$ Leech lattice, $\Lambda_{24}$ Leech lattice-shell code, Spherical sharp configuration, Spherical design, Universally optimal code, Universally optimal sphere packing, Universally optimal spherical code, Witting polytope code
H. Cohn and A. Kumar, “Uniqueness of the (22,891,1/4) spherical code”, (2007) arXiv:math/0607448. Appears in: $3_{21}$ polytope code, $\Lambda_{24}$ Leech lattice-shell code, Spherical sharp configuration, Spherical design, Witting polytope code
H. Cohn, J. H. Conway, N. D. Elkies, and A. Kumar, “TheD${}_{\text{4}}$Root System Is Not Universally Optimal”, Experimental Mathematics 16, 313 (2007) arXiv:math/0607447 DOI. Appears in: 24-cell code, Spherical design, Universally optimal spherical code
H. Cohn and Y. Zhao, “Energy-Minimizing Error-Correcting Codes”, IEEE Transactions on Information Theory 60, 7442 (2014) arXiv:1212.1913 DOI. Appears in: Ovoid code, Conference code, Sharp configuration, $q$-ary sharp configuration, $[24, 12, 8]$ Extended Golay code, $[2^r,2^r-r-1,4]$ Extended Hamming code, $[23, 12, 7]$ Golay code, Hadamard code, $[2^r-1,2^r-r-1,3]$ Hamming code, Maximum distance separable (MDS) code, $q$-ary Hamming code, $q$-ary simplex code, Ternary Golay code, Universally optimal code, Universally optimal $q$-ary code
H. Cohn, A. Kumar, and G. Minton, “Optimal simplices and codes in projective spaces”, Geometry & Topology 20, 1289 (2016) arXiv:1308.3188 DOI. Appears in: 24-cell code, Kerdock code, $t$-design, Universally optimal code
H. Cohn, “Packing, coding, and ground states”, (2016) arXiv:1603.05202. Appears in: $\Lambda_{24}$ Leech lattice-shell code, Spherical sharp configuration, Spherical design, Universally optimal code
H. Cohn, A. Kumar, S. Miller, D. Radchenko, and M. Viazovska, “The sphere packing problem in dimension $24$”, Annals of Mathematics 185, (2017) arXiv:1603.06518 DOI. Appears in: $E_8$ Gosset lattice, $\Lambda_{24}$ Leech lattice
H. Cohn, A. Kumar, S. D. Miller, D. Radchenko, and M. Viazovska, “Universal optimality of the $E_8$ and Leech lattices and interpolation formulas”, (2022) arXiv:1902.05438. Appears in: $E_8$ Gosset lattice, $\Lambda_{24}$ Leech lattice, Universally optimal sphere packing
H. Cohn, D. de Laat, and N. Leijenhorst, “Optimality of spherical codes via exact semidefinite programming bounds”, (2024) arXiv:2403.16874. Appears in: Kerdock spherical code, Spherical design
H. Cohn. "Kissing numbers." https://cohn.mit.edu/kissing-numbers. Appears in: Lattice-based code
A. Coladangelo, J. Liu, Q. Liu, and M. Zhandry, “Hidden Cosets and Applications to Unclonable Cryptography”, (2022) arXiv:2107.05692. Appears in: Qubit CSS code
C. J. Colbourn and J. H. Dinitz, editors , Handbook of Combinatorial Designs (Chapman and Hall/CRC, 2006) DOI. Appears in: Combinatorial design, Hadamard code, Spherical design, $t$-design
C. J. Colbourn, editor , CRC Handbook of Combinatorial Designs (CRC Press, 2010) DOI. Appears in: Combinatorial design, Self-dual linear code
P. Coleman, Introduction to Many-Body Physics (Cambridge University Press, 2015) DOI. Appears in: Hamiltonian-based code
L. Colmenarez, Z.-M. Huang, S. Diehl, and M. Müller, “Accurate optimal quantum error correction thresholds from coherent information”, Physical Review Research 6, (2024) arXiv:2312.06664 DOI. Appears in: Finite-dimensional quantum error-correcting code
I. Cong, S. Choi, and M. D. Lukin, “Quantum convolutional neural networks”, Nature Physics 15, 1273 (2019) arXiv:1810.03787 DOI. Appears in: Approximate quantum error-correcting code (AQECC)
A. Conlon, D. Pellegrino, and J. K. Slingerland, “Modified toric code models with flux attachment from Hopf algebra gauge theory”, Journal of Physics A: Mathematical and Theoretical 56, 295302 (2023) arXiv:2210.07909 DOI. Appears in: Hopf-algebra quantum-double code, Modular-qudit surface code
N. Connolly, V. Londe, A. Leverrier, and N. Delfosse, “Fast erasure decoder for hypergraph product codes”, Quantum 8, 1450 (2024) arXiv:2208.01002 DOI. Appears in: Hypergraph product (HGP) code
J. Conrad, C. Chamberland, N. P. Breuckmann, and B. M. Terhal, “The small stellated dodecahedron code and friends”, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, 20170323 (2018) arXiv:1712.07666 DOI. Appears in: Polyhedron code, $[[30,8,3]]$ Bring code, $[[9,1,3]]$ Surface-17 code
J. Conrad, J. Eisert, and F. Arzani, “Gottesman-Kitaev-Preskill codes: A lattice perspective”, Quantum 6, 648 (2022) arXiv:2109.14645 DOI. Appears in: Oscillator-into-oscillator GKP code, Gottesman-Kitaev-Preskill (GKP) code, Quantum lattice code
J. Conrad, A. G. Burchards, and S. T. Flammia, “Lattices, Gates, and Curves: GKP codes as a Rosetta stone”, (2024) arXiv:2407.03270. Appears in: Gottesman-Kitaev-Preskill (GKP) code
J. Conrad, J. Eisert, and S. T. Flammia, “Chasing shadows with Gottesman-Kitaev-Preskill codes”, (2024) arXiv:2411.00235. Appears in: Gottesman-Kitaev-Preskill (GKP) code
J. Conrad, The Fabulous World of GKP Codes, Freie Universität Berlin, 2024 arXiv:2412.02442 DOI. Appears in: Gottesman-Kitaev-Preskill (GKP) code
J. Conrad, J. Eisert, and J.-P. Seifert, “Good Gottesman-Kitaev-Preskill codes from the NTRU cryptosystem”, Quantum 8, 1398 (2024) arXiv:2303.02432 DOI. Appears in: NTRU-GKP code
J. Conrad, J. T. Iosue, A. G. Burchards, and V. V. Albert, “Continuous-variable designs and design-based shadow tomography from random lattices”, (2025) arXiv:2412.17909. Appears in: Gottesman-Kitaev-Preskill (GKP) code, $t$-design
S. D. Constantin and T. R. N. Rao, “On the theory of binary asymmetric error correcting codes”, Information and Control 40, 20 (1979) DOI. Appears in: Constantin-Rao (CR) code, $q$-ary code
I. Convy, H. Liao, S. Zhang, S. Patel, W. P. Livingston, H. N. Nguyen, I. Siddiqi, and K. B. Whaley, “Machine learning for continuous quantum error correction on superconducting qubits”, New Journal of Physics 24, 063019 (2022) arXiv:2110.10378 DOI. Appears in: Quantum repetition code
J. H. Conway and N. J. A. Sloane, “The Coxeter–Todd lattice, the Mitchell group, and related sphere packings”, Mathematical Proceedings of the Cambridge Philosophical Society 93, 421 (1983) DOI. Appears in: Coxeter-Todd $K_{12}$ lattice
J. H. Conway and N. J. A. Sloane, “On the Voronoi Regions of Certain Lattices”, SIAM Journal on Algebraic Discrete Methods 5, 294 (1984) DOI. Appears in: Construction-$A$ code, $E_7$ root lattice, $[7,4,3]$ Hamming code, $[7,3,4]$ simplex code
J. H. Conway and N. J. A. Sloane, “Orbit and coset analysis of the Golay and related codes”, IEEE Transactions on Information Theory 36, 1038 (1990) DOI. Appears in: Error-correcting code (ECC), $[23, 12, 7]$ Golay code, Group-orbit code
J. H. Conway and N. J. A. Sloane, “The Cell Structures of Certain Lattices”, Miscellanea Mathematica 71 (1991) DOI. Appears in: $E_7$ lattice-shell code, $E_6$ lattice-shell code, $3_{21}$ polytope code, Hessian polyhedron code
J. H. Conway and N. J. A. Sloane, “Self-dual codes over the integers modulo 4”, Journal of Combinatorial Theory, Series A 62, 30 (1993) DOI. Appears in: Octacode
J. H. Conway and N. J. A. Sloane, “Quaternary constructions for the binary single-error-correcting codes of Julin, Best and others”, Designs, Codes and Cryptography 4, 31 (1994) DOI. Appears in: Best $(10,40,4)$ code, Gray code, Julin-Golay code, $q$-ary code over $\mathbb{Z}_q$
J. H. Conway and N. J. A. Sloane, “Quaternary constructions for the binary single-error-correcting codes of Julin, Best and others”, Designs, Codes and Cryptography 4, 31 (1994) DOI. Appears in: Best $(10,40,4)$ code, Pentacode
J. H. Conway and N. J. A. Sloane, “The antipode construction for sphere packings”, Inventiones Mathematicae 123, 309 (1996) DOI. Appears in: Antipode lattice
J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups (Springer New York, 1999) DOI. Appears in: Anticode, Antipode lattice, Best $(10,40,4)$ code, Linear binary code, Binary quadratic-residue (QR) code, Binary code, Combinatorial design, Construction-$A$ code, Coxeter-Todd $K_{12}$ lattice, Divisible code, $[24, 12, 8]$ Extended Golay code, $[2^r,2^r-r-1,4]$ Extended Hamming code, Extended GRS code, $[23, 12, 7]$ Golay code, Linear code over $G$, $[2^r-1,2^r-r-1,3]$ Hamming code, $3_{21}$ polytope code, Hexacode, $A_2$ triangular lattice, Higman-Sims graph-adjacency code, Julin-Golay code, $\Lambda_{24}$ Leech lattice, $\Lambda_{24}$ Leech lattice-shell code, Narrow-sense RS code, Octacode, Pless symmetry code, Lattice-based code, Constant-energy code, Bose–Chaudhuri–Hocquenghem (BCH) code, Linear $q$-ary code, Rectified Hessian polyhedron code, Root lattice, Self-dual linear code, Unimodular lattice, Sphere packing, Spherical code, Spherical design, Ternary Golay code, Tetracode, Witting polytope code
J. Conway and N. Sloane, “Lexicographic codes: Error-correcting codes from game theory”, IEEE Transactions on Information Theory 32, 337 (1986) DOI. Appears in: Linear binary code, Binary quadratic-residue (QR) code, Combinatorial design, $[24, 12, 8]$ Extended Golay code, $[2^r-1,2^r-r-1,3]$ Hamming code, Lexicographic code, Single parity-check (SPC) code, Tetracode
R. L. Cook, P. J. Martin, and J. M. Geremia, “Optical coherent state discrimination using a closed-loop quantum measurement”, Nature 446, 774 (2007) DOI. Appears in: On-off keyed (OOK) c-q code
R. Cools, “Constructing cubature formulae: the science behind the art”, Acta Numerica 6, 1 (1997) DOI. Appears in: $t$-design
R. Cools, “An encyclopaedia of cubature formulas”, Journal of Complexity 19, 445 (2003) DOI. Appears in: $t$-design
D. Coppersmith and M. Sudan, “Reconstructing curves in three (and higher) dimensional space from noisy data”, Proceedings of the thirty-fifth annual ACM symposium on Theory of computing 136 (2003) DOI. Appears in: Interleaved RS (IRS) code
Corbett, P., English, B., Goel, A., Grcanac, T., Kleiman, S., Leong, J., & Sankar, S. (2004, March). Row-diagonal parity for double disk failure correction. In Proceedings of the 3rd USENIX Conference on File and Storage Technologies (pp. 1-14).. Appears in: Row-Diagonal Parity (RDP) code
Cormen, T. H., Leiserson, C. E., Rivest, R. L., & Stein, C. (2022). Introduction to algorithms. MIT press.. Appears in: Block code
D. G. Cory, M. D. Price, W. Maas, E. Knill, R. Laflamme, W. H. Zurek, T. F. Havel, and S. S. Somaroo, “Experimental Quantum Error Correction”, Physical Review Letters 81, 2152 (1998) arXiv:quant-ph/9802018 DOI. Appears in: Quantum repetition code
M. C. Coşkun, G. Durisi, T. Jerkovits, G. Liva, W. Ryan, B. Stein, and F. Steiner, “Efficient Error-Correcting Codes in the Short Blocklength Regime”, (2019) arXiv:1812.08562. Appears in: Small-distance block code
A. Cossidente and G. Marino, “Veronese embedding and two–character sets”, Designs, Codes and Cryptography 42, 103 (2006) DOI. Appears in: Two-weight code
A. Cossidente and O. H. King, “Some two-character sets”, Designs, Codes and Cryptography 56, 105 (2010) DOI. Appears in: Two-weight code
S. I. R. Costa, F. Oggier, A. Campello, J.-C. Belfiore, and E. Viterbo, Lattices Applied to Coding for Reliable and Secure Communications (Springer International Publishing, 2017) DOI. Appears in: Torus-layer spherical code (TLSC)
D. J. Costello, A. E. Pusane, C. R. Jones, and D. Divsalar, “A Comparison of ARA- and Protograph-Based LDPC Block and Convolutional Codes”, 2007 Information Theory and Applications Workshop (2007) DOI. Appears in: Spatially coupled LDPC (SC-LDPC) code
D. J. Costello Jr. and G. D. Forney Jr, “Channel Coding: The Road to Channel Capacity”, (2006) arXiv:cs/0611112. Appears in: Error-correcting code (ECC), Sphere packing
J. Cotler and A. Strominger, “The Universe as a Quantum Encoder”, (2022) arXiv:2201.11658. Appears in: Pastawski-Yoshida-Harlow-Preskill (HaPPY) code, Holographic tensor-network code
A. Couvreur, “The dual minimum distance of arbitrary-dimensional algebraic–geometric codes”, Journal of Algebra 350, 84 (2012) arXiv:0905.2345 DOI. Appears in: Plane-curve code, Residue AG code
A. Couvreur, “Codes and the Cartier Operator”, (2012) arXiv:1206.4728. Appears in: Cartier code, Goppa code
A. Couvreur, P. Gaborit, V. Gauthier-Umaña, A. Otmani, and J.-P. Tillich, “Distinguisher-Based Attacks on Public-Key Cryptosystems Using Reed-Solomon Codes”, (2014) arXiv:1307.6458. Appears in: Generalized RS (GRS) code
A. Couvreur, H. Randriambololona, "Algebraic Geometry Codes and Some Applications." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI. Appears in: Elliptic code, Evaluation AG code, Evaluation code, Generalized RS (GRS) code, Goppa code, Maximum distance separable (MDS) code, Narrow-sense RS code, Bose–Chaudhuri–Hocquenghem (BCH) code, Residue AG code
A. Cowtan and S. Majid, “Algebraic Aspects of Boundaries in the Kitaev Quantum Double Model”, (2022) arXiv:2208.06317. Appears in: Hopf-algebra quantum-double code
A. Cowtan and S. Burton, “CSS code surgery as a universal construction”, Quantum 8, 1344 (2024) arXiv:2301.13738 DOI. Appears in: Qubit CSS code
H. S. M. Coxeter and J. A. Todd, “An Extreme Duodenary Form”, Canadian Journal of Mathematics 5, 384 (1953) DOI. Appears in: Coxeter-Todd $K_{12}$ lattice
H. S. M. Coxeter, L. Few, and C. A. Rogers, “Covering space with equal spheres”, Mathematika 6, 147 (1959) DOI. Appears in: Sphere packing
H. S. M. Coxeter. Regular Complex Polytopes. Cambridge University Press, 1991.. Appears in: Hessian polyhedron code, Polytope code, Rectified Hessian polyhedron code, Witting polytope code
H. S. M. Coxeter. Regular polytopes. Courier Corporation, 1973.. Appears in: 120-cell code, 24-cell code, 600-cell code, Biorthogonal spherical code, $D_4$ hyper-diamond lattice, Dodecahedron code, Polytope code, Qutrit-Pauli group-representation code, Simplex spherical code
Craig Gidney. Stim. https://github.com/quantumlib/Stim, 2021.. Appears in: Qubit stabilizer code
J. Cramer, N. Kalb, M. A. Rol, B. Hensen, M. S. Blok, M. Markham, D. J. Twitchen, R. Hanson, and T. H. Taminiau, “Repeated quantum error correction on a continuously encoded qubit by real-time feedback”, Nature Communications 7, (2016) arXiv:1508.01388 DOI. Appears in: Quantum repetition code
Crandall, Ron. "Some notes on steganography." Posted on steganography mailing list 1998 (1998): 1-6.. Appears in: $[2^r-1,2^r-r-1,3]$ Hamming code
L. Crane and D. N. Yetter, “A categorical construction of 4D TQFTs”, (1993) arXiv:hep-th/9301062. Appears in: Walker-Wang model code
L. Crane, L. H. Kauffman, and D. N. Yetter, “Evaluating the Crane-Yetter Invariant”, (1993) arXiv:hep-th/9309063. Appears in: Walker-Wang model code
L. Crane, L. H. Kauffman, and D. N. Yetter, “State-Sum Invariants of 4-Manifolds I”, (1994) arXiv:hep-th/9409167. Appears in: Walker-Wang model code
S. Cree, K. Dolev, V. Calvera, and D. J. Williamson, “Fault-Tolerant Logical Gates in Holographic Stabilizer Codes Are Severely Restricted”, PRX Quantum 2, (2021) arXiv:2103.13404 DOI. Appears in: Pastawski-Yoshida-Harlow-Preskill (HaPPY) code, Holographic tensor-network code
C. Crepeau, D. Gottesman, and A. Smith, “Approximate Quantum Error-Correcting Codes and Secret Sharing Schemes”, (2005) arXiv:quant-ph/0503139. Appears in: Approximate quantum error-correcting code (AQECC), Approximate secret-sharing code
J. du Crest, M. Mhalla, and V. Savin, “Stabilizer Inactivation for Message-Passing Decoding of Quantum LDPC Codes”, (2023) arXiv:2205.06125. Appears in: Quantum LDPC (QLDPC) code
J. du Crest, M. Mhalla, and V. Savin, “A blindness property of the Min-Sum decoding for the toric code”, (2024) arXiv:2406.14968. Appears in: Kitaev surface code
B. Criger and B. Terhal, “Noise thresholds for the [4,2,2]-concatenated toric code”, Quantum Information and Computation 16, 1261 (2016) arXiv:1604.04062 DOI. Appears in: 2D color code, Concatenated qubit code, $[[4,2,2]]$ Four-qubit code, $[[6,4,2]]$ error-detecting code, Kitaev surface code, Honeycomb (6.6.6) color code
A. W. Cross, D. P. DiVincenzo, and B. M. Terhal, “A comparative code study for quantum fault-tolerance”, (2009) arXiv:0711.1556. Appears in: Bacon-Shor code, Concatenated Steane code, Qubit BCH code, $[[23, 1, 7]]$ Quantum Golay code, $[[15,1,3]]$ quantum Reed-Muller code, Five-qubit perfect code, Kitaev surface code
A. Cross, G. Smith, J. A. Smolin, and B. Zeng, “Codeword Stabilized Quantum Codes”, IEEE Transactions on Information Theory 55, 433 (2009) arXiv:0708.1021 DOI. Appears in: Codeword stabilized (CWS) code, $((9,12,3))$ qubit code, Qubit stabilizer code, $((5+2r,3\times 2^{2r+1},2))$ Rains code, Smolin-Smith-Wehner (SSW) code, Five-qubit perfect code
A. Cross, Z. He, A. Natarajan, M. Szegedy, and G. Zhu, “Quantum Locally Testable Code with Constant Soundness”, Quantum 8, 1501 (2024) arXiv:2209.11405 DOI. Appears in: Quantum check-product code, Distance-balanced code, Quantum locally testable code (QLTC), Tensor-product code
A. Cross, Z. He, P. Rall, and T. Yoder, “Improved QLDPC Surgery: Logical Measurements and Bridging Codes”, (2024) arXiv:2407.18393. Appears in: $[[144,12,12]]$ gross code
A. Cross and D. Vandeth, “Small Binary Stabilizer Subsystem Codes”, (2025) arXiv:2501.17447. Appears in: $[[2m,2m-2,2]]$ error-detecting code, Qubit CSS code, Qubit stabilizer code, $[[6,2,2]]$ $C_6$ code, Hermitian qubit code, $[[7,1,3]]$ Steane code
Cross, Andrew William. Fault-tolerant quantum computer architectures using hierarchies of quantum error-correcting codes. Diss. Massachusetts Institute of Technology, 2008.. Appears in: Codeword stabilized (CWS) code, $((10,24,3))$ qubit code, $((9,12,3))$ qubit code, $((5+2r,3\times 2^{2r+1},2))$ Rains code, Smolin-Smith-Wehner (SSW) code, Five-qubit perfect code
G. M. Crosswhite and D. Bacon, “Automated searching for quantum subsystem codes”, Physical Review A 83, (2011) arXiv:1009.2203 DOI. Appears in: Subsystem qubit stabilizer code
D. Cruz et al., “Efficient Quantum Algorithms for GHZ and W States, and Implementation on the IBM Quantum Computer”, Advanced Quantum Technologies 2, (2019) arXiv:1807.05572 DOI. Appears in: Quantum repetition code
D. Cruz, F. A. Monteiro, and B. C. Coutinho, “Quantum Error Correction Via Noise Guessing Decoding”, IEEE Access 11, 119446 (2023) arXiv:2208.02744 DOI. Appears in: Qubit stabilizer code
I. Csiszár and J. Körner, Information Theory (Cambridge University Press, 2011) DOI. Appears in: Error-correcting code (ECC)
S. X. Cui, S.-M. Hong, and Z. Wang, “Universal quantum computation with weakly integral anyons”, Quantum Information Processing 14, 2687 (2015) arXiv:1401.7096 DOI. Appears in: Dihedral $G=D_m$ quantum-double code
S. X. Cui, D. Gottesman, and A. Krishna, “Diagonal gates in the Clifford hierarchy”, Physical Review A 95, (2017) arXiv:1608.06596 DOI. Appears in: $[[2^r-1,1,3]]$ simplex code, Qubit code, Modular-qudit code
S. X. Cui, “Four dimensional topological quantum field theories from $G$-crossed braided categories”, Quantum Topology 10, 593 (2019) arXiv:1610.07628 DOI. Appears in: $G$-enriched Walker-Wang model code
S. X. Cui, D. Ding, X. Han, G. Penington, D. Ranard, B. C. Rayhaun, and Z. Shangnan, “Kitaev’s quantum double model as an error correcting code”, Quantum 4, 331 (2020) arXiv:1908.02829 DOI. Appears in: Quantum-double code
S. X. Cui, C. Galindo, and D. Romero, “Twisted Kitaev quantum double model as local topological order”, (2024) arXiv:2411.08675. Appears in: Twisted quantum double (TQD) code
S. X. Cui, C. Galindo, and D. Romero, “Abelian Group Quantum Error Correction in Kitaev’s Model”, (2024) arXiv:2404.08552. Appears in: Abelian quantum-double stabilizer code
E. Culf, T. Vidick, and V. V. Albert, “Group coset monogamy games and an application to device-independent continuous-variable QKD”, (2022) arXiv:2212.03935. Appears in: Analog stabilizer code, Group GKP code
E. L. Cusack, “Error control codes for QAM signalling”, Electronics Letters 20, 62 (1984) DOI. Appears in: Barnes-Wall (BW) lattice, Reed-Muller (RM) code
C. D. Cushen and R. L. Hudson, “A quantum-mechanical central limit theorem”, Journal of Applied Probability 8, 454 (1971) DOI. Appears in: Binomial code, Square-lattice GKP code, GNU PI code, Spin cat code, Spin GKP code, Two-component cat code
J. Czartowski and K. Życzkowski, “Quantum Pushforward Designs”, (2024) arXiv:2412.09672. Appears in: $t$-design
A. D’Arrigo, G. Benenti, G. Falci, and C. Macchiavello, “Classical and quantum capacities of a fully correlated amplitude damping channel”, Physical Review A 88, (2013) arXiv:1309.2219 DOI. Appears in: Amplitude-damping (AD) code
A. D’Arrigo, G. Benenti, G. Falci, and C. Macchiavello, “Information transmission over an amplitude damping channel with an arbitrary degree of memory”, Physical Review A 92, (2015) arXiv:1510.05313 DOI. Appears in: Amplitude-damping (AD) code
E. B. Da Silva, R. Palazzo, and S. R. Costa, “Improving the performance of asymmetric M-PAM signal constellations in Euclidean space by embedding them in hyperbolic space”, 1998 Information Theory Workshop (Cat. No.98EX131) DOI. Appears in: Hyperbolic sphere packing, Pulse-amplitude modulation (PAM) code
A. Dahlberg and S. Wehner, “Transforming graph states using single-qubit operations”, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, 20170325 (2018) arXiv:1805.05305 DOI. Appears in: Cluster-state code, Qubit stabilizer code
A. Dahlberg, J. Helsen, and S. Wehner, “How to transform graph states using single-qubit operations: computational complexity and algorithms”, (2018) arXiv:1805.05306. Appears in: Cluster-state code, Qubit stabilizer code
S. Dai and R. Li, “Locality vs Quantum Codes”, (2024) arXiv:2409.15203. Appears in: Lattice stabilizer code
M. Dalai, “Lower Bounds on the Probability of Error for Classical and Classical-Quantum Channels”, IEEE Transactions on Information Theory 59, 8027 (2013) arXiv:1201.5411 DOI. Appears in: Classical-quantum (c-q) code
N. Dalla Pozza and G. Pierobon, “Optimality of square-root measurements in quantum state discrimination”, Physical Review A 91, (2015) arXiv:1504.04908 DOI. Appears in: Coherent-state c-q code
E. Dallas, F. Andreadakis, and D. Lidar, “No $((n,K,d< 127))$ Code Can Violate the Quantum Hamming Bound”, IEEE BITS the Information Theory Magazine 2, 33 (2022) arXiv:2208.11800 DOI. Appears in: Perfect quantum code
W. van Dam, F. Magniez, M. Mosca, and M. Santha, “Self-testing of universal and fault-tolerant sets of quantum gates”, Proceedings of the thirty-second annual ACM symposium on Theory of computing 688 (2000) arXiv:quant-ph/9904108 DOI. Appears in: Qubit stabilizer code
W. van Dam and M. Howard, “Tight Noise Thresholds for Quantum Computation with Perfect Stabilizer Operations”, Physical Review Letters 103, (2009) arXiv:0907.3189 DOI. Appears in: Qubit code
W. van Dam and M. Howard, “Noise thresholds for higher-dimensional systems using the discrete Wigner function”, Physical Review A 83, (2011) arXiv:1011.2497 DOI. Appears in: Qubit code, Modular-qudit code
O. Damen, A. Chkeif, and J.-C. Belfiore, “Lattice code decoder for space-time codes”, IEEE Communications Letters 4, 161 (2000) DOI. Appears in: Linear STC
A. K. Daniel, R. N. Alexander, and A. Miyake, “Computational universality of symmetry-protected topologically ordered cluster phases on 2D Archimedean lattices”, Quantum 4, 228 (2020) arXiv:1907.13279 DOI. Appears in: Cluster-state code, Symmetry-protected topological (SPT) code, Square-lattice cluster-state code, Lattice stabilizer code
Daniel J. Bernstein, "Understanding binary-Goppa decoding." Cryptology ePrint Archive (2022).. Appears in: Goppa code
L. E. Danielsen, “On Self-Dual Quantum Codes, Graphs, and Boolean Functions”, (2005) arXiv:quant-ph/0503236. Appears in: Qubit stabilizer code, Hermitian qubit code
L. E. Danielsen and M. G. Parker, “On the classification of all self-dual additive codes over GF(4) of length up to 12”, Journal of Combinatorial Theory, Series A 113, 1351 (2006) arXiv:math/0504522 DOI. Appears in: Dodecacode, Qubit stabilizer code, Hermitian qubit code
C. Dankert, “Efficient Simulation of Random Quantum States and Operators”, (2005) arXiv:quant-ph/0512217. Appears in: $t$-design
C. Dankert, R. Cleve, J. Emerson, and E. Livine, “Exact and approximate unitary 2-designs and their application to fidelity estimation”, Physical Review A 80, (2009) arXiv:quant-ph/0606161 DOI. Appears in: $t$-design
A. S. Darmawan and D. Poulin, “Linear-time general decoding algorithm for the surface code”, Physical Review E 97, (2018) arXiv:1801.01879 DOI. Appears in: Kitaev surface code
A. S. Darmawan, Y. Nakata, S. Tamiya, and H. Yamasaki, “Low-depth random Clifford circuits for quantum coding against Pauli noise using a tensor-network decoder”, Physical Review Research 6, (2024) arXiv:2212.05071 DOI. Appears in: Local Haar-random circuit qubit code
P. Das, A. Locharla, and C. Jones, “LILLIPUT: A Lightweight Low-Latency Lookup-Table Based Decoder for Near-term Quantum Error Correction”, (2021) arXiv:2108.06569. Appears in: Kitaev surface code
N. R. Dash, S. Dutta, R. Srikanth, and S. Banerjee, “Bounds on concatenated entanglement-assisted quantum error-correcting codes”, (2024) arXiv:2412.16082. Appears in: EA MDS code, EA qubit stabilizer code, Concatenated qubit code
R. Dastbasteh and P. Lisonek, “New quantum codes from self-dual codes over F_4”, (2022) arXiv:2211.00891. Appears in: Quantum duadic code, $[[13,1,5]]$ cyclic code, Hermitian qubit code
R. Dastbasteh, J. E. Martinez, A. Nemec, A. deMarti iOlius, and P. C. Bofill, “An infinite class of quantum codes derived from duadic constacyclic codes”, (2024) arXiv:2312.06504. Appears in: Constacyclic code, Hermitian qubit code
H. Dau, I. M. Duursma, H. M. Kiah, and O. Milenkovic, “Repairing Reed-Solomon Codes With Multiple Erasures”, IEEE Transactions on Information Theory 64, 6567 (2018) arXiv:1612.01361 DOI. Appears in: Distributed-storage code, Generalized RS (GRS) code
G. Dauphinais and D. Poulin, “Fault-Tolerant Quantum Error Correction for non-Abelian Anyons”, Communications in Mathematical Physics 355, 519 (2017) arXiv:1607.02159 DOI. Appears in: Fibonacci string-net code, String-net code
G. Dauphinais, L. Ortiz, S. Varona, and M. A. Martin-Delgado, “Quantum error correction with the semion code”, New Journal of Physics 21, 053035 (2019) arXiv:1810.08204 DOI. Appears in: Double-semion stabilizer code
G. Dauphinais, D. W. Kribs, and M. Vasmer, “Stabilizer Formalism for Operator Algebra Quantum Error Correction”, Quantum 8, 1261 (2024) arXiv:2304.11442 DOI. Appears in: Bacon-Shor code, Hybrid stabilizer code, Operator-algebra (OA) qubit stabilizer code
Davenport, H., & Hajos, G. (1951). Aufgabe 35. Math. Lapok, 58.. Appears in: Spherical code
M. C. Davey and D. J. C. MacKay, “Low density parity check codes over GF(q)”, 1998 Information Theory Workshop (Cat. No.98EX131) DOI. Appears in: $q$-ary LDPC code
David J. C. MacKay. 2002. Information Theory, Inference & Learning Algorithms. Cambridge University Press, USA. Appears in: Luby transform (LT) code
David J. C. MacKay. Information Theory, Inference and Learning Algorithms. Cambridge university press, 2003.. Appears in: Low-density parity-check (LDPC) code, Repeat-accumulate (RA) code
G. Davidoff, P. Sarnak, and A. Valette, Elementary Number Theory, Group Theory and Ramanujan Graphs (Cambridge University Press, 2001) DOI. Appears in: Expander code, Margulis LDPC code, High-dimensional expander (HDX) code
J. Davis, N. Fabre, and U. Chabaud, “Identifying quantum resources in encoded computations”, (2024) arXiv:2407.18394. Appears in: Bosonic code
N. Davis, M. E. Shirokov, and M. M. Wilde, “Energy-constrained two-way assisted private and quantum capacities of quantum channels”, Physical Review A 97, (2018) arXiv:1801.08102 DOI. Appears in: Bosonic code
A. Davydov, M. Mueger, D. Nikshych, and V. Ostrik, “The Witt group of non-degenerate braided fusion categories”, (2011) arXiv:1009.2117. Appears in: Topological code
M. Davydova, N. Tantivasadakarn, and S. Balasubramanian, “Floquet Codes without Parent Subsystem Codes”, PRX Quantum 4, (2023) arXiv:2210.02468 DOI. Appears in: Floquet color code, Fracton Floquet code, Honeycomb Floquet code
M. Davydova, N. Tantivasadakarn, S. Balasubramanian, and D. Aasen, “Quantum computation from dynamic automorphism codes”, Quantum 8, 1448 (2024) arXiv:2307.10353 DOI. Appears in: Cubic honeycomb color code, Dynamical automorphism (DA) code, Abelian topological code, Honeycomb (6.6.6) color code
C. M. Dawson and M. A. Nielsen, “The Solovay-Kitaev algorithm”, (2005) arXiv:quant-ph/0505030. Appears in: Qubit code
C. M. Dawson, H. L. Haselgrove, and M. A. Nielsen, “Noise thresholds for optical cluster-state quantum computation”, Physical Review A 73, (2006) arXiv:quant-ph/0601066 DOI. Appears in: Bosonic rotation code, $[[12,2,4]]$ carbon code, Square-lattice GKP code, Number-phase code, Qubit stabilizer code, Two-component cat code
C. M. Dawson, H. L. Haselgrove, and M. A. Nielsen, “Noise Thresholds for Optical Quantum Computers”, Physical Review Letters 96, (2006) arXiv:quant-ph/0509060 DOI. Appears in: Raussendorf-Bravyi-Harrington (RBH) cluster-state code
A. De and L. P. Pryadko, “Universal set of dynamically protected gates for bipartite qubit networks: Soft pulse implementation of the [[5,1,3]] quantum error-correcting code”, Physical Review A 93, (2016) arXiv:1509.01239 DOI. Appears in: Five-qubit perfect code
W. De Roeck, V. Khemani, Y. Li, N. O’Dea, and T. Rakovszky, “LDPC stabilizer codes as gapped quantum phases: stability under graph-local perturbations”, (2024) arXiv:2411.02384. Appears in: Commuting-projector Hamiltonian code, Hamiltonian-based code, Quantum LDPC (QLDPC) code, Topological code
D. M. Debroy and K. R. Brown, “Extended flag gadgets for low-overhead circuit verification”, Physical Review A 102, (2020) arXiv:2009.07752 DOI. Appears in: Coherent-parity-check (CPC) code, Qubit stabilizer code
D. M. Debroy, M. Li, S. Huang, and K. R. Brown, “Logical Performance of 9 Qubit Compass Codes in Ion Traps with Crosstalk Errors”, (2020) arXiv:1910.08495. Appears in: $[[9,1,3]]$ Surface-17 code
D. M. Debroy, L. Egan, C. Noel, A. Risinger, D. Zhu, D. Biswas, M. Cetina, C. Monroe, and K. R. Brown, “Optimizing Stabilizer Parities for Improved Logical Qubit Memories”, Physical Review Letters 127, (2021) arXiv:2105.05068 DOI. Appears in: $[[9,1,3]]$ Shor code
R. de Budaand W. Kassem, About lattices and the random coding theorem, in Abstracts of Papers, IEEE Inter. Symp. Info. Theory 1981, IEEE Press, NY 1981, p. 145. Appears in: Lattice-based code
L. Decreusefond and G. Zemor, “On the error-correcting capabilities of cycle codes of graphs”, Proceedings of 1994 IEEE International Symposium on Information Theory DOI. Appears in: Cycle LDPC code
J. Dehaene and B. De Moor, “Clifford group, stabilizer states, and linear and quadratic operations over GF(2)”, Physical Review A 68, (2003) arXiv:quant-ph/0304125 DOI. Appears in: Qubit stabilizer code, Qubit code
C. Delaney, K. P. Seshadreesan, I. MacCormack, A. Galda, S. Guha, and P. Narang, “Demonstration of a quantum advantage by a joint detection receiver for optical communication using quantum belief propagation on a trapped-ion device”, Physical Review A 106, (2022) arXiv:2102.13052 DOI. Appears in: BPSK c-q code
Delaunay, B. N., and S. S. Ryskov. "Solution of the problem of least dense lattice covering of a four-dimensional space by equal spheres." Sov. Math. Dokl. Vol. 4. 1963.. Appears in: $A_n^{\perp}$ lattice
C. Delcamp and A. Tiwari, “From gauge to higher gauge models of topological phases”, Journal of High Energy Physics 2018, (2018) arXiv:1802.10104 DOI. Appears in: Two-gauge theory code
C. Delcamp and A. Tiwari, “On 2-form gauge models of topological phases”, Journal of High Energy Physics 2019, (2019) arXiv:1901.02249 DOI. Appears in: Walker-Wang model code, Two-gauge theory code
N. Delfosse and G. Zémor, “Upper Bounds on the Rate of Low Density Stabilizer Codes for the Quantum Erasure Channel”, (2012) arXiv:1205.7036. Appears in: Quantum LDPC (QLDPC) code, 2D hyperbolic surface code
N. Delfosse, “Tradeoffs for reliable quantum information storage in surface codes and color codes”, 2013 IEEE International Symposium on Information Theory 917 (2013) arXiv:1301.6588 DOI. Appears in: 2D color code, Homological code, Hyperbolic color code
N. Delfosse, “Decoding color codes by projection onto surface codes”, Physical Review A 89, (2014) arXiv:1308.6207 DOI. Appears in: 2D color code, Honeycomb (6.6.6) color code
N. Delfosse, P. Iyer, and D. Poulin, “Generalized surface codes and packing of logical qubits”, (2016) arXiv:1606.07116. Appears in: Homological code, Rotated surface code, Kitaev surface code
N. Delfosse and B. W. Reichardt, “Short Shor-style syndrome sequences”, (2020) arXiv:2008.05051. Appears in: Hypercube code, $[[15, 7, 3]]$ quantum Hamming code, $[[16,6,4]]$ Tesseract color code
N. Delfosse and G. Zémor, “Linear-time maximum likelihood decoding of surface codes over the quantum erasure channel”, Physical Review Research 2, (2020) arXiv:1703.01517 DOI. Appears in: 3D surface code, Crystalline-circuit qubit code, Kitaev surface code
N. Delfosse, “Hierarchical decoding to reduce hardware requirements for quantum computing”, (2020) arXiv:2001.11427. Appears in: Kitaev surface code
N. Delfosse, M. E. Beverland, and M. A. Tremblay, “Bounds on stabilizer measurement circuits and obstructions to local implementations of quantum LDPC codes”, (2021) arXiv:2109.14599. Appears in: Hierarchical code, Hypergraph product (HGP) code, Quantum LDPC (QLDPC) code, Quantum expander code
N. Delfosse and M. B. Hastings, “Union-Find Decoders For Homological Product Codes”, Quantum 5, 406 (2021) arXiv:2009.14226 DOI. Appears in: Homological product code
N. Delfosse and N. H. Nickerson, “Almost-linear time decoding algorithm for topological codes”, Quantum 5, 595 (2021) arXiv:1709.06218 DOI. Appears in: Kitaev surface code
N. Delfosse, B. W. Reichardt, and K. M. Svore, “Beyond Single-Shot Fault-Tolerant Quantum Error Correction”, IEEE Transactions on Information Theory 68, 287 (2022) arXiv:2002.05180 DOI. Appears in: Qubit CSS code, Single-shot code
N. Delfosse and A. Paetznick, “Spacetime codes of Clifford circuits”, (2023) arXiv:2304.05943. Appears in: Quantum LDPC (QLDPC) code, Spacetime circuit code, Subsystem spacetime circuit code, Kitaev surface code
N. Delfosse, A. Paetznick, J. Haah, and M. B. Hastings, “Splitting decoders for correcting hypergraph faults”, (2023) arXiv:2309.15354. Appears in: Qubit stabilizer code
N. Delfosse and G. Zémor, “Correction of circuit faults in a stacked quantum memory using rank-metric codes”, (2024) arXiv:2411.09173. Appears in: Gabidulin code, Quantum Gabidulin code
N. Delfosse and E. Tham, “Low-cost noise reduction for Clifford circuits”, (2024) arXiv:2407.06583. Appears in: Coherent-parity-check (CPC) code, Qubit stabilizer code
P. Delsarte, “On cyclic codes that are invariant under the general linear group”, IEEE Transactions on Information Theory 16, 760 (1970) DOI. Appears in: Generalized RM (GRM) code, Cyclic linear $q$-ary code
P. Delsarte, J. M. Goethals, and F. J. Mac Williams, “On generalized ReedMuller codes and their relatives”, Information and Control 16, 403 (1970) DOI. Appears in: Generalized RM (GRM) code
P. Delsarte, “Four fundamental parameters of a code and their combinatorial significance”, Information and Control 23, 407 (1973) DOI. Appears in: Orthogonal array (OA), Perfect binary code, $q$-ary code
P. Delsarte and J. M. Goethals, “Unrestricted codes with the golay parameters are unique”, Discrete Mathematics 12, 211 (1975) DOI. Appears in: $[24, 12, 8]$ Extended Golay code, $[23, 12, 7]$ Golay code, Self-dual linear code, Ternary Golay code
P. Delsarte and J. M. Goethals, “Alternating bilinear forms over GF(q)”, Journal of Combinatorial Theory, Series A 19, 26 (1975) DOI. Appears in: Delsarte-Goethals (DG) code, Goethals code, Hergert code, Preparata code, Reed-Muller (RM) code
P. Delsarte, “On subfield subcodes of modified Reed-Solomon codes (Corresp.)”, IEEE Transactions on Information Theory 21, 575 (1975) DOI. Appears in: Alternant code, Generalized RS (GRS) code
P. Delsarte, “Association schemes and t-designs in regular semilattices”, Journal of Combinatorial Theory, Series A 20, 230 (1976) DOI. Appears in: Constant-weight code
P. Delsarte, J. M. Goethals, and J. J. Seidel, “Spherical codes and designs”, Geometriae Dedicata 6, 363 (1977) DOI. Appears in: $[23, 12, 7]$ Golay code, Icosahedron code, $\Lambda_{24}$ Leech lattice-shell code, Spherical code, Spherical design, $t$-design
P. Delsarte, “Bilinear forms over a finite field, with applications to coding theory”, Journal of Combinatorial Theory, Series A 25, 226 (1978) DOI. Appears in: Gabidulin code, Maximum-rank distance (MRD) code, Rank-metric code
P. Delsarte and V. I. Levenshtein, “Association schemes and coding theory”, IEEE Transactions on Information Theory 44, 2477 (1998) DOI. Appears in: $[24, 12, 8]$ Extended Golay code, Orthogonal array (OA), $t$-design
Ph. Delsarte, “Weights of linear codes and strongly regular normed spaces”, Discrete Mathematics 3, 47 (1972) DOI. Appears in: Projective two-weight code
Ph. Delsarte, “Hahn Polynomials, Discrete Harmonics, andt-Designs”, SIAM Journal on Applied Mathematics 34, 157 (1978) DOI. Appears in: Constant-weight code, Orthogonal array (OA), Subspace design, $t$-design
P. Delsarte, “Bounds for unrestricted codes, by linear programming,” Philips Research Reports, vol. 27, pp. 272–289, 1972. Appears in: Universally optimal $q$-ary code
Delsarte, Philippe. "An algebraic approach to the association schemes of coding theory." Philips Res. Rep. Suppl. 10 (1973). Appears in: Completely regular code
Delsarte, Philippe. "An algebraic approach to the association schemes of coding theory." Philips Res. Rep. Suppl. 10 (1973): vi+-97.. Appears in: Combinatorial design, Constant-weight code, Orthogonal array (OA), Subspace design, $t$-design
Delsarte, Philippe. "Bounds for unrestricted codes, by linear programming." (1972).. Appears in: Binary code, Orthogonal array (OA)
R. Demkowicz-Dobrzański, J. Czajkowski, and P. Sekatski, “Adaptive Quantum Metrology under General Markovian Noise”, Physical Review X 7, (2017) arXiv:1704.06280 DOI. Appears in: Error-corrected sensing code
B. Demoen, P. Vanheuverzwijn, and A. Verbeure, “Completely positive quasi-free maps of the CCR-algebra”, Reports on Mathematical Physics 15, 27 (1979) DOI. Appears in: Bosonic code
J. M. Dempster, B. Fu, D. G. Ferguson, D. I. Schuster, and J. Koch, “Understanding degenerate ground states of a protected quantum circuit in the presence of disorder”, Physical Review B 90, (2014) arXiv:1402.7310 DOI. Appears in: Zero-pi qubit code
J. Dengis, R. König, and F. Pastawski, “An optimal dissipative encoder for the toric code”, New Journal of Physics 16, 013023 (2014) arXiv:1310.1036 DOI. Appears in: Qubit stabilizer code, Toric code
E. Dennis, “Toward fault-tolerant quantum computation without concatenation”, Physical Review A 63, (2001) arXiv:quant-ph/9905027 DOI. Appears in: Qubit stabilizer code
E. Dennis, A. Kitaev, A. Landahl, and J. Preskill, “Topological quantum memory”, Journal of Mathematical Physics 43, 4452 (2002) arXiv:quant-ph/0110143 DOI. Appears in: 2D lattice stabilizer code, 3D surface code, Loop toric code, Bacon-Shor code, Clifford-deformed surface code (CDSC), Cluster-state code, Homological code, Quantum LDPC (QLDPC) code, Quantum-double code, Qubit CSS code, Qubit stabilizer code, Qubit code, Raussendorf-Bravyi-Harrington (RBH) cluster-state code, Rotated surface code, Self-correcting quantum code, Single-shot code, Kitaev surface code, Toric code
R. H. F. Denniston, “Some maximal arcs in finite projective planes”, Journal of Combinatorial Theory 6, 317 (1969) DOI. Appears in: Denniston code
A. Denys and A. Leverrier, “The 2T-qutrit, a two-mode bosonic qutrit”, Quantum 7, 1032 (2023) arXiv:2210.16188 DOI. Appears in: 2T-qutrit code
A. Denys and A. Leverrier, “Quantum error-correcting codes with a covariant encoding”, (2024) arXiv:2306.11621. Appears in: Cat code, Clifford group-representation QSC, Covariant block quantum code, Group-representation code, Clifford spin code, One-hot quantum code, Five-qubit perfect code, $[[7,1,3]]$ Steane code, $SU(3)$ spin code
C. Derby, J. Klassen, J. Bausch, and T. Cubitt, “Compact fermion to qubit mappings”, Physical Review B 104, (2021) arXiv:2003.06939 DOI. Appears in: Derby-Klassen (DK) code, Fermion-into-qubit code
C. Derby and J. Klassen, “A Compact Fermion to Qubit Mapping Part 2: Alternative Lattice Geometries”, (2021) arXiv:2101.10735. Appears in: Derby-Klassen (DK) code
Derby, Charles. Compact fermion to qubit mappings for quantum simulation. Diss. UCL (University College London), 2023.. Appears in: 2D color code, Ball-Verstraete-Cirac (BVC) code, Derby-Klassen (DK) code, Rotated surface code
P.-J. H. S. Derks, A. Townsend-Teague, A. G. Burchards, and J. Eisert, “Designing fault-tolerant circuits using detector error models”, (2024) arXiv:2407.13826. Appears in: Qubit stabilizer code, Honeycomb (6.6.6) color code
É. Descamps, A. Keller, and P. Milman, “Gottesman-Kitaev-Preskill Encoding in Continuous Modal Variables of Single Photons”, Physical Review Letters 132, (2024) arXiv:2310.12618 DOI. Appears in: Square-lattice GKP code
E. Descamps, A. Saharyan, A. Chivet, A. Keller, and P. Milman, “Modes, states and superselection rules in quantum optics and quantum information”, (2025) arXiv:2501.03943. Appears in: Bosonic code
B. Desef and M. B. Plenio, “Optimizing quantum codes with an application to the loss channel with partial erasure information”, Quantum 6, 667 (2022) arXiv:2105.13233 DOI. Appears in: Permutation-invariant (PI) code
D. Deutsch, “Uncertainty in Quantum Measurements”, Physical Review Letters 50, 631 (1983) DOI. Appears in: Qubit CSS code
S. Devadas and A. R. Newton, “Decomposition and factorization of sequential finite state machines”, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 8, 1206 (1989) DOI. Appears in: One-hot code
T. Devakul and D. J. Williamson, “Universal quantum computation using fractal symmetry-protected cluster phases”, Physical Review A 98, (2018) arXiv:1806.04663 DOI. Appears in: Cluster-state code, Symmetry-protected topological (SPT) code, Square-lattice cluster-state code, Lattice stabilizer code
I. Devetak and P. W. Shor, “The capacity of a quantum channel for simultaneous transmission of classical and quantum information”, (2004) arXiv:quant-ph/0311131. Appears in: Hybrid QECC
I. Devetak, “The private classical capacity and quantum capacity of a quantum channel”, (2004) arXiv:quant-ph/0304127. Appears in: Haar-random qubit code, Quantum error-correcting code (QECC)
I. Devetak, A. W. Harrow, and A. Winter, “A Family of Quantum Protocols”, Physical Review Letters 93, (2004) arXiv:quant-ph/0308044 DOI. Appears in: Maximal-entanglement EA Galois-qudit stabilizer code
I. Devetak, A. W. Harrow, and A. J. Winter, “A Resource Framework for Quantum Shannon Theory”, IEEE Transactions on Information Theory 54, 4587 (2008) arXiv:quant-ph/0512015 DOI. Appears in: Maximal-entanglement EA Galois-qudit stabilizer code
S. J. Devitt, A. G. Fowler, A. M. Stephens, A. D. Greentree, L. C. L. Hollenberg, W. J. Munro, and K. Nemoto, “Architectural design for a topological cluster state quantum computer”, New Journal of Physics 11, 083032 (2009) arXiv:0808.1782 DOI. Appears in: Cluster-state code
S. J. Devitt, W. J. Munro, and K. Nemoto, “Quantum error correction for beginners”, Reports on Progress in Physics 76, 076001 (2013) arXiv:0905.2794 DOI. Appears in: Quantum error-correcting code (QECC)
C. Di, T. J. Richardson, and R. L. Urbanke, “Weight Distribution of Low-Density Parity-Check Codes”, IEEE Transactions on Information Theory 52, 4839 (2006) DOI. Appears in: Irregular LDPC code
C. Di Martino, Z. Kalbarczyk, R. K. Iyer, F. Baccanico, J. Fullop, and W. Kramer, “Lessons Learned from the Analysis of System Failures at Petascale: The Case of Blue Waters”, 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks (2014) DOI. Appears in: Error-correcting code (ECC)
B. Dias and R. König, “Classical simulation of non-Gaussian bosonic circuits”, Physical Review A 110, (2024) arXiv:2403.19059 DOI. Appears in: Bosonic code
L. DiCarlo, M. D. Reed, L. Sun, B. R. Johnson, J. M. Chow, J. M. Gambetta, L. Frunzio, S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, “Preparation and measurement of three-qubit entanglement in a superconducting circuit”, Nature 467, 574 (2010) arXiv:1004.4324 DOI. Appears in: Quantum repetition code
N. Didier, J. Bourassa, and A. Blais, “Fast Quantum Nondemolition Readout by Parametric Modulation of Longitudinal Qubit-Oscillator Interaction”, Physical Review Letters 115, (2015) DOI. Appears in: Very small logical qubit (VSLQ) code
T. G. Dietterich and G. Bakiri, “Solving Multiclass Learning Problems via Error-Correcting Output Codes”, (1995) arXiv:cs/9501101. Appears in: Binary BCH code, Error-correcting output code (ECOC), Hadamard code
R. Dijkgraaf and E. Witten, “Topological gauge theories and group cohomology”, Communications in Mathematical Physics 129, 393 (1990) DOI. Appears in: Dijkgraaf-Witten gauge theory code
R. Dijkgraaf and E. Witten, “Topological gauge theories and group cohomology”, Communications in Mathematical Physics 129, 393 (1990) DOI. Appears in: Chiral semion Walker-Wang model code, Dijkgraaf-Witten gauge theory code, Double-semion stabilizer code, Abelian TQD stabilizer code
R. Dijkgraaf, V. Pasquier, and P. Roche, “Quasi hope algebras, group cohomology and orbifold models”, Nuclear Physics B - Proceedings Supplements 18, 60 (1991) DOI. Appears in: Twisted quantum double (TQD) code
A. G. Dimakis, P. B. Godfrey, Y. Wu, M. J. Wainwright, and K. Ramchandran, “Network Coding for Distributed Storage Systems”, IEEE Transactions on Information Theory 56, 4539 (2010) DOI. Appears in: Product-matrix (PM) code, Regenerating code (RGC)
M. T. DiMario and F. E. Becerra, “Robust Measurement for the Discrimination of Binary Coherent States”, Physical Review Letters 121, (2018) arXiv:1807.05199 DOI. Appears in: BPSK c-q code
M. T. DiMario, L. Kunz, K. Banaszek, and F. E. Becerra, “Optimized communication strategies with binary coherent states over phase noise channels”, npj Quantum Information 5, (2019) arXiv:1907.12515 DOI. Appears in: BPSK c-q code
M. T. DiMario and F. E. Becerra, “Phase tracking for sub-shot-noise-limited receivers”, Physical Review Research 2, (2020) DOI. Appears in: BPSK c-q code
M. T. DiMario and F. E. Becerra, “Demonstration of optimal non-projective measurement of binary coherent states with photon counting”, npj Quantum Information 8, (2022) arXiv:2207.12234 DOI. Appears in: BPSK c-q code, PSK c-q code
C. Ding, Codes from Difference Sets (WORLD SCIENTIFIC, 2014) DOI. Appears in: Difference-set cyclic (DSC) code, Generalized RM (GRM) code, Hadamard code, Hyperoval code
C. Ding, H. Liu, and V. D. Tonchev, “All binary linear codes that are invariant under $\PSL_2(n)$”, (2017) arXiv:1704.01199. Appears in: Quadratic-residue (QR) code
C. Ding and C. Tang, “Infinite families of near MDS codes holding $t$-designs”, (2019) arXiv:1910.08265. Appears in: Binary BCH code, Combinatorial design
C. Ding, C. Tang, and V. D. Tonchev, “The Projective General Linear Group $\mathrm{PGL}_2(\mathrm{GF}(2^m))$ and Linear Codes of Length $2^m+1$”, (2020) arXiv:2010.09448. Appears in: Combinatorial design, Cyclic linear $q$-ary code
H. Q. Dinh, T. Bag, A. K. Upadhyay, R. Bandi, and R. Tansuchat, “A class of skew cyclic codes and application in quantum codes construction”, Discrete Mathematics 344, 112189 (2021) DOI. Appears in: Quantum maximum-distance-separable (MDS) code, Skew-cyclic CSS code
I. Dinur, M. Sudan, and A. Wigderson, “Robust Local Testability of Tensor Products of LDPC Codes”, Lecture Notes in Computer Science 304 (2006) DOI. Appears in: Low-density parity-check (LDPC) code, Tensor-product code
I. Dinur, “The PCP theorem by gap amplification”, Journal of the ACM 54, 12 (2007) DOI. Appears in: Dinur code, Tensor-product code
I. Dinur, S. Evra, R. Livne, A. Lubotzky, and S. Mozes, “Locally Testable Codes with constant rate, distance, and locality”, (2021) arXiv:2111.04808. Appears in: Balanced product (BP) code, Left-right Cayley complex code, Locally testable code (LTC), Tensor-product code
I. Dinur, M.-H. Hsieh, T.-C. Lin, and T. Vidick, “Good Quantum LDPC Codes with Linear Time Decoders”, (2022) arXiv:2206.07750. Appears in: Dinur-Hsieh-Lin-Vidick (DHLV) code, Tensor-product code
I. Dinur, T.-C. Lin, and T. Vidick, “Expansion of higher-dimensional cubical complexes with application to quantum locally testable codes”, (2024) arXiv:2402.07476. Appears in: Dinur-Lin-Vidick (DLV) code, Quantum locally testable code (QLTC)
D. P. DiVincenzo and P. W. Shor, “Fault-Tolerant Error Correction with Efficient Quantum Codes”, Physical Review Letters 77, 3260 (1996) arXiv:quant-ph/9605031 DOI. Appears in: Quantum data-syndrome (QDS) code, Qubit stabilizer code, Five-qubit perfect code, Subsystem spacetime circuit code
D. P. DiVincenzo and P. Aliferis, “Effective Fault-Tolerant Quantum Computation with Slow Measurements”, Physical Review Letters 98, (2007) arXiv:quant-ph/0607047 DOI. Appears in: Hypergraph product (HGP) code, Qubit stabilizer code, Qubit code
D. Divsalar, S. Dolinar, J. Thorpe, and C. Jones, “Constructing LDPC codes from simple loop-free encoding modules”, IEEE International Conference on Communications, 2005. ICC 2005. 2005 DOI. Appears in: Protograph LDPC code, Repeat-accumulate-accumulate (RAA) code
D. Divsalar and F. Pollara, “Turbo codes for PCS applications”, Proceedings IEEE International Conference on Communications ICC ’95 DOI. Appears in: Turbo code
D. Divsalar, C. Jones, S. Dolinar, and J. Thorpe, “Protograph based LDPC codes with minimum distance linearly growing with block size”, GLOBECOM ’05. IEEE Global Telecommunications Conference, 2005. (2005) DOI. Appears in: Accumulate-repeat-accumulate (ARA) code, Irregular repeat-accumulate (IRA) code, Protograph LDPC code
D. Divsalar, S. Dolinar, and C. Jones, “Protograph LDPC Codes over Burst Erasure Channels”, MILCOM 2006 (2006) DOI. Appears in: Protograph LDPC code
D. Divsalar and L. Dolecek, “Enumerators for protograph-based ensembles of nonbinary LDPC codes”, 2011 IEEE International Symposium on Information Theory Proceedings (2011) DOI. Appears in: $q$-ary protograph LDPC code
D. Divsalar and L. Dolecek, “On the typical minimum distance of protograph-based non-binary LDPC codes”, 2012 Information Theory and Applications Workshop (2012) DOI. Appears in: $q$-ary protograph LDPC code
Divsalar, Dariush, and Fabrizio Pollara. "Turbo codes for deep-space communications." The Telecommunications and Data Acquisition Report 29-39 (SEE N95-21532 06-32) (1995).. Appears in: Turbo code
Divsalar, Dariush, Hui Jin, and Robert J. McEliece. "Coding theorems for" turbo-like" codes." Proceedings of the annual Allerton Conference on Communication control and Computing. Vol. 36. University Of Illinois, 1998.. Appears in: Repeat-accumulate (RA) code
I. B. Djordjevic, “Photonic entanglement-assisted quantum low-density parity-check encoders and decoders”, Optics Letters 35, 1464 (2010) DOI. Appears in: EA QLDPC code
I. Djurdjevic, Jun Xu, K. Abdel-Ghaffar, and Shu Lin, “A class of low-density parity-check codes constructed based on Reed-Solomon codes with two information symbols”, IEEE Communications Letters 7, 317 (2003) DOI. Appears in: Quasi-cyclic LDPC (QC-LDPC) code
V. V. Dodonov, I. A. Malkin, and V. I. Man’ko, “Even and odd coherent states and excitations of a singular oscillator”, Physica 72, 597 (1974) DOI. Appears in: Cat code, Two-component cat code
S. M. Dodunekov and I. N. Landgev, “On near-MDS codes”, Proceedings of 1994 IEEE International Symposium on Information Theory 427 DOI. Appears in: Maximum distance separable (MDS) code, Projective geometry code
S. M. Dodunekov and J. E. M. Nilsson, “Algebraic decoding of the Zetterberg codes”, IEEE Transactions on Information Theory 38, 1570 (1992) DOI. Appears in: Quasi-perfect code, Zetterberg code
S. Dodunekov, Optimal linear codes, Ph.D. Thesis, Sofia, 1985.. Appears in: Griesmer code
Doherty, A., Gimeno-segovia, M., Litinski, D., Nickerson, N., Pant, M., Rudolph, T. and Sparrow, C., Psiquantum, Corp., 2024. GENERATION AND MEASUREMENT OF ENTANGLED SYSTEMS OF PHOTONIC GKP QUBITS. U.S. Patent Application 18/273,753.. Appears in: Fusion-based quantum computing (FBQC) code, Square-lattice GKP code
L. Dolecek, D. Divsalar, Y. Sun, and B. Amiri, “Non-Binary Protograph-Based LDPC Codes: Enumerators, Analysis, and Designs”, IEEE Transactions on Information Theory 60, 3913 (2014) DOI. Appears in: $q$-ary protograph LDPC code
K. Dolev, V. Calvera, S. S. Cree, and D. J. Williamson, “Gauging the bulk: generalized gauging maps and holographic codes”, Journal of High Energy Physics 2022, (2022) arXiv:2108.11402 DOI. Appears in: Pastawski-Yoshida-Harlow-Preskill (HaPPY) code, Holographic tensor-network code
S. J. Dolinar, Jr., “A near-optimum receiver structure for the detection of M-ary optical PPM signals”, The Telecommunications and Data Acquisition Progress Report 42 72: December 1982; NASA: Pasadena, CA, (1983). Appears in: PPM c-q code
Dolinar, Samuel Joseph. "An optimum receiver for the binary coherent state quantum channel." Research Laboratory of Electronics, MIT, Quarterly Progress Report 11 (1973): 115-120.. Appears in: On-off keyed (OOK) c-q code
W. Donnelly, D. Marolf, B. Michel, and J. Wien, “Living on the edge: a toy model for holographic reconstruction of algebras with centers”, Journal of High Energy Physics 2017, (2017) arXiv:1611.05841 DOI. Appears in: Pastawski-Yoshida-Harlow-Preskill (HaPPY) code
S. Doplicher, R. Haag, and J. E. Roberts, “Local observables and particle statistics I”, Communications in Mathematical Physics 23, 199 (1971) DOI. Appears in: Topological code
S. Doplicher, R. Haag, and J. E. Roberts, “Local observables and particle statistics II”, Communications in Mathematical Physics 35, 49 (1974) DOI. Appears in: Topological code
J. Dorier, F. Becca, and F. Mila, “Quantum compass model on the square lattice”, Physical Review B 72, (2005) arXiv:cond-mat/0501708 DOI. Appears in: Bacon-Shor code, Compass code, Hamiltonian-based code
D. Doron, J. Mosheiff, and M. Wootters, “When Do Low-Rate Concatenated Codes Approach The Gilbert-Varshamov Bound?”, (2024) arXiv:2405.08584. Appears in: Concatenated code
M. Doroudiani and V. Karimipour, “Planar maximally entangled states”, Physical Review A 102, (2020) arXiv:2004.00906 DOI. Appears in: Planar-perfect-tensor code
B. Douçot and J. Vidal, “Pairing of Cooper Pairs in a Fully Frustrated Josephson-Junction Chain”, Physical Review Letters 88, (2002) arXiv:cond-mat/0202115 DOI. Appears in: Zero-pi qubit code
B. Douçot, M. V. Feigel’man, L. B. Ioffe, and A. S. Ioselevich, “Protected qubits and Chern-Simons theories in Josephson junction arrays”, Physical Review B 71, (2005) arXiv:cond-mat/0403712 DOI. Appears in: Quantum parity code (QPC)
B. Douçot and L. B. Ioffe, “Physical implementation of protected qubits”, Reports on Progress in Physics 75, 072001 (2012) DOI. Appears in: Quantum parity code (QPC)
S. T. Dougherty, J. Gildea, R. Taylor, and A. Tylyshchak, “Group rings, G-codes and constructions of self-dual and formally self-dual codes”, Designs, Codes and Cryptography 86, 2115 (2017) DOI. Appears in: $[24, 12, 8]$ Extended Golay code, Group-algebra code
S. Dougherty, J.-L. Kim, and P. Solé, “Open Problems in Coding Theory”, Noncommutative Rings and Their Applications 79 (2015) DOI. Appears in: Error-correcting code (ECC), Self-dual linear code
S. T. Dougherty, "Codes over rings." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI. Appears in: Gray code, Quaternary linear code over $\mathbb{Z}_4$, Reed-Muller (RM) code
M. Dowling and S. Gao, “Fast Decoding of Expander Codes”, IEEE Transactions on Information Theory 64, 972 (2018) DOI. Appears in: Expander code
C. Downey and J. Karlof, “On the existence of&lt;tex&gt;[M, n]&lt;/tex&gt;group codes for the Gaussian channel with&lt;tex&gt;[M, n]&lt;/tex&gt;odd”, IEEE Transactions on Information Theory 23, 500 (1977) DOI. Appears in: Slepian group-orbit code
M. Du, C. Zhang, Y.-T. Poon, and B. Zeng, “Characterizing Quantum Codes via the Coefficients in Knill-Laflamme Conditions”, (2024) arXiv:2410.07983. Appears in: Approximate quantum error-correcting code (AQECC), $((7,2,3))$ Pollatsek-Ruskai code, $[[7,1,3]]$ Steane code
A. Dua, I. H. Kim, M. Cheng, and D. J. Williamson, “Sorting topological stabilizer models in three dimensions”, Physical Review B 100, (2019) arXiv:1908.08049 DOI. Appears in: 3D fermionic surface code, 3D lattice stabilizer code, 3D surface code, Chamon model code, Fibonacci fractal spin-liquid code, Type-II fractal spin-liquid code, Fracton stabilizer code, Haah cubic code (CC), Hsieh-Halasz (HH) code, Hsieh-Halasz-Balents (HHB) code, Qudit cubic code, Sierpinsky fractal spin-liquid (SFSL) code, Kitaev surface code, Abelian topological code, X-cube model code
A. Dua, A. Kubica, L. Jiang, S. T. Flammia, and M. J. Gullans, “Clifford-Deformed Surface Codes”, PRX Quantum 5, (2024) arXiv:2201.07802 DOI. Appears in: Asymmetric quantum code, Clifford-deformed surface code (CDSC), Dynamically-generated QECC
A. Dua, N. Tantivasadakarn, J. Sullivan, and T. D. Ellison, “Engineering 3D Floquet Codes by Rewinding”, PRX Quantum 5, (2024) arXiv:2307.13668 DOI. Appears in: XYZ ruby Floquet code
A. Dua, T. Jochym-O'Connor, and G. Zhu, “Quantum error correction with fractal topological codes”, Quantum 7, 1122 (2023) arXiv:2201.03568 DOI. Appears in: Fractal surface code
R. Duan, M. Grassl, Z. Ji, and B. Zeng, “Multi-error-correcting amplitude damping codes”, 2010 IEEE International Symposium on Information Theory (2010) arXiv:1001.2356 DOI. Appears in: Amplitude-damping (AD) code, Constant-excitation (CE) code, Dual-rail quantum code, Concatenated bosonic code, Quantum parity code (QPC), Concatenated qubit code, Qubit CSS code, Qubit stabilizer code, $[[4,2,2]]$ Four-qubit code
K. S. Dubovitskii, “Bit-flip errors in dissipative cat qubits: Second-order perturbation theory”, Physical Review A 111, (2025) arXiv:2407.17299 DOI. Appears in: Two-component cat code
G. Duclos-Cianci and D. Poulin, “A renormalization group decoding algorithm for topological quantum codes”, (2010) arXiv:1006.1362. Appears in: 2D lattice stabilizer code
G. Duclos-Cianci and D. Poulin, “Fast Decoders for Topological Quantum Codes”, Physical Review Letters 104, (2010) arXiv:0911.0581 DOI. Appears in: Kitaev surface code, Toric code
G. Duclos-Cianci and D. Poulin, “Fault-Tolerant Renormalization Group Decoder for Abelian Topological Codes”, (2013) arXiv:1304.6100. Appears in: Kitaev surface code
G. Duclos-Cianci and D. Poulin, “Reducing the quantum-computing overhead with complex gate distillation”, Physical Review A 91, (2015) arXiv:1403.5280 DOI. Appears in: Qubit stabilizer code
Duclos-Cianci, Guillaume, Héctor Bombın, and David Poulin. "Fast decoding algorithm for subspace and subsystem color codes and local equivalence of topological phases." Personal communication (2011).. Appears in: Square-octagon (4.8.8) color code
G. Dueck and J. Korner, “Reliability function of a discrete memoryless channel at rates above capacity (Corresp.)”, IEEE Transactions on Information Theory 25, 82 (1979) DOI. Appears in: Error-correcting code (ECC)
K. R. Duffy, J. Li, and M. Medard, “Guessing noise, not code-words”, 2018 IEEE International Symposium on Information Theory (ISIT) (2018) DOI. Appears in: Finite-dimensional error-correcting code (ECC)
K. R. Duffy, J. Li, and M. Medard, “Capacity-Achieving Guessing Random Additive Noise Decoding”, IEEE Transactions on Information Theory 65, 4023 (2019) arXiv:1802.07010 DOI. Appears in: Finite-dimensional error-correcting code (ECC)
K. Duivenvoorden, N. P. Breuckmann, and B. M. Terhal, “Renormalization Group Decoder for a Four-Dimensional Toric Code”, IEEE Transactions on Information Theory 65, 2545 (2019) arXiv:1708.09286 DOI. Appears in: 3D surface code, Loop toric code, Homological code, Quantum repetition code
T. M. Duman and M. Salehi, “New performance bounds for turbo codes”, IEEE Transactions on Communications 46, 717 (1998) DOI. Appears in: Turbo code
I. Dumer, “Maximum likelihood decoding with reduced complexity”, Proceedings of IEEE International Symposium on Information Theory 396 DOI. Appears in: Linear $q$-ary code
I. Dumer, A. A. Kovalev, and L. P. Pryadko, “Thresholds for Correcting Errors, Erasures, and Faulty Syndrome Measurements in Degenerate Quantum Codes”, Physical Review Letters 115, (2015) arXiv:1412.6172 DOI. Appears in: Quantum LDPC (QLDPC) code, Qubit CSS code
Dumer, Ilya I. "Concatenated codes and their multilevel generalizations." Handbook of coding theory (1998).. Appears in: Generalized concatenated code (GCC)
R. Duncan and M. Lucas, “Verifying the Steane code with Quantomatic”, Electronic Proceedings in Theoretical Computer Science 171, 33 (2014) arXiv:1306.4532 DOI. Appears in: $[[7,1,3]]$ Steane code
F. Dupuis, “The decoupling approach to quantum information theory”, (2010) arXiv:1004.1641. Appears in: Approximate quantum error-correcting code (AQECC)
F. Dupuis, M. Berta, J. Wullschleger, and R. Renner, “One-Shot Decoupling”, Communications in Mathematical Physics 328, 251 (2014) arXiv:1012.6044 DOI. Appears in: Approximate quantum error-correcting code (AQECC)
A. Dür, “The automorphism groups of Reed-Solomon codes”, Journal of Combinatorial Theory, Series A 44, 69 (1987) DOI. Appears in: Extended GRS code
W. Dür, G. Vidal, and J. I. Cirac, “Three qubits can be entangled in two inequivalent ways”, Physical Review A 62, (2000) arXiv:quant-ph/0005115 DOI. Appears in: W-state code
W. Dür and H.-J. Briegel, “Entanglement Purification for Quantum Computation”, Physical Review Letters 90, (2003) arXiv:quant-ph/0210069 DOI. Appears in: Qubit CSS code
W. Dür, L. Hartmann, M. Hein, M. Lewenstein, and H.-J. Briegel, “Entanglement in Spin Chains and Lattices with Long-Range Ising-Type Interactions”, Physical Review Letters 94, (2005) arXiv:quant-ph/0407075 DOI. Appears in: Cluster-state code, XP stabilizer code
W. Dür and H. J. Briegel, “Entanglement purification and quantum error correction”, Reports on Progress in Physics 70, 1381 (2007) arXiv:0705.4165 DOI. Appears in: Cluster-state code
T. DURT, B.-G. ENGLERT, I. BENGTSSON, and K. ŻYCZKOWSKI, “ON MUTUALLY UNBIASED BASES”, International Journal of Quantum Information 08, 535 (2010) arXiv:1004.3348 DOI. Appears in: $t$-design
S. Dutta and P. P. Kurur, “Quantum Cyclic Code”, (2010) arXiv:1007.1697. Appears in: Cyclic quantum code
S. Dutta and P. P. Kurur, “Quantum Cyclic Code of length dividing $p^{t}+1$”, (2011) arXiv:1011.5814. Appears in: Frobenius code, Five-qubit perfect code
S. Dutta, D. Biswas, and P. Mandayam, “Noise-adapted qudit codes for amplitude-damping noise”, (2024) arXiv:2406.02444. Appears in: Approximate quantum error-correcting code (AQECC), $[[4,2,2]]_{G}$ four group-qudit code
S. Dutta, A. Jain, and P. Mandayam, “Smallest quantum codes for amplitude damping noise”, (2024) arXiv:2410.00155. Appears in: Post-selected PI code, Approximate quantum error-correcting code (AQECC)
I. M. Duursma, C. Rentería, and H. Tapia-Recillas, “Reed-Muller Codes on Complete Intersections”, Applicable Algebra in Engineering, Communication and Computing 11, 455 (2001) DOI. Appears in: Complete-intersection RM-type code
Z. Dvir, S. Kopparty, S. Saraf, and M. Sudan, “Extensions to the Method of Multiplicities, with applications to Kakeya Sets and Mergers”, (2009) arXiv:0901.2529. Appears in: Multiplicity code
B. Eastin and E. Knill, “Restrictions on Transversal Encoded Quantum Gate Sets”, Physical Review Letters 102, (2009) arXiv:0811.4262 DOI. Appears in: Block quantum code
J. N. Eberhardt, F. R. F. Pereira, and V. Steffan, “Pruning qLDPC codes: Towards bivariate bicycle codes with open boundary conditions”, (2024) arXiv:2412.04181. Appears in: 2D lattice stabilizer code, Bivariate bicycle (BB) code, Honeycomb (6.6.6) color code
J. N. Eberhardt and V. Steffan, “Logical Operators and Fold-Transversal Gates of Bivariate Bicycle Codes”, (2024) arXiv:2407.03973. Appears in: Two-block group-algebra (2BGA) codes, Bivariate bicycle (BB) code
Y. Edel and J. Bierbauer, “Twisted BCH-codes”, Journal of Combinatorial Designs 5, 377 (1997) DOI. Appears in: Twisted BCH code
J. Edmonds, “Paths, Trees, and Flowers”, Canadian Journal of Mathematics 17, 449 (1965) DOI. Appears in: Raussendorf-Bravyi-Harrington (RBH) cluster-state code, Kitaev surface code
J. Edmonds, “Maximum matching and a polyhedron with 0,1-vertices”, Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics 69B, 125 (1965) DOI. Appears in: Raussendorf-Bravyi-Harrington (RBH) cluster-state code, Kitaev surface code
L. Egan et al., “Fault-Tolerant Operation of a Quantum Error-Correction Code”, (2021) arXiv:2009.11482. Appears in: $[[9,1,3,3]]$ Nine-qubit Bacon-Shor code
R. Egan, “A survey of complex generalized weighing matrices and a construction of quantum error-correcting codes”, (2023) arXiv:2309.07522. Appears in: Complex Hadamard spherical code, Hermitian Galois-qudit code
Q. Eggerickx, A. Wills, T.-C. Lin, K. De Greve, and M.-H. Hsieh, “Almost Linear Decoder for Optimal Geometrically Local Quantum Codes”, (2024) arXiv:2411.02928. Appears in: Lattice stabilizer code
D. Ehrhard, “Decoding Algebraic-Geometric Codes by solving a key equation”, Lecture Notes in Mathematics 18 (1992) DOI. Appears in: Evaluation AG code
D. Ehrhard, “Achieving the designed error capacity in decoding algebraic-geometric codes”, IEEE Transactions on Information Theory 39, 743 (1993) DOI. Appears in: Evaluation AG code
A. Eickbusch et al., “Demonstrating dynamic surface codes”, (2024) arXiv:2412.14360. Appears in: Kitaev surface code
Einarsson, Göran. Performance of polyphase signals on a Gaussian channel. 1966.. Appears in: Polyphase code
Einarsson, Göran. "Polyphase coding for a Gaussian channel(Polyphase coding for Gaussian channel, investigating PM signal transmission over channel disturbed by additive white Gaussian noise)." Ericsson Technics 24.2 (1968): 75-130.. Appears in: Polyphase code
A. Einstein, B. Podolsky, and N. Rosen, “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?”, Physical Review 47, 777 (1935) DOI. Appears in: Analog repetition code
J. Eisert, S. Scheel, and M. B. Plenio, “Distilling Gaussian States with Gaussian Operations is Impossible”, Physical Review Letters 89, (2002) arXiv:quant-ph/0204052 DOI. Appears in: Analog stabilizer code, Oscillator-into-oscillator GKP code
J. Eisert and M. M. Wolf, “Gaussian quantum channels”, (2005) arXiv:quant-ph/0505151. Appears in: Bosonic code
J. Eisert and T. J. Osborne, “General Entanglement Scaling Laws from Time Evolution”, Physical Review Letters 97, (2006) arXiv:quant-ph/0603114 DOI. Appears in: Kitaev surface code, Topological code
A. Ekert and C. Macchiavello, “Error Correction in Quantum Communication”, (1996) arXiv:quant-ph/9602022. Appears in: Block quantum code, Perfect quantum code
L. Eldar and A. W. Harrow, “Local Hamiltonians Whose Ground States Are Hard to Approximate”, 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS) 427 (2017) arXiv:1510.02082 DOI. Appears in: Hypergraph product (HGP) code, Locally testable code (LTC), Quantum locally testable code (QLTC), Qubit CSS code
L. Eldar and A. W. Harrow, “Local Hamiltonians Whose Ground States Are Hard to Approximate”, 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS) 427 (2017) DOI. Appears in: Quantum locally testable code (QLTC)
Y. C. Eldar and G. D. Forney Jr, “On Quantum Detection and the Square-Root Measurement”, (2000) arXiv:quant-ph/0005132. Appears in: Coherent-state c-q code
Y. C. Eldar and G. D. Forney, “On quantum detection and the square-root measurement”, IEEE Transactions on Information Theory 47, 858 (2001) DOI. Appears in: PSK c-q code
Y. C. Eldar, A. Megretski, and G. C. Verghese, “Optimal Detection of Symmetric Mixed Quantum States”, (2002) arXiv:quant-ph/0211111. Appears in: Coherent-state c-q code
E. Eleftheriou and S. Olcer, “Low-density parity-check codes for digital subscriber lines”, 2002 IEEE International Conference on Communications. Conference Proceedings. ICC 2002 (Cat. No.02CH37333) DOI. Appears in: Array-based LDPC (AB-LDPC) code
P. Elias, “Error-free Coding”, Transactions of the IRE Professional Group on Information Theory 4, 29 (1954) DOI. Appears in: Tensor-product code
N. D. Elkies, “Excellent nonlinear codes from modular curves”, (2001) arXiv:math/0104115. Appears in: Nonlinear AG code
N. D. Elkies, “Still better nonlinear codes from modular curves”, (2003) arXiv:math/0308046. Appears in: Nonlinear AG code
T. D. Ellison, Y.-A. Chen, A. Dua, W. Shirley, N. Tantivasadakarn, and D. J. Williamson, “Pauli Stabilizer Models of Twisted Quantum Doubles”, PRX Quantum 3, (2022) arXiv:2112.11394 DOI. Appears in: 2D lattice stabilizer code, Double-semion stabilizer code, Abelian topological code, Twisted quantum double (TQD) code, Abelian TQD stabilizer code, Lattice subsystem code
T. D. Ellison, Y.-A. Chen, A. Dua, W. Shirley, N. Tantivasadakarn, and D. J. Williamson, “Pauli topological subsystem codes from Abelian anyon theories”, Quantum 7, 1137 (2023) arXiv:2211.03798 DOI. Appears in: Double-semion stabilizer code, Kitaev honeycomb code, Abelian quantum-double stabilizer code, Modular-qudit surface code, $\mathbb{Z}_q^{(1)}$ subsystem code, Chiral semion subsystem code, Three-fermion (3F) subsystem code, Kitaev surface code, Topological code, Abelian topological code, Abelian TQD stabilizer code, Lattice subsystem code, Walker-Wang model code, $\mathbb{Z}_3\times\mathbb{Z}_9$-fusion subsystem code
T. D. Ellison, J. Sullivan, and A. Dua, “Floquet codes with a twist”, (2023) arXiv:2306.08027. Appears in: Honeycomb Floquet code, Twist-defect surface code
S. J. Elman, A. Chapman, and S. T. Flammia, “Free Fermions Behind the Disguise”, Communications in Mathematical Physics 388, 969 (2021) arXiv:2012.07857 DOI. Appears in: Fermion code, Fermion-into-qubit code
D. V. Else, I. Schwarz, S. D. Bartlett, and A. C. Doherty, “Symmetry-Protected Phases for Measurement-Based Quantum Computation”, Physical Review Letters 108, (2012) arXiv:1201.4877 DOI. Appears in: Cluster-state code, Symmetry-protected topological (SPT) code, Lattice stabilizer code
C. Eltschka and J. Siewert, “MaximumN-body correlations do not in general imply genuine multipartite entanglement”, Quantum 4, 229 (2020) arXiv:1908.04220 DOI. Appears in: Cluster-state code
M. Elyasi and S. Mohajer, “Determinant Coding: A Novel Framework for Exact-Repair Regenerating Codes”, IEEE Transactions on Information Theory 62, 6683 (2016) DOI. Appears in: Determinant code
K. Ender, R. ter Hoeven, B. E. Niehoff, M. Drieb-Schön, and W. Lechner, “Parity Quantum Optimization: Compiler”, Quantum 7, 950 (2023) arXiv:2105.06233 DOI. Appears in: Lechner-Hauke-Zoller (LHZ) code
K. Engdahl, K. Sh. Zigangirov, “To the Theory of Low-Density Convolutional Codes. I”, Probl. Peredachi Inf., 35:4 (1999), 12–28; Problems Inform. Transmission, 35:4 (1999), 295–310. Appears in: LDPC convolutional code (LDPC-CC), Spatially coupled LDPC (SC-LDPC) code
L. H. English, D. J. Williamson, and S. D. Bartlett, “Thresholds for post-selected quantum error correction from statistical mechanics”, (2024) arXiv:2410.07598. Appears in: Toric code
H. E. Ercan, J. Ghosh, D. Crow, V. N. Premakumar, R. Joynt, M. Friesen, and S. N. Coppersmith, “Measurement-free implementations of small-scale surface codes for quantum-dot qubits”, Physical Review A 97, (2018) arXiv:1708.08683 DOI. Appears in: $[[9,1,3]]$ Surface-17 code
M. Ergen, “Basics of Cellular Communication”, Mobile Broadband 19 (2008) DOI. Appears in: Cyclic redundancy check (CRC) code, Single parity-check (SPC) code
A. Erhard et al., “Entangling logical qubits with lattice surgery”, Nature 589, 220 (2021) arXiv:2006.03071 DOI. Appears in: Rotated surface code, $[[4,2,2]]$ Four-qubit code
Eric Huang and Arthur Pesah. PanQEC. https://github.com/panqec/panqec, 2023.. Appears in: Qubit stabilizer code
Eric Sabo. CodingTheory. https://github.com/esabo/CodingTheory. Appears in: Galois-qudit code, Linear $q$-ary code
T. Ericson, and V. Zinoviev, eds. Codes on Euclidean spheres. Elsevier, 2001.. Appears in: Binary antipodal code, Binary balanced spherical code, Binary group-orbit code, Linear binary code, $[2^m,m+1,2^{m-1}]$ First-order RM code, Biorthogonal spherical code, Cameron-Goethals-Seidel (CGS) isotropic subspace code, Construction-$A$ code, Coxeter-Todd $K_{12}$ lattice, Disphenoidal 288-cell code, $D_n$ checkerboard lattice, $D_3$ face-centered cubic (fcc) lattice, $E_8$ Gosset lattice, $E_7$ root lattice, $E_6$ root lattice, $[23, 12, 7]$ Golay code, Linear code over $G$, Group-orbit code, $[8,4,4]$ extended Hamming code, Hessian polyhedron code, Hexacode, $\mathbb{Z}^n$ hypercubic lattice, Icosahedron code, Kerdock code, Kerdock spherical code, $\Lambda_{16}$ Barnes-Wall lattice, Lattice-shell code, $\Lambda_{24}$ Leech lattice, Single parity-check (SPC) code, Permutation spherical code, Lattice-based code, Constant-energy code, Polyphase code, Projective geometry code, $q$-ary Hamming code, $q$-ary repetition code, Reed-Muller (RM) code, Repetition code, $[7,3,4]$ simplex code, $[2^m-1,m,2^{m-1}]$ simplex code, Simplex spherical code, Slepian group-orbit code, Snub-cube code, Sphere packing, Spherical code, Spherical design, Square-antiprism code, Torus-layer spherical code (TLSC)
Y. Erlich and D. Zielinski, “DNA Fountain enables a robust and efficient storage architecture”, Science 355, 950 (2017) DOI. Appears in: DNA storage code, Fountain code
S. Escalera, O. Pujol, and P. Radeva, “On the Decoding Process in Ternary Error-Correcting Output Codes”, IEEE Transactions on Pattern Analysis and Machine Intelligence 32, 120 (2010) DOI. Appears in: Error-correcting output code (ECOC)
Escalera, Sergio, Oriol Pujol, and Petia Radeva. "Error-correcting output codes library." The Journal of Machine Learning Research 11 (2010): 661-664.. Appears in: Error-correcting output code (ECOC)
G. Escobar-Arrieta and M. Gutiérrez, “Improved performance of the Bacon-Shor code with Steane’s syndrome extraction method”, (2024) arXiv:2403.01659. Appears in: Bacon-Shor code
H. Esfahanizadeh, A. Hareedy, and L. Dolecek, “Finite-Length Construction of High Performance Spatially-Coupled Codes via Optimized Partitioning and Lifting”, IEEE Transactions on Communications 67, 3 (2019) DOI. Appears in: Spatially coupled LDPC (SC-LDPC) code
M. Esmaeili, T. A. Gulliver, N. P. Secord, and S. A. Mahmoud, “A link between quasi-cyclic codes and convolutional codes”, IEEE Transactions on Information Theory 44, 431 (1998) DOI. Appears in: Convolutional code, Quasi-cyclic code
P. Etingof, D. Nikshych, and V. Ostrik, “Weakly group-theoretical and solvable fusion categories”, (2009) arXiv:0809.3031. Appears in: String-net code
P. Etingof, D. Nikshych, and V. Ostrik, “On fusion categories”, (2017) arXiv:math/0203060. Appears in: Multi-fusion string-net code, Hopf-algebra quantum-double code
ETSI, ETSI. "Digital video broadcasting (dvb); second generation framing structure, channel coding and modulation systems for broadcasting, interactive services, news gathering and other broadband satellite applications." Part II: S2-Extensions (DVB-S2X) (2005): 22-27.. Appears in: Irregular repeat-accumulate (IRA) code
T. Etzion and A. Vardy, “Perfect binary codes: constructions, properties, and enumeration”, IEEE Transactions on Information Theory 40, 754 (1994) DOI. Appears in: Orthogonal array (OA), Perfect code, Perfect binary code
T. Etzion, “Optimal constant weight codes over Zk and generalized designs”, Discrete Mathematics 169, 55 (1997) DOI. Appears in: Constant-weight code
T. Etzion, A. Trachtenberg, and A. Vardy, “Which codes have cycle-free Tanner graphs?”, IEEE Transactions on Information Theory 45, 2173 (1999) DOI. Appears in: Tanner code
Z. W. E. Evans, A. M. Stephens, J. H. Cole, and L. C. L. Hollenberg, “Error correction optimisation in the presence of X/Z asymmetry”, (2007) arXiv:0709.3875. Appears in: Asymmetric quantum code, Concatenated Steane code
Z. W. E. Evans and A. M. Stephens, “Message passing in fault-tolerant quantum error correction”, Physical Review A 78, (2008) arXiv:0806.2188 DOI. Appears in: $[[9,1,3,3]]$ Nine-qubit Bacon-Shor code
Z. W. E. Evans and A. M. Stephens, “Optimal correction of concatenated fault-tolerant quantum codes”, Quantum Information Processing 11, 1511 (2011) arXiv:0902.4506 DOI. Appears in: Concatenated qubit code, $[[4,2,2]]$ Four-qubit code
G. Evenbly and G. Vidal, “Class of Highly Entangled Many-Body States that can be Efficiently Simulated”, Physical Review Letters 112, (2014) arXiv:1210.1895 DOI. Appears in: Branching MERA code
G. Evenbly, “Hyperinvariant Tensor Networks and Holography”, Physical Review Letters 119, (2017) arXiv:1704.04229 DOI. Appears in: Hyperinvariant tensor-network (HTN) code
S. J. Evered et al., “Probing topological matter and fermion dynamics on a neutral-atom quantum computer”, (2025) arXiv:2501.18554. Appears in: Kitaev honeycomb code
S. Evra, T. Kaufman, and G. Zémor, “Decodable quantum LDPC codes beyond the $\sqrt{n}$ distance barrier using high dimensional expanders”, (2020) arXiv:2004.07935. Appears in: Distance-balanced code, Hemicubic code, Hypersphere product code, Quantum locally testable code (QLTC), High-dimensional expander (HDX) code
S. Evra and O. Parzanchevski, “Arithmeticity, thinness and efficiency of qutrit Clifford+T gates”, (2024) arXiv:2401.16120. Appears in: Modular-qudit code
M. F. Ezerman and R. Kirov, “Nonbinary Quantum Codes from Two-Point Divisors on Hermitian Curves”, (2011) arXiv:1102.3605. Appears in: Asymmetric quantum code, Hermitian code
M. F. Ezerman, S. Ling, and P. Sole, “Additive Asymmetric Quantum Codes”, IEEE Transactions on Information Theory 57, 5536 (2011) arXiv:1002.4088 DOI. Appears in: Hermitian Galois-qudit code
M. F. Ezerman, S. Jitman, S. Ling, and D. V. Pasechnik, “CSS-Like Constructions of Asymmetric Quantum Codes”, IEEE Transactions on Information Theory 59, 6732 (2013) arXiv:1207.6512 DOI. Appears in: Asymmetric quantum code
M. F. EZERMAN, S. JITMAN, H. M. KIAH, and S. LING, “PURE ASYMMETRIC QUANTUM MDS CODES FROM CSS CONSTRUCTION: A COMPLETE CHARACTERIZATION”, International Journal of Quantum Information 11, 1350027 (2013) arXiv:1006.1694 DOI. Appears in: Asymmetric quantum code, Quantum maximum-distance-separable (MDS) code
M. F. Ezerman, "Quantum Error-Control Codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI. Appears in: Galois-qudit stabilizer code, True Galois-qudit stabilizer code, Self-dual linear code, Self-dual additive code, Hermitian qubit code, Hermitian Galois-qudit code
C. Fabre and N. Treps, “Modes and states in quantum optics”, Reviews of Modern Physics 92, (2020) arXiv:1912.09321 DOI. Appears in: Bosonic code
N. Fabre et al., “Generation of a time-frequency grid state with integrated biphoton frequency combs”, Physical Review A 102, (2020) arXiv:1904.01351 DOI. Appears in: Square-lattice GKP code
P. Facchi, G. Florio, G. Parisi, and S. Pascazio, “Maximally multipartite entangled states”, Physical Review A 77, (2008) arXiv:0710.2868 DOI. Appears in: Perfect-tensor code
P. Facchi, G. Florio, U. Marzolino, G. Parisi, and S. Pascazio, “Classical statistical mechanics approach to multipartite entanglement”, Journal of Physics A: Mathematical and Theoretical 43, 225303 (2010) arXiv:1002.2592 DOI. Appears in: Perfect-tensor code
A. Fahimniya, H. Dehghani, K. Bharti, S. Mathew, A. J. Kollár, A. V. Gorshkov, and M. J. Gullans, “Fault-tolerant hyperbolic Floquet quantum error correcting codes”, (2024) arXiv:2309.10033. Appears in: Hyperbolic Floquet code
P. Faist, S. Nezami, V. V. Albert, G. Salton, F. Pastawski, P. Hayden, and J. Preskill, “Continuous Symmetries and Approximate Quantum Error Correction”, Physical Review X 10, (2020) arXiv:1902.07714 DOI. Appears in: Covariant block quantum code, Eigenstate thermalization hypothesis (ETH) code, $[[4,2,2]]_{G}$ four group-qudit code, Group GKP code, Group-based QPC, Group-based quantum repetition code, Pastawski-Yoshida-Harlow-Preskill (HaPPY) code, $[[2m,2m-2,2]]$ error-detecting code, Random quantum code, $[[5,1,3]]_{\mathbb{Z}_q}$ modular-qudit code, Three-rotor code, Four-rotor code, Five-rotor code, W-state code
P. Faist, M. P. Woods, V. V. Albert, J. M. Renes, J. Eisert, and J. Preskill, “Time-Energy Uncertainty Relation for Noisy Quantum Metrology”, PRX Quantum 4, (2023) arXiv:2207.13707 DOI. Appears in: Covariant block quantum code, Metrological code, Qubit stabilizer code
G. Falcão, V. Silva, L. Sousa, and J. Marinho, “High coded data rate and multicodeword WiMAX LDPC decoding on Cell/BE”, Electronics Letters 44, 1415 (2008) DOI. Appears in: Quasi-cyclic LDPC (QC-LDPC) code
C. Faloutsos, “Access methods for text”, ACM Computing Surveys 17, 49 (1985) DOI. Appears in: Superimposed code
J. L. Fan, “Array Codes as LDPC Codes”, Constrained Coding and Soft Iterative Decoding 195 (2001) DOI. Appears in: Array-based LDPC (AB-LDPC) code, B-code, Reed-Solomon (RS) code
J. Fan, H. Chen, and J. Xu, “Constructions of q-ary entanglement-assisted quantum MDS codes with minimum distance greater than q + 1”, (2016) arXiv:1602.02235. Appears in: EA MDS code, Maximum distance separable (MDS) code
J. Fan, Y. Li, M.-H. Hsieh, and H. Chen, “On Quantum Tensor Product Codes”, (2017) arXiv:1605.09598. Appears in: Maximum distance separable (MDS) code, Cyclic linear $q$-ary code, Quantum tensor-product code, Reversible code
J. Fan, J. Li, Y. Zhou, M.-H. Hsieh, and H. V. Poor, “Entanglement-assisted concatenated quantum codes”, Proceedings of the National Academy of Sciences 119, (2022) arXiv:2202.08084 DOI. Appears in: $[[3, 1, 3;2]]$ EA code, EA Galois-qudit stabilizer code, Concatenated quantum code, Five-qubit perfect code
J. Fan, J. Li, Y. Wang, Y. Li, M.-H. Hsieh, and J. Du, “Partially Concatenated Calderbank-Shor-Steane Codes Achieving the Quantum Gilbert-Varshamov Bound Asymptotically”, IEEE Transactions on Information Theory 69, 262 (2023) DOI. Appears in: Alternant code, Qubit CSS code
J. Fan, M. Steinberg, A. Jahn, C. Cao, A. Sarkar, and S. Feld, “LEGO_HQEC: A Software Tool for Analyzing Holographic Quantum Codes”, (2024) arXiv:2410.22861. Appears in: Tensor-network code
J. Fan, M. Steinberg, A. Jahn, C. Cao, and S. Feld, “Overcoming the Zero-Rate Hashing Bound with Holographic Quantum Error Correction”, (2024) arXiv:2408.06232. Appears in: Pastawski-Yoshida-Harlow-Preskill (HaPPY) code, Surface-code-fragment (SCF) holographic code, Six-qubit-tensor holographic code, Heptagon holographic code
R. Fan, Y. Bao, E. Altman, and A. Vishwanath, “Diagnostics of Mixed-State Topological Order and Breakdown of Quantum Memory”, PRX Quantum 5, (2024) arXiv:2301.05689 DOI. Appears in: 2D lattice stabilizer code
Y. Fan and L. Zhang, “Galois self-dual constacyclic codes”, Designs, Codes and Cryptography 84, 473 (2016) DOI. Appears in: Dual linear code
Y. Fan et al., “Experimental realization of a topologically protected Hadamard gate via braiding Fibonacci anyons”, (2022) arXiv:2210.12145. Appears in: Fibonacci string-net code
Y. Fan, W. Fischler, and E. Kubischta, “Quantum error correction in the lowest Landau level”, Physical Review A 107, (2023) arXiv:2210.16957 DOI. Appears in: Landau-level spin code
M. Fang and D. Su, “Quantum memory based on concatenating surface codes and quantum Hamming codes”, (2024) arXiv:2407.16176. Appears in: $[[2^r-1, 2^r-2r-1, 3]]$ quantum Hamming code, Concatenated qubit code, Kitaev surface code
X. Fang et al., “CaliScalpel: In-Situ and Fine-Grained Qubit Calibration Integrated with Surface Code Quantum Error Correction”, (2024) arXiv:2412.02036. Appears in: Kitaev surface code
Y. Fang, G. Bi, Y. L. Guan, and F. C. M. Lau, “A Survey on Protograph LDPC Codes and Their Applications”, IEEE Communications Surveys & Tutorials 17, 1989 (2015) DOI. Appears in: Protograph LDPC code
Fang-Wei Fu, A. J. Han Vinck, and Shi-Yi Shen, “On the constructions of constant-weight codes”, IEEE Transactions on Information Theory 44, 328 (1998) DOI. Appears in: Constant-weight code
Fan, John L. "Array codes as low-density parity-check codes." Proc. 2nd Int. Symp. on Turbo Codes & Related Topics, Brest, France, Sept. 2000.. Appears in: Array-based LDPC (AB-LDPC) code
Fano, Robert M. The transmission of information. Vol. 65. Cambridge, MA, USA: Massachusetts Institute of Technology, Research Laboratory of Electronics, 1949.. Appears in: Block code
E. Farhi and S. P. Jordan, “Efficiently constructing a quantum uniform superposition over bit strings near a binary linear code”, (2024) arXiv:2404.16129. Appears in: Linear binary code, Qubit stabilizer code
J. Farinholt, “Quantum LDPC Codes Constructed from Point-Line Subsets of the Finite Projective Plane”, (2012) arXiv:1207.0732. Appears in: Finite-geometry LDPC (FG-LDPC) code, Finite-geometry (FG) QLDPC code
J. I. Farran, “Decoding Algebraic Geometry codes by a key equation”, (1999) arXiv:math/9910151. Appears in: Quantum Goppa code
P. G. Farrell, “Linear binary anticodes”, Electronics Letters 6, 419 (1970) DOI. Appears in: Anticode
P. G. Farrell and A. Farrag, “Further properties of linear binary anticodes”, Electronics Letters 10, 340 (1974) DOI. Appears in: Anticode
T. Farrelly, R. J. Harris, N. A. McMahon, and T. M. Stace, “Parallel decoding of multiple logical qubits in tensor-network codes”, (2020) arXiv:2012.07317. Appears in: Heptagon holographic code, Tensor-network code
T. Farrelly, R. J. Harris, N. A. McMahon, and T. M. Stace, “Tensor-Network Codes”, Physical Review Letters 127, (2021) arXiv:2009.10329 DOI. Appears in: Six-qubit-tensor holographic code, Holographic tensor-network code, Tensor-network code
T. Farrelly, D. K. Tuckett, and T. M. Stace, “Local tensor-network codes”, New Journal of Physics 24, 043015 (2022) arXiv:2109.11996 DOI. Appears in: Tensor-network code, Qubit stabilizer code, Modular-qudit stabilizer code, Rotated surface code, Honeycomb (6.6.6) color code
O. Fawzi and R. Renner, “Quantum Conditional Mutual Information and Approximate Markov Chains”, Communications in Mathematical Physics 340, 575 (2015) arXiv:1410.0664 DOI. Appears in: Approximate quantum error-correcting code (AQECC)
O. Fawzi, A. Grospellier, and A. Leverrier, “Constant Overhead Quantum Fault-Tolerance with Quantum Expander Codes”, 2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS) 743 (2018) arXiv:1808.03821 DOI. Appears in: Quantum LDPC (QLDPC) code, Quantum expander code, Single-shot code
O. Fawzi, A. Grospellier, and A. Leverrier, “Efficient decoding of random errors for quantum expander codes”, Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing 521 (2018) arXiv:1711.08351 DOI. Appears in: Quantum expander code
O. Fawzi, A. Müller-Hermes, and A. Shayeghi, “A Lower Bound on the Space Overhead of Fault-Tolerant Quantum Computation”, (2022) arXiv:2202.00119 DOI. Appears in: Qubit code
U. U. Fayyaz and J. R. Barry, “Polar codes for partial response channels”, 2013 IEEE International Conference on Communications (ICC) 4337 (2013) DOI. Appears in: Polar code
U. U. Fayyaz and J. R. Barry, “Low-Complexity Soft-Output Decoding of Polar Codes”, IEEE Journal on Selected Areas in Communications 32, 958 (2014) DOI. Appears in: Polar code
A. Fazeli, S. Lovett, and A. Vardy, “Nontrivial t-designs over finite fields exist for all t”, Journal of Combinatorial Theory, Series A 127, 149 (2014) DOI. Appears in: Subspace design, $t$-design
A. Fazeli, A. Vardy, and E. Yaakobi, “PIR with Low Storage Overhead: Coding instead of Replication”, (2015) arXiv:1505.06241. Appears in: Locally recoverable code (LRC), Private information retrieval (PIR) code
N. Fazio, R. Harper, and S. Bartlett, “Logical Noise Bias in Magic State Injection”, (2024) arXiv:2401.10982. Appears in: $[[7,1,3]]$ Steane code
N. Fazio, M. Webster, and Z. Cai, “Low-overhead Magic State Circuits with Transversal CNOTs”, (2025) arXiv:2501.10291. Appears in: Qubit stabilizer code
C. Fechisin, N. Tantivasadakarn, and V. V. Albert, “Non-invertible symmetry-protected topological order in a group-based cluster state”, (2024) arXiv:2312.09272. Appears in: Group-based cluster-state code, Group GKP code, Group-based quantum code
K. Feher, “Modems for emerging digital cellular-mobile radio system”, IEEE Transactions on Vehicular Technology 40, 355 (1991) DOI. Appears in: Quadrature PSK (QPSK) code
H. G. Feichtinger and T. Strohmer, editors , Gabor Analysis and Algorithms (Birkhäuser Boston, 1998) DOI. Appears in: Square-lattice GKP code
W. Feit. Some remarks on weight functions of spaces over GF(2), unpublished (1972). Appears in: Dual linear code, $[23, 12, 7]$ Golay code, $[7,4,3]$ Hamming code, $[7,3,4]$ simplex code
L. Fejes Toth, Sur Ia representation d' une population infinie par une nombre fini d'elements, AMAH 10 (1959), 299-304. Appears in: $A_2$ triangular lattice
L. Fejes Toth, Uber die Abschatzung des kiirzesten Abstandes zweier Punkte eines auf einer Kugelflache liegenden Punktsystemes, Jber. Deut. Math. Verein., Vol. 53, pp. 66-68, 1943.. Appears in: Spherical code
J. Feldman, M. J. Wainwright, and D. R. Karger, “Using Linear Programming to Decode Binary Linear Codes”, IEEE Transactions on Information Theory 51, 954 (2005) DOI. Appears in: Low-density parity-check (LDPC) code
J. Feldman, T. Malkin, R. A. Servedio, C. Stein, and M. J. Wainwright, “LP Decoding Corrects a Constant Fraction of Errors”, IEEE Transactions on Information Theory 53, 82 (2007) DOI. Appears in: Expander code
J. Feldman, “LP Decoding”, Encyclopedia of Algorithms 1177 (2016) DOI. Appears in: Low-density parity-check (LDPC) code
J. Feldman. Decoding Error-Correcting Codes via Linear Programming. PhD thesis, Massachusetts Institute of Technology, 2003.. Appears in: Low-density parity-check (LDPC) code
M. Fellner, A. Messinger, K. Ender, and W. Lechner, “Universal Parity Quantum Computing”, Physical Review Letters 129, (2022) arXiv:2205.09505 DOI. Appears in: Lechner-Hauke-Zoller (LHZ) code
G.-L. Feng and T. R. N. Rao, “Decoding algebraic-geometric codes up to the designed minimum distance”, IEEE Transactions on Information Theory 39, 37 (1993) DOI. Appears in: Evaluation AG code, Evaluation code
K. Feng and Z. Ma, “A Finite Gilbert–Varshamov Bound for Pure Stabilizer Quantum Codes”, IEEE Transactions on Information Theory 50, 3323 (2004) DOI. Appears in: Block quantum code
K. Feng and C. Xing, “A new construction of quantum error-correcting codes”, Transactions of the American Mathematical Society 360, 2007 (2007) DOI. Appears in: $((5+2r,3\times 2^{2r+1},2))$ Rains code, Smolin-Smith-Wehner (SSW) code
Feng-Wen Sun and H. C. A. van Tilborg, “The Leech lattice, the octacode, and decoding algorithms”, IEEE Transactions on Information Theory 41, 1097 (1995) DOI. Appears in: $\Lambda_{24}$ Leech lattice, Octacode
P. M. Fenwick, “A new data structure for cumulative frequency tables”, Software: Practice and Experience 24, 327 (1994) DOI. Appears in: Bravyi-Kitaev transformation (BKT) code
A. R. Ferdinand, M. T. DiMario, and F. E. Becerra, “Multi-state discrimination below the quantum noise limit at the single-photon level”, npj Quantum Information 3, (2017) arXiv:1711.00074 DOI. Appears in: PSK c-q code
J. Fern, J. Kempe, S. N. Simic, and S. Sastry, “Generalized Performance of Concatenated Quantum Codes—A Dynamical Systems Approach”, IEEE Transactions on Automatic Control 51, 448 (2006) arXiv:quant-ph/0409084 DOI. Appears in: Concatenated qubit code
M. Fernandez and J. J. Urroz, “A study of the separating property in Reed-Solomon codes by bounding the minimum distance”, Designs, Codes and Cryptography 90, 427 (2022) DOI. Appears in: Frameproof (FP) code
C. Fernández-González, N. Schuch, M. M. Wolf, J. I. Cirac, and D. Pérez-García, “Gapless Hamiltonians for the Toric Code Using the Projected Entangled Pair State Formalism”, Physical Review Letters 109, (2012) arXiv:1111.5817 DOI. Appears in: Hamiltonian-based code, Kitaev surface code
H. C. Ferreira, A. J. H. Vinck, T. G. Swart, and I. deBeer, “Permutation Trellis Codes”, IEEE Transactions on Communications 53, 1782 (2005) DOI. Appears in: Code in permutations, Convolutional code
K. B. Ferreira, S. Levy, J. Hemmert, and K. Pedretti, “Understanding Memory Failures on a Petascale Arm System”, Proceedings of the 31st International Symposium on High-Performance Parallel and Distributed Computing (2022) DOI. Appears in: Error-correcting code (ECC)
A. J. Ferris and D. Poulin, “Branching MERA codes: a natural extension of polar codes”, (2013) arXiv:1312.4575. Appears in: Branching MERA code, Polar code, Tensor-network code
A. J. Ferris and D. Poulin, “Branching MERA codes: A natural extension of classical and quantum polar codes”, 2014 IEEE International Symposium on Information Theory (2014) DOI. Appears in: Branching MERA code, Polar code
A. J. Ferris and D. Poulin, “Tensor Networks and Quantum Error Correction”, Physical Review Letters 113, (2014) arXiv:1312.4578 DOI. Appears in: Branching MERA code, Quantum convolutional code, Tensor-network code, Quantum parity code (QPC), Quantum polar code
B. Ferté and X. Cao, “Solvable Model of Quantum-Darwinism-Encoding Transitions”, Physical Review Letters 132, (2024) arXiv:2305.03694 DOI. Appears in: Tensor-network code, Quantum parity code (QPC)
E. Fetaya, “Homological Error Correcting Codes and Systolic Geometry”, (2011) arXiv:1108.2886. Appears in: Freedman-Meyer-Luo code
E. Fetaya, “Bounding the distance of quantum surface codes”, Journal of Mathematical Physics 53, (2012) DOI. Appears in: Freedman-Meyer-Luo code, Homological code
L. Fidkowski, J. Haah, and M. B. Hastings, “Exactly solvable model for a 4+1D beyond-cohomology symmetry-protected topological phase”, Physical Review B 101, (2020) arXiv:1912.05565 DOI. Appears in: Chen-Hsin invertible-order code, Abelian topological code
L. Fidkowski, J. Haah, and M. B. Hastings, “Gravitational anomaly of (3+1) -dimensional Z2 toric code with fermionic charges and fermionic loop self-statistics”, Physical Review B 106, (2022) arXiv:2110.14654 DOI. Appears in: 3D fermionic surface code, Homological code, Chen-Hsin invertible-order code, Abelian topological code
L. Fidkowski, J. Haah, and M. B. Hastings, “A QCA for every SPT”, (2024) arXiv:2407.07951. Appears in: Bosonization code, Chen-Hsin invertible-order code, Symmetry-protected topological (SPT) code, Three-fermion (3F) Walker-Wang model code
L. Fidkowski and M. B. Hastings, “Pumping Chirality in Three Dimensions”, (2024) arXiv:2309.15903. Appears in: 3D bosonization code, Three-fermion (3F) Walker-Wang model code
Fiete, I. R., & Seung, H. S. (2007). Neural network models of birdsong production, learning, and coding. New Encyclopedia of Neuroscience. Eds. L. Squire, T. Albright, F. Bloom, F. Gage, and N. Spitzer. Elsevier.. Appears in: Unary code
U. Fincke and M. Pohst, “Improved methods for calculating vectors of short length in a lattice, including a complexity analysis”, Mathematics of Computation 44, 463 (1985) DOI. Appears in: Lattice-based code
M. Finiasz and N. Sendrier, “Security Bounds for the Design of Code-Based Cryptosystems”, Lecture Notes in Computer Science 88 (2009) DOI. Appears in: Random code
M. Firer, M. M. S. Alves, J. A. Pinheiro, and L. Panek, Poset Codes: Partial Orders, Metrics and Coding Theory (Springer International Publishing, 2018) DOI. Appears in: Poset code
M. Firer, "Alternative Metrics." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI. Appears in: Editing code, Poset code, Subspace code
U. A. First and T. Kaufman, “Cosystolic Expansion of Sheaves on Posets with Applications to Good 2-Query Locally Testable Codes and Lifted Codes”, (2024) arXiv:2403.19388. Appears in: Generalized homological-product CSS code, Locally testable code (LTC), Tanner code
A. Fischer and A. Miyake, “Hardness results for decoding the surface code with Pauli noise”, Quantum 8, 1511 (2024) arXiv:2309.10331 DOI. Appears in: Kitaev surface code
W. Fish, J. D. Key, and E. Mwambene, “Partial permutation decoding for simplex codes”, Advances in Mathematics of Communications 6, 505 (2012) DOI. Appears in: $q$-ary simplex code
M. P. A. Fisher, V. Khemani, A. Nahum, and S. Vijay, “Random Quantum Circuits”, Annual Review of Condensed Matter Physics 14, 335 (2023) arXiv:2207.14280 DOI. Appears in: Random-circuit code
R. A. FISHER, “THE THEORY OF CONFOUNDING IN FACTORIAL EXPERIMENTS IN RELATION TO THE THEORY OF GROUPS”, Annals of Eugenics 11, 341 (1941) DOI. Appears in: $q$-ary simplex code, $[2^m-1,m,2^{m-1}]$ simplex code
R. A. FISHER, “A SYSTEM OF CONFOUNDING FOR FACTORS WITH MORE THAN TWO ALTERNATIVES, GIVING COMPLETELY ORTHOGONAL CUBES AND HIGHER POWERS”, Annals of Eugenics 12, 283 (1943) DOI. Appears in: $q$-ary Hamming code
R. A. Fisher, M. M. Nieto, and V. D. Sandberg, “Impossibility of naively generalizing squeezed coherent states”, Physical Review D 29, 1107 (1984) DOI. Appears in: Bosonic code
S. T. Flammia, N. C. Menicucci, and O. Pfister, “The optical frequency comb as a one-way quantum computer”, Journal of Physics B: Atomic, Molecular and Optical Physics 42, 114009 (2009) arXiv:0811.2799 DOI. Appears in: Analog-cluster-state code
S. T. Flammia, J. Haah, M. J. Kastoryano, and I. H. Kim, “Limits on the storage of quantum information in a volume of space”, Quantum 1, 4 (2017) arXiv:1610.06169 DOI. Appears in: Approximate quantum error-correcting code (AQECC), Lattice stabilizer code
A. S. Fletcher, P. W. Shor, and M. Z. Win, “Channel-Adapted Quantum Error Correction for the Amplitude Damping Channel”, (2007) arXiv:0710.1052. Appears in: Amplitude-damping (AD) code, Amplitude-damping CWS code, Dual-rail quantum code, Concatenated qubit code
A. S. Fletcher, “Channel-Adapted Quantum Error Correction”, (2007) arXiv:0706.3400. Appears in: Approximate quantum error-correcting code (AQECC), Qudit-into-oscillator code
A. S. Fletcher, P. W. Shor, and M. Z. Win, “Structured near-optimal channel-adapted quantum error correction”, Physical Review A 77, (2008) arXiv:0708.3658 DOI. Appears in: Approximate quantum error-correcting code (AQECC)
C. Flühmann, T. L. Nguyen, M. Marinelli, V. Negnevitsky, K. Mehta, and J. P. Home, “Encoding a qubit in a trapped-ion mechanical oscillator”, Nature 566, 513 (2019) arXiv:1807.01033 DOI. Appears in: Square-lattice GKP code
C. Flühmann and J. P. Home, “Direct Characteristic-Function Tomography of Quantum States of the Trapped-Ion Motional Oscillator”, Physical Review Letters 125, (2020) arXiv:1907.06478 DOI. Appears in: Square-lattice GKP code
G. B. Folland, “Harmonic Analysis in Phase Space. (AM-122)”, (1989) DOI. Appears in: Square-lattice GKP code
D. Forlivesi, L. Valentini, and M. Chiani, “Logical Error Rates of XZZX and Rotated Quantum Surface Codes”, (2023) arXiv:2312.17057. Appears in: Rotated surface code, XZZX surface code
D. Forlivesi, L. Valentini, and M. Chiani, “Spanning Tree Matching Decoder for Quantum Surface Codes”, IEEE Communications Letters 28, 1509 (2024) arXiv:2405.01151 DOI. Appears in: Kitaev surface code
G. D. Forney, “Codes on graphs: normal realizations”, 2000 IEEE International Symposium on Information Theory (Cat. No.00CH37060) DOI. Appears in: Tanner code
G. D. Forney, “Coset codes. I. Introduction and geometrical classification”, IEEE Transactions on Information Theory 34, 1123 (1988) DOI. Appears in: Barnes-Wall (BW) lattice, Reed-Muller (RM) code
G. D. Forney, “Geometrically uniform codes”, IEEE Transactions on Information Theory 37, 1241 (1991) DOI. Appears in: Linear code over $G$
G. D. Forney and G. Ungerboeck, “Modulation and coding for linear Gaussian channels”, IEEE Transactions on Information Theory 44, 2384 (1998) DOI. Appears in: Binary antipodal code, $[2^m,m+1,2^{m-1}]$ First-order RM code, Biorthogonal spherical code
G. D. Forney, M. Grassl, and S. Guha, “Convolutional and Tail-Biting Quantum Error-Correcting Codes”, IEEE Transactions on Information Theory 53, 865 (2007) arXiv:quant-ph/0511016 DOI. Appears in: Hexacode, Quantum convolutional code, Reed-Solomon (RS) code, Five-qubit perfect code, Hermitian qubit code
G. Forney, “Generalized minimum distance decoding”, IEEE Transactions on Information Theory 12, 125 (1966) DOI. Appears in: Concatenated code, Linear $q$-ary code, Tensor-product code
Forney, G. D. (2003). 6.451 Principles of Digital Communication II, Spring 2003.. Appears in: Binary antipodal code, $[2^m,m+1,2^{m-1}]$ First-order RM code, Biorthogonal spherical code, $[2^m-1,m,2^{m-1}]$ simplex code, Simplex spherical code
G. D. Forney, Jr (1966). Concatenated Codes. MIT Press, Cambridge, MA.. Appears in: Concatenated code, Tensor-product code
Forney Jr GD, Sloane NJ, Trott MD. The Nordstrom-Robinson code is the binary image of the octacode. In Coding and Quantization: DIMACS/IEEE workshop 1992 Oct 19 (pp. 19-26). Amer. Math. Soc... Appears in: Nordstrom-Robinson (NR) code, Octacode
Forney Jr GD, Sloane NJ, Trott MD. The Nordstrom-Robinson code is the binary image of the octacode. InCoding and Quantization: DIMACS/IEEE workshop 1992 Oct 19 (pp. 19-26). Amer. Math. Soc... Appears in: Nordstrom-Robinson (NR) code, Self-dual linear code
G.D. Forney, Jr., S.M. thesis, Massachusetts Institute of Technology, 1963 (unpublished).. Appears in: Bosonic c-q code
G. D. Forney, Jr., “Why quasi cyclic codes are interesting,” unpublished note, 1970.. Appears in: Convolutional code, Quasi-cyclic code
G. J. Foschini and M. J. Gans, Wireless Personal Communications 6, 311 (1998) DOI. Appears in: Spacetime code (STC)
G. Foschini, R. Gitlin, and S. Weinstein, “Optimization of Two-Dimensional Signal Constellations in the Presence of Gaussian Noise”, IEEE Transactions on Communications 22, 28 (1974) DOI. Appears in: $A_2$ triangular lattice
T. Fösel, P. Tighineanu, T. Weiss, and F. Marquardt, “Reinforcement Learning with Neural Networks for Quantum Feedback”, Physical Review X 8, (2018) arXiv:1802.05267 DOI. Appears in: Neural network quantum code
T. Fösel, M. Y. Niu, F. Marquardt, and L. Li, “Quantum circuit optimization with deep reinforcement learning”, (2021) arXiv:2103.07585. Appears in: Qubit code
M. P. C. Fossorier, “Quasi-Cyclic Low-Density Parity-Check Codes From Circulant Permutation Matrices”, IEEE Transactions on Information Theory 50, 1788 (2004) DOI. Appears in: Abelian LP code, Concatenated GKP code, Quasi-cyclic LDPC (QC-LDPC) code
A. G. Fowler, C. D. Hill, and L. C. L. Hollenberg, “Quantum-error correction on linear-nearest-neighbor qubit arrays”, Physical Review A 69, (2004) arXiv:quant-ph/0311116 DOI. Appears in: Five-qubit perfect code
A. G. Fowler, “Towards Large-Scale Quantum Computation”, (2005) arXiv:quant-ph/0506126. Appears in: $[[7,1,3]]$ Steane code
A. G. Fowler, A. M. Stephens, and P. Groszkowski, “High-threshold universal quantum computation on the surface code”, Physical Review A 80, (2009) arXiv:0803.0272 DOI. Appears in: Bivariate bicycle (BB) code, Kitaev surface code
A. G. Fowler, “Constructing arbitrary Steane code single logical qubit fault-tolerant gates”, (2010) arXiv:quant-ph/0411206. Appears in: $[[7,1,3]]$ Steane code
A. G. Fowler, “Two-dimensional color-code quantum computation”, Physical Review A 83, (2011) arXiv:0806.4827 DOI. Appears in: 3D color code, Square-octagon (4.8.8) color code
A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, “Surface codes: Towards practical large-scale quantum computation”, Physical Review A 86, (2012) arXiv:1208.0928 DOI. Appears in: Rotated surface code, Kitaev surface code, Abelian topological code, Twist-defect surface code
A. G. Fowler, “Low-overhead surface code logical Hadamard”, (2012) arXiv:1202.2639. Appears in: Kitaev surface code
A. G. Fowler, A. C. Whiteside, and L. C. L. Hollenberg, “Towards Practical Classical Processing for the Surface Code”, Physical Review Letters 108, (2012) arXiv:1110.5133 DOI. Appears in: Kitaev surface code
A. G. Fowler, A. C. Whiteside, and L. C. L. Hollenberg, “Towards practical classical processing for the surface code: Timing analysis”, Physical Review A 86, (2012) arXiv:1202.5602 DOI. Appears in: Kitaev surface code
A. G. Fowler, A. C. Whiteside, A. L. McInnes, and A. Rabbani, “Topological Code Autotune”, Physical Review X 2, (2012) arXiv:1202.6111 DOI. Appears in: Kitaev surface code
A. G. Fowler, “Proof of Finite Surface Code Threshold for Matching”, Physical Review Letters 109, (2012) arXiv:1206.0800 DOI. Appears in: Kitaev surface code
A. G. Fowler, “Time-optimal quantum computation”, (2013) arXiv:1210.4626. Appears in: Qubit stabilizer code
A. G. Fowler, “Optimal complexity correction of correlated errors in the surface code”, (2013) arXiv:1310.0863. Appears in: Kitaev surface code
A. G. Fowler and S. J. Devitt, “A bridge to lower overhead quantum computation”, (2013) arXiv:1209.0510. Appears in: Kitaev surface code
A. G. Fowler, “Minimum weight perfect matching of fault-tolerant topological quantum error correction in average $O(1)$ parallel time”, (2014) arXiv:1307.1740. Appears in: Raussendorf-Bravyi-Harrington (RBH) cluster-state code, Kitaev surface code
J. S. Frame, “The classes and representations of the groups of 27 lines and 28 bitangents”, Annali di Matematica Pura ed Applicata 32, 83 (1951) DOI. Appears in: Hessian polyhedron code
Franz, M. Leone, A. Montanari, and F. Ricci-Tersenghi, “Dynamic phase transition for decoding algorithms”, Physical Review E 66, (2002) arXiv:cond-mat/0205051 DOI. Appears in: Hamiltonian-based code, Low-density parity-check (LDPC) code
N. E. Frattini et al., “Observation of Pairwise Level Degeneracies and the Quantum Regime of the Arrhenius Law in a Double-Well Parametric Oscillator”, Physical Review X 14, (2024) arXiv:2209.03934 DOI. Appears in: Two-component cat code
Frazer, W. D. "A graph theoretic approach to linear codes." Proc. Second Annual Allerton Conf. On Circuit & System Theory. 1964.. Appears in: Cycle code
M. Frederic Ezerman, M. Grassl, S. Ling, F. Özbudak, and B. Özkaya, “Characterization of Nearly Self-Orthogonal Quasi-Twisted Codes and Related Quantum Codes”, IEEE Transactions on Information Theory 71, 499 (2025) arXiv:2405.15057 DOI. Appears in: Block quantum code, Galois-qudit stabilizer code, Modular-qudit stabilizer code, Hermitian Galois-qudit code
D. S. Freed and F. Quinn, “Chern-Simons theory with finite gauge group”, Communications in Mathematical Physics 156, 435 (1993) arXiv:hep-th/9111004 DOI. Appears in: Dijkgraaf-Witten gauge theory code
D. S. Freed, “Short-range entanglement and invertible field theories”, (2014) arXiv:1406.7278. Appears in: Hamiltonian-based code
M. H. Freedman and D. A. Meyer, “Projective plane and planar quantum codes”, (1998) arXiv:quant-ph/9810055. Appears in: Modular-qudit surface code, Projective-plane surface code, $[[9,1,3]]$ Shor code, $[[9,1,3]]_{\mathbb{Z}_q}$ modular-qudit code, Kitaev surface code
M. H. Freedman, “Z${}_{\text{2}}$–Systolic-Freedom”, Geometry & Topology Monographs 113 (1999) DOI. Appears in: Freedman-Meyer-Luo code
M. H. Freedman, M. J. Larsen, and Z. Wang, “The Two-Eigenvalue Problem and Density¶of Jones Representation of Braid Groups”, Communications in Mathematical Physics 228, 177 (2002) arXiv:math/0103200 DOI. Appears in: String-net code
M. H. Freedman and M. B. Hastings, “Quantum Systems on Non-$k$-Hyperfinite Complexes: A Generalization of Classical Statistical Mechanics on Expander Graphs”, (2013) arXiv:1301.1363. Appears in: Approximate quantum error-correcting code (AQECC), Homological product code, Quantum locally testable code (QLTC), Quantum Tanner code, Random stabilizer code
M. H. Freedman and M. B. Hastings, “Double Semions in Arbitrary Dimension”, Communications in Mathematical Physics 347, 389 (2016) arXiv:1507.05676 DOI. Appears in: Double-semion stabilizer code
M. Freedman, M. Larsen, and Z. Wang, “A modular functor which is universal for quantum computation”, (2000) arXiv:quant-ph/0001108. Appears in: Fibonacci string-net code, String-net code
M. Freedman and M. B. Hastings, “Building manifolds from quantum codes”, (2021) arXiv:2012.02249. Appears in: Good QLDPC code, Quantum LDPC (QLDPC) code, Qubit CSS code, Abelian topological code, Lattice stabilizer code
B. C. A. Freire, N. Delfosse, and A. Leverrier, “Optimizing hypergraph product codes with random walks, simulated annealing and reinforcement learning”, (2025) arXiv:2501.09622. Appears in: Hypergraph product (HGP) code, Neural network quantum code
K. Friedl and M. Sudan, “Some Improvements to Total Degree Tests”, (2013) arXiv:1307.3975. Appears in: Locally testable code (LTC)
J. Friedman and J.-P. Tillich, “Generalized Alon--Boppana Theorems and Error-Correcting Codes”, SIAM Journal on Discrete Mathematics 19, 700 (2005) DOI. Appears in: Binary code
L. Frunzio and S. Singh, “Error-Correcting Surface Codes Get Experimental Vetting”, Physics 15, (2022) DOI. Appears in: $[[9,1,3]]$ Surface-17 code
X. Fu and D. Gottesman, “Error Correction in Dynamical Codes”, (2024) arXiv:2403.04163. Appears in: Dynamical automorphism (DA) code
J. Fuchs, C. Schweigert, and A. Valentino, “Bicategories for Boundary Conditions and for Surface Defects in 3-d TFT”, Communications in Mathematical Physics 321, 543 (2013) arXiv:1203.4568 DOI. Appears in: Topological code
T. Fuchs, D. Gross, F. Krahmer, R. Kueng, and D. G. Mixon, “Sketching with Kerdock’s crayons: Fast sparsifying transforms for arbitrary linear maps”, (2021) arXiv:2105.05879. Appears in: Cluster-state code, Kerdock code, $t$-design
Fuchs, Jürgen. Affine Lie algebras and quantum groups: An Introduction, with applications in conformal field theory. Cambridge university press, 1995.. Appears in: Topological code
J. C. M. de la Fuente, T. D. Ellison, M. Cheng, and D. J. Williamson, “Topological stabilizer models on continuous variables”, (2024) arXiv:2411.04993. Appears in: Analog surface code, $U(1)_{2n} \times U(1)_{-2m}$ Chern-Simons GKP code, Compactified $\mathbb{R}$ gauge theory code, GKP-surface code, Integer-homology bosonic CSS code, Homological rotor code, Abelian topological code, Lattice stabilizer code
J. C. M. de la Fuente, J. Old, A. Townsend-Teague, M. Rispler, J. Eisert, and M. Müller, “The XYZ ruby code: Making a case for a three-colored graphical calculus for quantum error correction in spacetime”, (2024) arXiv:2407.08566. Appears in: XYZ ruby Floquet code, Spacetime circuit code
J. C. M. de la Fuente, “Dynamical weight reduction of Pauli measurements”, (2024) arXiv:2410.12527. Appears in: Qubit stabilizer code
P. Fuentes, J. Etxezarreta Martinez, P. M. Crespo, and J. Garcia-Frias, “Approach for the construction of non-Calderbank-Steane-Shor low-density-generator-matrix–based quantum codes”, Physical Review A 102, (2020) DOI. Appears in: Low-density generator-matrix (LDGM) code, Quantum LDPC (QLDPC) code
P. Fuentes, J. E. Martinez, P. M. Crespo, and J. Garcia-Frias, “Performance of non-CSS LDGM-based quantum codes over the misidentified depolarizing channel”, 2020 IEEE International Conference on Quantum Computing and Engineering (QCE) (2020) DOI. Appears in: Low-density generator-matrix (LDGM) code, Quantum LDPC (QLDPC) code
P. Fuentes, J. E. Martinez, P. M. Crespo, and J. Garcia-Frias, “Design of low-density-generator-matrix–based quantum codes for asymmetric quantum channels”, Physical Review A 103, (2021) DOI. Appears in: Low-density generator-matrix (LDGM) code, Quantum LDPC (QLDPC) code
K. Fujii and K. Yamamoto, “Entanglement purification with double selection”, Physical Review A 80, (2009) arXiv:0811.2639 DOI. Appears in: $[[7,1,3]]$ Steane code
K. Fujii and K. Yamamoto, “Topological one-way quantum computation on verified logical cluster states”, Physical Review A 82, (2010) arXiv:1008.2048 DOI. Appears in: Tree cluster-state code
K. Fujii and Y. Tokunaga, “Fault-Tolerant Topological One-Way Quantum Computation with Probabilistic Two-Qubit Gates”, Physical Review Letters 105, (2010) arXiv:1008.3752 DOI. Appears in: Tree cluster-state code
K. Fujii and Y. Tokunaga, “Error and loss tolerances of surface codes with general lattice structures”, Physical Review A 86, (2012) arXiv:1202.2743 DOI. Appears in: Toric code
K. Fujii, “Quantum Computation with Topological Codes: from qubit to topological fault-tolerance”, (2015) arXiv:1504.01444. Appears in: Qubit CSS code, Raussendorf-Bravyi-Harrington (RBH) cluster-state code, Kitaev surface code
E. Fujiwara, Code Design for Dependable Systems (Wiley, 2005) DOI. Appears in: Array code
Y. Fujiwara, D. Clark, P. Vandendriessche, M. De Boeck, and V. D. Tonchev, “Entanglement-assisted quantum low-density parity-check codes”, Physical Review A 82, (2010) arXiv:1008.4747 DOI. Appears in: Combinatorial design, EA combinatorial-design QLDPC code
Y. Fujiwara and M.-H. Hsieh, “Adaptively correcting quantum errors with entanglement”, (2011) arXiv:1104.5004. Appears in: Asymmetric quantum code, EA qubit stabilizer code
Y. Fujiwara, “Block synchronization for quantum information”, Physical Review A 87, (2013) arXiv:1206.0260 DOI. Appears in: Binary BCH code, Block quantum code, Quantum synchronizable code
Y. Fujiwara and V. D. Tonchev, “A Characterization of Entanglement-Assisted Quantum Low-Density Parity-Check Codes”, IEEE Transactions on Information Theory 59, 3347 (2013) arXiv:1108.0679 DOI. Appears in: EA QLDPC code, Low-density parity-check (LDPC) code
Y. Fujiwara, “Quantum Error Correction via Less Noisy Qubits”, Physical Review Letters 110, (2013) arXiv:1302.5081 DOI. Appears in: EA qubit stabilizer code
Y. Fujiwara, “Ability of stabilizer quantum error correction to protect itself from its own imperfection”, Physical Review A 90, (2014) arXiv:1409.2559 DOI. Appears in: Quantum data-syndrome (QDS) code, Primitive narrow-sense BCH code, Qubit code, $[[7,1,3]]$ Steane code
Y. Fujiwara, “Global stabilizer quantum error correction with combinatorial arrays”, 2015 IEEE International Symposium on Information Theory (ISIT) (2015) DOI. Appears in: Quantum data-syndrome (QDS) code
K. Fukui, A. Tomita, and A. Okamoto, “Analog Quantum Error Correction with Encoding a Qubit into an Oscillator”, Physical Review Letters 119, (2017) arXiv:1706.03011 DOI. Appears in: Concatenated GKP code, Quantum repetition code
K. Fukui, A. Tomita, A. Okamoto, and K. Fujii, “High-Threshold Fault-Tolerant Quantum Computation with Analog Quantum Error Correction”, Physical Review X 8, (2018) arXiv:1712.00294 DOI. Appears in: Cluster-state code, GKP CV-cluster-state code, Concatenated GKP code, GKP-surface code, Rotated surface code, $[[4,2,2]]$ Four-qubit code, $[[6,2,2]]$ $C_6$ code
K. Fukui, T. Matsuura, and N. C. Menicucci, “Efficient Concatenated Bosonic Code for Additive Gaussian Noise”, Physical Review Letters 131, (2023) arXiv:2102.01374 DOI. Appears in: Concatenated GKP code, Quantum parity code (QPC)
“Full length article”, Chaos, Solitons & Fractals 10, 1749 (1999) arXiv:quant-ph/9802007 DOI. Appears in: Modular-qudit code
A. Furusawa and P. van Loock, Quantum Teleportation and Entanglement (Wiley, 2011) DOI. Appears in: Cluster-state code, Analog-cluster-state code, Hybrid qudit-oscillator code
K. Furuya, N. Lashkari, and S. Ouseph, “Real-space RG, error correction and Petz map”, Journal of High Energy Physics 2022, (2022) arXiv:2012.14001 DOI. Appears in: Approximate operator-algebra QECC, Holographic code, Operator-algebra QECC (OAQECC), Renormalization group (RG) cat code
K. Furuya, N. Lashkari, and M. Moosa, “Renormalization group and approximate error correction”, Physical Review D 106, (2022) arXiv:2112.05099 DOI. Appears in: Renormalization group (RG) cat code
E. M. Gabidulin, Theory of Codes with Maximum Rank Distance, Problemy Peredachi Informacii, Volume 21, Issue 1, 3–16 (1985). Appears in: Gabidulin code
E. M. Gabidulin, "Theory of Codes with Maximum Rank Distance", Problemy Peredachi Informacii, Volume 21, Issue 1, 3–16 (1985). Appears in: Maximum-rank distance (MRD) code
P. Gaborit and A. Otmani, “Experimental constructions of self-dual codes”, Finite Fields and Their Applications 9, 372 (2003) DOI. Appears in: Self-dual linear code
P. Gaborit and G. Zemor, “Asymptotic Improvement of the Gilbert–Varshamov Bound for Linear Codes”, IEEE Transactions on Information Theory 54, 3865 (2008) arXiv:0708.4164 DOI. Appears in: Wozencraft ensemble code
P. Gaborit, O. Ruatta, J. Schrek, and G. Zémor, “RankSign: An Efficient Signature Algorithm Based on the Rank Metric”, Lecture Notes in Computer Science 88 (2014) DOI. Appears in: Low-rank parity-check (LRPC) code
P. Gaborit, A. Hauteville, D. H. Phan, and J.-P. Tillich, “Identity-Based Encryption from Codes with Rank Metric”, Lecture Notes in Computer Science 194 (2017) DOI. Appears in: Rank-metric code
P. Gaborit, W. C. Huffman, J.-L. Kim, and V. Pless, “On additive GF(4) codes,” in Codes and Association Schemes (DIMACS Workshop, November 9–12, 1999), eds. A. Barg and S. Litsyn. Providence, RI: American Mathematical Society, 2001, pp. 135–149.. Appears in: Self-dual additive code
Gaborit, P., Murat, G., Ruatta, O., & Zemor, G. (2013, April). Low rank parity check codes and their application to cryptography. In Proceedings of the Workshop on Coding and Cryptography WCC (Vol. 2013).. Appears in: Low-density parity-check (LDPC) code, Low-rank parity-check (LRPC) code
M. Gachechiladze, O. Gühne, and A. Miyake, “Changing the circuit-depth complexity of measurement-based quantum computation with hypergraph states”, Physical Review A 99, (2019) arXiv:1805.12093 DOI. Appears in: Cluster-state code, XP stabilizer code
P. Gács, “Reliable computation with cellular automata”, Proceedings of the fifteenth annual ACM symposium on Theory of computing - STOC ’83 32 (1983) DOI. Appears in: Repetition code
P. Gács, Journal of Statistical Physics 103, 45 (2001) arXiv:math/0003117 DOI. Appears in: Repetition code
F. Gaitan, Quantum Error Correction and Fault Tolerant Quantum Computing (CRC Press, 2018) DOI. Appears in: Quantum error-correcting code (QECC)
C. Galindo and F. Hernando, “On the generalization of the construction of quantum codes from Hermitian self-orthogonal codes”, Designs, Codes and Cryptography 90, 1103 (2022) arXiv:2012.11998 DOI. Appears in: Hermitian Galois-qudit code
R. Gallager, “Low-density parity-check codes”, IEEE Transactions on Information Theory 8, 21 (1962) DOI. Appears in: Gallager (GL) code, Low-density parity-check (LDPC) code
R. Gallager, Information Theory and Reliable Communication (Springer Vienna, 1972) DOI. Appears in: Binary BCH code, Error-correcting code (ECC), Bose–Chaudhuri–Hocquenghem (BCH) code
R. Gallager, Low-density parity check codes. 1963. PhD thesis, MIT Cambridge, MA.. Appears in: Gallager (GL) code, Low-density parity-check (LDPC) code, Quasi-cyclic LDPC (QC-LDPC) code
B. A. Galler and M. J. Fisher, “An improved equivalence algorithm”, Communications of the ACM 7, 301 (1964) DOI. Appears in: Kitaev surface code
A. E. Gamal, L. Hemachandra, I. Shperling, and V. Wei, “Using simulated annealing to design good codes”, IEEE Transactions on Information Theory 33, 116 (1987) DOI. Appears in: Annealing-based spherical code, Spherical code
R. A. Games, “The packing problem for projective geometries over GF(3) with dimension greater than five”, Journal of Combinatorial Theory, Series A 35, 126 (1983) DOI. Appears in: Ovoid code, $[56,6,36]_3$ Hill-cap code, $[78,6,56]_4$ Hill-cap code, Hyperoval code, Projective two-weight code, Ternary Golay code
A. Ganti, U. Onunkwo, and K. Young, “Family of[[6k,2k,2]]codes for practical and scalable adiabatic quantum computation”, Physical Review A 89, (2014) arXiv:1309.1674 DOI. Appears in: $[[6r,2r,2]]$ Ganti-Onunkwo-Young code
S. Gao, “A New Algorithm for Decoding Reed-Solomon Codes”, Communications, Information and Network Security 55 (2003) DOI. Appears in: Reed-Solomon (RS) code
A. Garcia and H. Stichtenoth, “A tower of Artin-Schreier extensions of function fields attaining the Drinfeld-Vladut bound”, Inventiones Mathematicae 121, 211 (1995) DOI. Appears in: Algebraic-geometry (AG) code
A. Garcia and H. Stichtenoth, “On the Asymptotic Behaviour of Some Towers of Function Fields over Finite Fields”, Journal of Number Theory 61, 248 (1996) DOI. Appears in: Algebraic-geometry (AG) code
H. J. García and I. L. Markov, “Simulation of Quantum Circuits via Stabilizer Frames”, (2017) arXiv:1712.03554. Appears in: Qubit code
H. J. García, I. L. Markov, and A. W. Cross, “On the Geometry of Stabilizer States”, (2017) arXiv:1711.07848. Appears in: Qubit stabilizer code
J. Garcia-Frias and Wei Zhong, “Approaching Shannon performance by iterative decoding of linear codes with low-density generator matrix”, IEEE Communications Letters 7, 266 (2003) DOI. Appears in: Low-density generator-matrix (LDGM) code
J. Garcia-Frias and Kejing Liu, “Design of near-optimum quantum error-correcting codes based on generator and parity-check matrices of LDGM codes”, 2008 42nd Annual Conference on Information Sciences and Systems (2008) DOI. Appears in: Low-density generator-matrix (LDGM) code, Quantum LDPC (QLDPC) code
J. von zur Gathen and J. Gerhard, Modern Computer Algebra (Cambridge University Press, 2013) DOI. Appears in: Reed-Solomon (RS) code
C.F. Gauss, Besprechung des Buchs von L.A. Seeber, Untersuchungen uber die Eigenschaften der positiven terndren quadratischen Formen usw. Gottingsche Gelehrte Anzeigen, July 9, 1831 = Werke, II, pp. 18g8-196, 1876.. Appears in: $D_3$ face-centered cubic (fcc) lattice
R. Gautier, A. Sarlette, and M. Mirrahimi, “Combined Dissipative and Hamiltonian Confinement of Cat Qubits”, PRX Quantum 3, (2022) arXiv:2112.05545 DOI. Appears in: Two-component cat code
J. Gavriel, Daniel, A. Shaw, M. J. Bremner, A. Paler, and S. J. Devitt, “Transversal Injection: A method for direct encoding of ancilla states for non-Clifford gates using stabiliser codes”, (2022) arXiv:2211.10046. Appears in: Kitaev surface code
V. V. Gayatri and P. K. Sarvepalli, “Decoding Algorithms for Hypergraph Subsystem Codes and Generalized Subsystem Surface Codes”, (2018) arXiv:1805.12542. Appears in: 2D subsystem color code, Generalized five-squares code, Subsystem modular-qudit stabilizer code, Sarvepalli-Brown subsystem code, Kitaev surface code
J. Gazeau, Coherent States in Quantum Physics (Wiley, 2009) DOI. Appears in: Coherent-state c-q code
D. Geberth, O. Kern, G. Alber, and I. Jex, “Stabilization of quantum information by combined dynamical decoupling and detected-jump error correction”, The European Physical Journal D 46, 381 (2007) arXiv:0712.1480 DOI. Appears in: Dual-rail quantum code
G. van der Geer and M. van der Vlugt, “Generalized Hamming Weights of Melas Codes and Dual Melas Codes”, SIAM Journal on Discrete Mathematics 7, 554 (1994) DOI. Appears in: Melas code
O. Geil and T. Hoholdt, “Footprints or generalized Bezout’s theorem”, IEEE Transactions on Information Theory 46, 635 (2000) DOI. Appears in: Hyperbolic evaluation code
O. Geil and T. Høholdt, “On Hyperbolic Codes”, Lecture Notes in Computer Science 159 (2001) DOI. Appears in: Hyperbolic evaluation code, Reed-Muller (RM) code
O. Geil, “On codes from norm–trace curves”, Finite Fields and Their Applications 9, 351 (2003) DOI. Appears in: Evaluation AG code, Hermitian code, Norm-trace code
O. Geil, “Evaluation Codes from an Affine Variety Code Perspective”, Series on Coding Theory and Cryptology 153 (2008) DOI. Appears in: Evaluation code
I. M. Gel’fand, A. V. Zelevinskii, and M. M. Kapranov, “Hypergeometric functions and toral manifolds”, Functional Analysis and Its Applications 23, 94 (1989) DOI. Appears in: Tiger code
M. R. Geller, J. M. Martinis, A. T. Sornborger, P. C. Stancil, E. J. Pritchett, H. You, and A. Galiautdinov, “Universal quantum simulation with prethreshold superconducting qubits: Single-excitation subspace method”, (2015) arXiv:1505.04990. Appears in: One-hot quantum code
P. Gemmell and M. Sudan, “Highly resilient correctors for polynomials”, Information Processing Letters 43, 169 (1992) DOI. Appears in: Reed-Solomon (RS) code
“Generalized tail-biting convolutional codes,” Ph.D. dissertation, Univ. of Massachusetts, Amherst, 1985.. Appears in: Convolutional code, Quasi-cyclic code
E. Génetay Johansen and T. Simula, “Fibonacci Anyons Versus Majorana Fermions: A Monte Carlo Approach to the Compilation of Braid Circuits in SU(2)k Anyon Models”, PRX Quantum 2, (2021) arXiv:2008.10790 DOI. Appears in: Fibonacci string-net code, Majorana stabilizer code
C. Gerhard and T. A. Brun, “Weakly Fault-Tolerant Computation in a Quantum Error-Detecting Code”, (2024) arXiv:2408.14828. Appears in: $[[2m,2m-2,2]]$ error-detecting code
C. C. Gerry and R. Grobe, “Nonclassical properties of correlated two-mode Schrödinger cat states”, Physical Review A 51, 1698 (1995) DOI. Appears in: Pair-cat code
A. Gersho, “Asymptotically optimal block quantization”, IEEE Transactions on Information Theory 25, 373 (1979) DOI. Appears in: $A_2$ triangular lattice
J. M. Gertler, B. Baker, J. Li, S. Shirol, J. Koch, and C. Wang, “Protecting a bosonic qubit with autonomous quantum error correction”, Nature 590, 243 (2021) arXiv:2004.09322 DOI. Appears in: Two-component cat code
J. M. Gertler, S. van Geldern, S. Shirol, L. Jiang, and C. Wang, “Experimental Realization and Characterization of Stabilized Pair Coherent States”, (2022) arXiv:2209.11643. Appears in: Pair-cat code
M. E. Gertsenshtein and V. B. Vasil’ev, “Waveguides with Random Inhomogeneities and Brownian Motion In the Lobachevsky Plane”, Theory of Probability & Its Applications 4, 391 (1959) DOI. Appears in: Hyperbolic sphere packing
R. Ghani, “Combining labeled and unlabeled data for text classification with a large number of categories”, Proceedings 2001 IEEE International Conference on Data Mining DOI. Appears in: Error-correcting output code (ECOC)
V. Gheorghiu, S. Y. Looi, and R. B. Griffiths, “Location of quantum information in additive graph codes”, Physical Review A 81, (2010) arXiv:0912.2017 DOI. Appears in: Modular-qudit cluster-state code
V. Gheorghiu, “Standard form of qudit stabilizer groups”, Physics Letters A 378, 505 (2014) arXiv:1101.1519 DOI. Appears in: Modular-qudit stabilizer code
V. Gheorghiu, M. Mosca, and P. Mukhopadhyay, “T-count and T-depth of any multi-qubit unitary”, npj Quantum Information 8, (2022) arXiv:2110.10292 DOI. Appears in: Qubit code
S. R. Ghorpade and G. Lachaud, “Higher Weights of Grassmann Codes”, Coding Theory, Cryptography and Related Areas 122 (2000) DOI. Appears in: Schubert code
S. R. Ghorpade and M. A. Tsfasman, “Schubert varieties, linear codes and enumerative combinatorics”, Finite Fields and Their Applications 11, 684 (2005) DOI. Appears in: Schubert code
K. S. Gibbons, M. J. Hoffman, and W. K. Wootters, “Discrete phase space based on finite fields”, Physical Review A 70, (2004) arXiv:quant-ph/0401155 DOI. Appears in: Galois-qudit code, Modular-qudit stabilizer code
C. Gidney and A. G. Fowler, “Efficient magic state factories with a catalyzed|CCZ⟩to2|T⟩transformation”, Quantum 3, 135 (2019) arXiv:1812.01238 DOI. Appears in: Kitaev surface code
C. Gidney and A. G. Fowler, “Flexible layout of surface code computations using AutoCCZ states”, (2019) arXiv:1905.08916. Appears in: Kitaev surface code
C. Gidney, M. Newman, A. Fowler, and M. Broughton, “A Fault-Tolerant Honeycomb Memory”, Quantum 5, 605 (2021) arXiv:2108.10457 DOI. Appears in: Honeycomb Floquet code
C. Gidney, “Stim: a fast stabilizer circuit simulator”, Quantum 5, 497 (2021) arXiv:2103.02202 DOI. Appears in: Qubit stabilizer code, Spacetime circuit code, Kitaev surface code
C. Gidney, M. Newman, and M. McEwen, “Benchmarking the Planar Honeycomb Code”, Quantum 6, 813 (2022) arXiv:2202.11845 DOI. Appears in: Honeycomb Floquet code
C. Gidney and C. Jones, “New circuits and an open source decoder for the color code”, (2023) arXiv:2312.08813. Appears in: 2D color code, Generalized 2D color code, Bivariate bicycle (BB) code, Honeycomb (6.6.6) color code
C. Gidney, “A Pair Measurement Surface Code on Pentagons”, Quantum 7, 1156 (2023) arXiv:2206.12780 DOI. Appears in: Honeycomb Floquet code, Kitaev surface code
C. Gidney, M. Newman, P. Brooks, and C. Jones, “Yoked surface codes”, (2023) arXiv:2312.04522. Appears in: Quantum multi-dimensional parity-check (QMDPC) code, Yoked surface code
C. Gidney, “Cleaner magic states with hook injection”, (2023) arXiv:2302.12292. Appears in: Kitaev surface code
C. Gidney and D. Bacon, “Less Bacon More Threshold”, (2023) arXiv:2305.12046. Appears in: Bacon-Shor code
C. Gidney, “Inplace Access to the Surface Code Y Basis”, Quantum 8, 1310 (2024) arXiv:2302.07395 DOI. Appears in: Kitaev surface code
C. Gidney, N. Shutty, and C. Jones, “Magic state cultivation: growing T states as cheap as CNOT gates”, (2024) arXiv:2409.17595. Appears in: Kitaev surface code
G. Giedke and J. Ignacio Cirac, “Characterization of Gaussian operations and distillation of Gaussian states”, Physical Review A 66, (2002) arXiv:quant-ph/0204085 DOI. Appears in: Analog stabilizer code
E. N. Gilbert, “A Comparison of Signalling Alphabets”, Bell System Technical Journal 31, 504 (1952) DOI. Appears in: $q$-ary code
E. N. Gilbert, “Gray Codes and Paths on the n-Cube”, Bell System Technical Journal 37, 815 (1958) DOI. Appears in: Gray code
L. Gilles, B. M. Garraway, and P. L. Knight, “Generation of nonclassical light by dissipative two-photon processes”, Physical Review A 49, 2785 (1994) DOI. Appears in: Cat code, Two-component cat code
M. Gimeno-Segovia, P. Shadbolt, D. E. Browne, and T. Rudolph, “From Three-Photon Greenberger-Horne-Zeilinger States to Ballistic Universal Quantum Computation”, Physical Review Letters 115, (2015) arXiv:1410.3720 DOI. Appears in: Cluster-state code, Quantum repetition code
R. M. Gingrich, P. Kok, H. Lee, F. Vatan, and J. P. Dowling, “All Linear Optical Quantum Memory Based on Quantum Error Correction”, Physical Review Letters 91, (2003) arXiv:quant-ph/0306098 DOI. Appears in: $[[4,2,2]]$ Four-qubit code
V. V. Ginzburg, “Multidimensional Signals for a Continuous Channel”, Probl. Peredachi Inf., 20:1 (1984), 28–46; Problems Inform. Transmission, 20:1 (1984), 20–34. Appears in: Polyphase code
V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, J. H. Shapiro, and H. P. Yuen, “Classical Capacity of the Lossy Bosonic Channel: The Exact Solution”, Physical Review Letters 92, (2004) arXiv:quant-ph/0308012 DOI. Appears in: Bosonic c-q code, Coherent-state c-q code
V. Giovannetti and R. Fazio, “Information-capacity description of spin-chain correlations”, Physical Review A 71, (2005) arXiv:quant-ph/0405110 DOI. Appears in: Amplitude-damping (AD) code
V. Giovannetti, R. García-Patrón, N. J. Cerf, and A. S. Holevo, “Ultimate classical communication rates of quantum optical channels”, Nature Photonics 8, 796 (2014) arXiv:1312.6225 DOI. Appears in: Bosonic c-q code
S. M. Girvin, “Circuit QED: superconducting qubits coupled to microwave photons”, Quantum Machines: Measurement and Control of Engineered Quantum Systems 113 (2014) DOI. Appears in: Kitaev current-mirror qubit code, Zero-pi qubit code
S. M. Girvin and K. Yang, Modern Condensed Matter Physics (Cambridge University Press, 2019) DOI. Appears in: Hamiltonian-based code
S. M. Girvin, “Introduction to quantum error correction and fault tolerance”, SciPost Physics Lecture Notes (2023) arXiv:2111.08894 DOI. Appears in: Bosonic $q$-ary expansion, Bosonic code, Repetition code
D. M. Gitman and A. L. Shelepin, “Coherent states of SU(N) groups”, Journal of Physics A: Mathematical and General 26, 313 (1993) DOI. Appears in: Tiger code, Two-mode binomial code
S. Gladchenko, D. Olaya, E. Dupont-Ferrier, B. Douçot, L. B. Ioffe, and M. E. Gershenson, “Superconducting nanocircuits for topologically protected qubits”, Nature Physics 5, 48 (2008) arXiv:0802.2295 DOI. Appears in: Quantum parity code (QPC)
S. Glancy and E. Knill, “Error analysis for encoding a qubit in an oscillator”, Physical Review A 73, (2006) arXiv:quant-ph/0510107 DOI. Appears in: Square-lattice GKP code
A. Glazyrin, “Moments of isotropic measures and optimal projective codes”, (2020) arXiv:1904.11159. Appears in: Universally optimal code
S. Glock, D. Kühn, A. Lo, and D. Osthus, “The existence of designs via iterative absorption: hypergraph $F$-designs for arbitrary $F$”, (2020) arXiv:1611.06827. Appears in: Combinatorial design, $t$-design
D. G. Glynn, “The non-classical 10-arc of PG(4, 9)”, Discrete Mathematics 59, 43 (1986) DOI. Appears in: Glynn code
J. M. Goethals and S. L. Snover, “Nearly perfect binary codes”, Discrete Mathematics 3, 65 (1972) DOI. Appears in: Nearly perfect code, Preparata code
J. M. Goethals, “Two dual families of nonlinear binary codes”, Electronics Letters 10, 471 (1974) DOI. Appears in: Goethals code
J. M. Goethals and J. J. Seidel, “Cubature Formulae, Polytopes, and Spherical Designs”, The Geometric Vein 203 (1981) DOI. Appears in: Pentakis dodecahedron code, Spherical design
J.-M. Goethals, “On the Golay perfect binary code”, Journal of Combinatorial Theory, Series A 11, 178 (1971) DOI. Appears in: $[24, 12, 8]$ Extended Golay code, Nordstrom-Robinson (NR) code
J.-M. Goethals, “The extended Nadler code is unique (Corresp.)”, IEEE Transactions on Information Theory 23, 132 (1977) DOI. Appears in: Nadler code, Nordstrom-Robinson (NR) code
J. M. Goethals and H. C. A. Van Tilborg. “Uniformly packed codes”. In Philips Research Reports 30.1 (1975). Appears in: Completely regular code, Uniformly packed code
M. Gökduman, H. Yao, and H. D. Pfister, “Erasure Decoding for Quantum LDPC Codes via Belief Propagation with Guided Decimation”, 2024 60th Annual Allerton Conference on Communication, Control, and Computing 1 (2024) arXiv:2411.08177 DOI. Appears in: Hypergraph product (HGP) code
M. Golay, “Binary coding”, Transactions of the IRE Professional Group on Information Theory 4, 23 (1954) DOI. Appears in: Julin-Golay code
M. J. E. Golay, Notes on digital coding, Proc. IEEE, 37 (1949) 657.. Appears in: $[24, 12, 8]$ Extended Golay code, $[2^r,2^r-r-1,4]$ Extended Hamming code, $[23, 12, 7]$ Golay code, $[7,4,3]$ Hamming code, $[8,4,4]$ extended Hamming code, $[2^r-1,2^r-r-1,3]$ Hamming code, $q$-ary Hamming code, Ternary Golay code
L. Gold, J. Little, and H. Schenck, “Cayley–Bacharach and evaluation codes on complete intersections”, Journal of Pure and Applied Algebra 196, 91 (2005) DOI. Appears in: Complete-intersection RM-type code
R. Gold, “Optimal binary sequences for spread spectrum multiplexing (Corresp.)”, IEEE Transactions on Information Theory 13, 619 (1967) DOI. Appears in: Gold code
G. A. Goldin, R. Menikoff, and D. H. Sharp, “Particle statistics from induced representations of a local current group”, Journal of Mathematical Physics 21, 650 (1980) DOI. Appears in: Topological code
O. Goldreich, H. Karloff, L. J. Schulman, and L. Trevisan, “Lower bounds for linear locally decodable codes and private information retrieval”, Proceedings 17th IEEE Annual Conference on Computational Complexity DOI. Appears in: Locally decodable code (LDC)
O. Goldreich and M. Sudan, “Locally testable codes and PCPs of almost-linear length”, Journal of the ACM 53, 558 (2006) DOI. Appears in: Goldreich-Sudan code
O. Goldreich, “Short Locally Testable Codes and Proofs: A Survey in Two Parts”, Lecture Notes in Computer Science 65 (2010) DOI. Appears in: Locally testable code (LTC)
A. Goldsmith, S. A. Jafar, N. Jindal, and S. Vishwanath, “Capacity limits of MIMO channels”, IEEE Journal on Selected Areas in Communications 21, 684 (2003) DOI. Appears in: Spacetime code (STC)
L. Golowich and V. Guruswami, “Quantum Locally Recoverable Codes”, (2023) arXiv:2311.08653. Appears in: Galois-qudit CSS code, Locally correctable code (LCC), Locally recoverable code (LRC), $q$-ary LDPC code, Linear $q$-ary code, Quantum LDPC (QLDPC) code, Quantum locally recoverable code (QLRC), Random quantum code, Quantum Tamo-Barg (QTB) code
L. Golowich and T. Kaufman, “NLTS Hamiltonians and Strongly-Explicit SoS Lower Bounds from Low-Rate Quantum LDPC Codes”, (2023) arXiv:2311.09503. Appears in: Quantum locally testable code (QLTC)
L. Golowich and T.-C. Lin, “Quantum LDPC Codes with Transversal Non-Clifford Gates via Products of Algebraic Codes”, (2024) arXiv:2410.14662. Appears in: Balanced product (BP) code, Expander code, Galois-qudit expander code, Generalized RM (GRM) code, $q$-ary linear LTC, Qubit CSS code, Reed-Solomon (RS) code
L. Golowich and V. Guruswami, “Asymptotically Good Quantum Codes with Transversal Non-Clifford Gates”, (2024) arXiv:2408.09254. Appears in: Quantum AG code, Triorthogonal code, Tsfasman-Vladut-Zink (TVZ) code
L. Golowich and V. Guruswami, “Decoding Quasi-Cyclic Quantum LDPC Codes”, (2024) arXiv:2411.04464. Appears in: Abelian LP code
A. Gong, S. Cammerer, and J. M. Renes, “Graph Neural Networks for Enhanced Decoding of Quantum LDPC Codes”, (2023) arXiv:2310.17758. Appears in: Quantum LDPC (QLDPC) code
A. Gong and J. M. Renes, “Improved Logical Error Rate via List Decoding of Quantum Polar Codes”, (2023) arXiv:2304.04743. Appears in: Quantum polar code
A. Gong, S. Cammerer, and J. M. Renes, “Toward Low-latency Iterative Decoding of QLDPC Codes Under Circuit-Level Noise”, (2024) arXiv:2403.18901. Appears in: $[[144,12,12]]$ gross code, Quantum LDPC (QLDPC) code
A. Gong and J. M. Renes, “Computation with quantum Reed-Muller codes and their mapping onto 2D atom arrays”, (2024) arXiv:2410.23263. Appears in: Quantum divisible code, Quantum Reed-Muller code
M. Gong et al., “Experimental exploration of five-qubit quantum error-correcting code with superconducting qubits”, National Science Review 9, (2021) arXiv:1907.04507 DOI. Appears in: Five-qubit perfect code
C. González-Arciniegas, P. Nussenzveig, M. Martinelli, and O. Pfister, “Cluster States from Gaussian States: Essential Diagnostic Tools for Continuous-Variable One-Way Quantum Computing”, PRX Quantum 2, (2021) arXiv:1912.06463 DOI. Appears in: Analog stabilizer code, Analog-cluster-state code
M. González-Sarabia, C. Renterı́a, and H. Tapia-Recillas, “Reed-Muller-Type Codes Over the Segre Variety”, Finite Fields and Their Applications 8, 511 (2002) DOI. Appears in: Segre-variety RM-type code
K. Goodenough, D. Elkouss, and S. Wehner, “Assessing the performance of quantum repeaters for all phase-insensitive Gaussian bosonic channels”, New Journal of Physics 18, 063005 (2016) arXiv:1511.08710 DOI. Appears in: Bosonic code
K. Goodenough, S. de Bone, V. Addala, S. Krastanov, S. Jansen, D. Gijswijt, and D. Elkouss, “Near-Term n to k Distillation Protocols Using Graph Codes”, IEEE Journal on Selected Areas in Communications 42, 1830 (2024) arXiv:2303.11465 DOI. Appears in: Qubit stabilizer code
P. Gopalan, C. Huang, H. Simitci, and S. Yekhanin, “On the Locality of Codeword Symbols”, (2011) arXiv:1106.3625. Appears in: Optimal LRC
P. Gopalan, C. Huang, B. Jenkins, and S. Yekhanin, “Explicit Maximally Recoverable Codes with Locality”, (2013) arXiv:1307.4150. Appears in: Maximally recoverable (MR) code
S. Gopi, S. Kopparty, R. Oliveira, N. Ron-Zewi, and S. Saraf, “Locally Testable and Locally Correctable Codes approaching the Gilbert-Varshamov Bound”, IEEE Transactions on Information Theory 64, 5813 (2018) DOI. Appears in: Kopparty-Meir-Ron-Zewi-Saraf (KMRS) code
Gopi, Sivakanth. Locality in coding theory. Diss. Princeton University, 2018.. Appears in: Generalized RM (GRM) code, Hadamard code, Locally correctable code (LCC), Locally decodable code (LDC), $q$-ary linear LCC
V. D. Goppa, Geometry and Codes (Springer Netherlands, 1988) DOI. Appears in: Algebraic-geometry (AG) code, Evaluation code
V. D. Goppa, “Algebraico-geometric codes”, Izv. Akad. Nauk SSSR Ser. Mat., 46:4 (1982), 762–781; Izv. Math., 21:1 (1983), 75–91. Appears in: Algebraic-geometry (AG) code
V. D. Goppa, “Codes Associated with Divisors”, Probl. Peredachi Inf., 13:1 (1977), 33–39; Problems Inform. Transmission, 13:1 (1977), 22–27. Appears in: Algebraic-geometry (AG) code
V. D. Goppa, “Codes on algebraic curves”, Dokl. Akad. Nauk SSSR, 259:6 (1981), 1289–1290. Appears in: Algebraic-geometry (AG) code
V. D. Goppa, "A new class of linear error-correcting codes", Probl. Peredach. Inform., vol. 6, no. 3, pp. 24-30, Sept. 1970.. Appears in: Goppa code
V. D. Goppa, "Rational representation of codes and (Lg) codes", Probl. Peredach. Inform., vol. 7, no. 3, pp. 41-49, Sept. 1971.. Appears in: Goppa code
J. Gordon, “Quantum Effects in Communications Systems”, Proceedings of the IRE 50, 1898 (1962) DOI. Appears in: Bosonic c-q code
J. P. Gordon, in Advances in Quantum Electronics edited by J. R. Singer (Columbia University, New York, 1961), p. 509. Appears in: Bosonic c-q code
J.P. Gordon, in Quantum Electronics and Coherent Light, Proceedings of the International School of Physics "Enrico Fermi," Course XXXI, edited by PA. Miles (Academic, New York, 1964), p. 156.. Appears in: Bosonic c-q code
W. Gore, “Further results on product codes”, IEEE Transactions on Information Theory 16, 446 (1970) DOI. Appears in: Tensor-product code
W. Górecki, S. Zhou, L. Jiang, and R. Demkowicz-Dobrzański, “Optimal probes and error-correction schemes in multi-parameter quantum metrology”, Quantum 4, 288 (2020) arXiv:1901.00896 DOI. Appears in: Error-corrected sensing code
D. Gorenstein, W. W. Peterson, and N. Zierler, “Two-error correcting Bose-Chaudhuri codes are quasi-perfect”, Information and Control 3, 291 (1960) DOI. Appears in: Binary BCH code, Quasi-perfect code
D. Gorenstein and N. Zierler, “A Class of Error-Correcting Codes in $p^m $ Symbols”, Journal of the Society for Industrial and Applied Mathematics 9, 207 (1961) DOI. Appears in: Primitive narrow-sense BCH code, Bose–Chaudhuri–Hocquenghem (BCH) code, Reed-Solomon (RS) code
E. V. Gorkunov, “The group of permutation automorphisms of a q-ary hamming code”, Problems of Information Transmission 45, 309 (2009) DOI. Appears in: $q$-ary Hamming code
D. Gosset, V. Kliuchnikov, M. Mosca, and V. Russo, “An algorithm for the T-count”, (2013) arXiv:1308.4134. Appears in: Qubit code
D. Gosset, R. Kothari, and K. Wu, “Quantum state preparation with optimal T-count”, (2024) arXiv:2411.04790. Appears in: Qubit code
Gosset, Thorold. "On the regular and semi-regular figures in space of n dimensions." Messenger of Mathematics 29 (1900): 43-48.. Appears in: $E_8$ Gosset lattice, $3_{21}$ polytope code, Hessian polyhedron code
M. de Gosson, Symplectic Geometry and Quantum Mechanics (Birkhäuser Basel, 2006) DOI. Appears in: Bosonic code
A. Goswami, M. Mhalla, and V. Savin, “Fault-Tolerant Preparation of Quantum Polar Codes Encoding One Logical Qubit”, (2023) arXiv:2209.06673. Appears in: Quantum polar code, Kitaev surface code
H. Goto, “Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network”, Scientific Reports 6, (2016) arXiv:1510.02566 DOI. Appears in: Two-component cat code
H. Goto, “Minimizing resource overheads for fault-tolerant preparation of encoded states of the Steane code”, Scientific Reports 6, (2016) DOI. Appears in: $[[7,1,3]]$ Steane code
H. Goto, Y. Ho, and T. Kanao, “Measurement-free fault-tolerant logical-zero-state encoding of the distance-three nine-qubit surface code in a one-dimensional qubit array”, Physical Review Research 5, (2023) arXiv:2303.17211 DOI. Appears in: $[[9,1,3]]$ Surface-17 code
H. Goto, “High-performance fault-tolerant quantum computing with many-hypercube codes”, Science Advances 10, (2024) arXiv:2403.16054 DOI. Appears in: Concatenated qubit code, $[[6,4,2]]$ error-detecting code
D. Gottesman, “Pasting Quantum Codes”, (1996) arXiv:quant-ph/9607027. Appears in: Concatenated quantum code, Perfect quantum code, Hermitian qubit code
D. Gottesman, “Class of quantum error-correcting codes saturating the quantum Hamming bound”, Physical Review A 54, 1862 (1996) arXiv:quant-ph/9604038 DOI. Appears in: $[[2^r, 2^r-r-2, 3]]$ Gottesman code, $[[8, 3, 3]]$ Eight-qubit Gottesman code
D. Gottesman, “Stabilizer Codes and Quantum Error Correction”, (1997) arXiv:quant-ph/9705052. Appears in: Perfect-tensor code, Amplitude-damping (AD) code, Perfect quantum code, Qubit CSS code, Qubit stabilizer code, Modular-qudit stabilizer code, Random stabilizer code, $[[11,1,5]]$ quantum dodecacode, $[[4,2,2]]$ Four-qubit code, Five-qubit perfect code, $[[8, 3, 3]]$ Eight-qubit Gottesman code, Hermitian qubit code
D. Gottesman, “The Heisenberg Representation of Quantum Computers”, (1998) arXiv:quant-ph/9807006. Appears in: Qubit code
D. Gottesman, “Theory of fault-tolerant quantum computation”, Physical Review A 57, 127 (1998) arXiv:quant-ph/9702029 DOI. Appears in: $[[2m,2m-2,2]]$ error-detecting code, Five-qubit perfect code, $[[6,4,2]]$ error-detecting code, Hermitian qubit code
D. Gottesman and I. L. Chuang, “Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations”, Nature 402, 390 (1999) arXiv:quant-ph/9908010 DOI. Appears in: $[[2^r-1,1,3]]$ simplex code, Qubit stabilizer code, Qubit code, Modular-qudit code
D. Gottesman, “An Introduction to Quantum Error Correction”, (2000) arXiv:quant-ph/0004072. Appears in: Quantum error-correcting code (QECC)
D. Gottesman, “Fault-tolerant quantum computation with local gates”, Journal of Modern Optics 47, 333 (2000) arXiv:quant-ph/9903099 DOI. Appears in: Concatenated qubit code, Qubit code
D. Gottesman, A. Kitaev, and J. Preskill, “Encoding a qubit in an oscillator”, Physical Review A 64, (2001) arXiv:quant-ph/0008040 DOI. Appears in: Coherent-state constellation code, Square-lattice GKP code, Hexagonal GKP code, Gottesman-Kitaev-Preskill (GKP) code, Quantum lattice code, Modular-qudit GKP code, Rotor GKP code
D. Gottesman and J. Preskill, “Secure quantum key distribution using squeezed states”, Physical Review A 63, (2001) arXiv:quant-ph/0008046 DOI. Appears in: Square-lattice GKP code, Gottesman-Kitaev-Preskill (GKP) code
D. Gottesman, “Quantum Error Correction and Fault-Tolerance”, (2005) arXiv:quant-ph/0507174. Appears in: Quantum error-correcting code (QECC)
D. Gottesman, “An Introduction to Quantum Error Correction and Fault-Tolerant Quantum Computation”, (2009) arXiv:0904.2557. Appears in: Quantum error-correcting code (QECC)
D. Gottesman, “Keeping One Step Ahead of Errors”, Physics 5, (2012) DOI. Appears in: Toric code
D. Gottesman, “Fault-Tolerant Quantum Computation with Constant Overhead”, (2014) arXiv:1310.2984. Appears in: Quantum LDPC (QLDPC) code
D. Gottesman, “Quantum fault tolerance in small experiments”, (2016) arXiv:1610.03507. Appears in: $[[4,2,2]]$ Four-qubit code
D. Gottesman and L. L. Zhang, “Fibre bundle framework for unitary quantum fault tolerance”, (2017) arXiv:1309.7062. Appears in: Honeycomb Floquet code, Gottesman-Kitaev-Preskill (GKP) code, Five-qubit perfect code, Kitaev surface code
D. Gottesman, “Opportunities and Challenges in Fault-Tolerant Quantum Computation”, (2022) arXiv:2210.15844. Appears in: Spacetime circuit code, Subsystem spacetime circuit code
D. Gottesman. Surviving as a quantum computer in a classical world (2024) URL. Appears in: Block quantum code, Concatenated Steane code, Finite-dimensional error-correcting code (ECC), $[[5,1,3]]_q$ Galois-qudit code, Galois-qudit color code, Galois-qudit CSS code, Galois-qudit code, Galois-qudit surface code, True Galois-qudit stabilizer code, Prime-qudit RS code, Quantum error-correcting code (QECC), Finite-dimensional quantum error-correcting code, Quantum AG code, Concatenated quantum code, Quantum convolutional code, Quantum-double code, Abelian quantum-double stabilizer code, Quantum Gabidulin code, Triorthogonal code, Concatenated qubit code, Qubit CSS code, Qubit stabilizer code, Qubit code, Modular-qudit code
G. Gour and N. R. Wallach, “Entanglement of subspaces and error-correcting codes”, Physical Review A 76, (2007) arXiv:0704.0251 DOI. Appears in: Perfect-tensor code, Concatenated qubit code, $((n,1,2))$ Bravyi-Lee-Li-Yoshida PI code
M. G. Gowda and P. K. Sarvepalli, “Quantum computation with generalized dislocation codes”, Physical Review A 102, (2020) DOI. Appears in: Modular-qudit surface code, Twist-defect surface code
M. G. Gowda and P. K. Sarvepalli, “Color codes with twists: Construction and universal-gate-set implementation”, Physical Review A 104, (2021) arXiv:2104.03669 DOI. Appears in: Twist-defect color code
M. G. Gowda, “Color codes with domino twists: Construction, logical measurements, and computation”, (2024) arXiv:2411.05402. Appears in: Twist-defect color code
W. T. Gowers, “An Almost m-wise Independent Random Permutation of the Cube”, Combinatorics, Probability and Computing 5, 119 (1996) DOI. Appears in: $t$-design
D. Goyeneche and K. Życzkowski, “Genuinely multipartite entangled states and orthogonal arrays”, Physical Review A 90, (2014) arXiv:1404.3586 DOI. Appears in: Perfect-tensor code, Orthogonal array (OA)
D. Goyeneche, D. Alsina, J. I. Latorre, A. Riera, and K. Życzkowski, “Absolutely maximally entangled states, combinatorial designs, and multiunitary matrices”, Physical Review A 92, (2015) arXiv:1506.08857 DOI. Appears in: Perfect-tensor code, Combinatorial design, Maximum distance separable (MDS) code, Modular-qudit cluster-state code, Three-qutrit code
D. Goyeneche, Z. Raissi, S. Di Martino, and K. Życzkowski, “Entanglement and quantum combinatorial designs”, Physical Review A 97, (2018) arXiv:1708.05946 DOI. Appears in: Perfect-tensor code, Orthogonal array (OA)
K. Gracie and M.-H. Hamon, “Turbo and Turbo-Like Codes: Principles and Applications in Telecommunications”, Proceedings of the IEEE 95, 1228 (2007) DOI. Appears in: Turbo code
L. Grans-Samuelsson, D. Aasen, and P. Bonderson, “A fault-tolerant pairwise measurement-based code on eight qubits”, (2024) arXiv:2409.13681. Appears in: Hastings-Haah Floquet code, Five-qubit perfect code
L. Grans-Samuelsson, R. V. Mishmash, D. Aasen, C. Knapp, B. Bauer, B. Lackey, M. P. da Silva, and P. Bonderson, “Improved Pairwise Measurement-Based Surface Code”, Quantum 8, 1429 (2024) arXiv:2310.12981 DOI. Appears in: Honeycomb Floquet code, Kitaev surface code
R. N. Grass, R. Heckel, M. Puddu, D. Paunescu, and W. J. Stark, “Robust Chemical Preservation of Digital Information on DNA in Silica with Error‐Correcting Codes”, Angewandte Chemie International Edition 54, 2552 (2015) DOI. Appears in: DNA storage code, Reed-Solomon (RS) code
M. Grassl, “Searching for linear codes with large minimum distance”, Algorithms and Computation in Mathematics 287 DOI. Appears in: Block quantum code, Galois-qudit stabilizer code, Qubit stabilizer code, Modular-qudit stabilizer code
M. Grassl, A. Klappenecker, and M. Rotteler, “Graphs, quadratic forms, and quantum codes”, Proceedings IEEE International Symposium on Information Theory, 45 arXiv:quant-ph/0703112 DOI. Appears in: Cluster-state code, Galois-qudit stabilizer code, Graph quantum code, Qubit stabilizer code, Modular-qudit cluster-state code, Modular-qudit stabilizer code, Stabilizer code, $[[7,1,3]]$ Steane code
M. Grassl and T. Beth, “A Note on Non-Additive Quantum Codes”, (1997) arXiv:quant-ph/9703016. Appears in: Galois-qudit USt code, Union stabilizer (USt) code
M. Grassl, Th. Beth, and T. Pellizzari, “Codes for the quantum erasure channel”, Physical Review A 56, 33 (1997) arXiv:quant-ph/9610042 DOI. Appears in: Qubit BCH code, $[[4,2,2]]$ Four-qubit code
M. Grassl and T. Beth, “Quantum BCH Codes”, (1999) arXiv:quant-ph/9910060. Appears in: Qubit BCH code
M. Grassl, W. Geiselmann, and T. Beth, “Quantum Reed—Solomon Codes”, Lecture Notes in Computer Science 231 (1999) arXiv:quant-ph/9910059 DOI. Appears in: Prime-qudit RS code
M. Grassl and T. Beth, “Cyclic quantum error–correcting codes and quantum shift registers”, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 456, 2689 (2000) arXiv:quant-ph/9910061 DOI. Appears in: Cyclic quantum code
M. GRASSL, M. RÖTTELER, and T. BETH, “EFFICIENT QUANTUM CIRCUITS FOR NON-QUBIT QUANTUM ERROR-CORRECTING CODES”, International Journal of Foundations of Computer Science 14, 757 (2003) arXiv:quant-ph/0211014 DOI. Appears in: Galois-qudit CSS code, Galois-qudit code, Galois-qudit stabilizer code
M. GRASSL, T. BETH, and M. RÖTTELER, “ON OPTIMAL QUANTUM CODES”, International Journal of Quantum Information 02, 55 (2004) arXiv:quant-ph/0312164 DOI. Appears in: Perfect-tensor code, Constacyclic code, Galois-qudit CSS code, Galois-qudit RS code, $[[2m,2m-2,2]]$ error-detecting code, Quantum maximum-distance-separable (MDS) code, Hermitian Galois-qudit code
M. Grassl and M. Rotteler, “Quantum block and convolutional codes from self-orthogonal product codes”, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005. 1018 (2005) arXiv:quant-ph/0703181 DOI. Appears in: Galois-qudit RS code, Quantum convolutional code, Quantum tensor-product code
M. Grassl and M. Rotteler, “Non-catastrophic Encoders and Encoder Inverses for Quantum Convolutional Codes”, 2006 IEEE International Symposium on Information Theory (2006) arXiv:quant-ph/0602129 DOI. Appears in: Quantum convolutional code
M. Grassl, “Classical Information Theory and Classical Error Correction”, Lectures on Quantum Information 3 (2006) DOI. Appears in: Qubit stabilizer code
M. Grassl and M. Rotteler, “Constructions of Quantum Convolutional Codes”, 2007 IEEE International Symposium on Information Theory 816 (2007) arXiv:quant-ph/0703182 DOI. Appears in: Quantum convolutional code
M. Grassl and M. Rotteler, “Non-additive quantum codes from Goethals and Preparata codes”, 2008 IEEE Information Theory Workshop (2008) arXiv:0801.2144 DOI. Appears in: Galois-qudit USt code, Goethals code, Union stabilizer (USt) code, Preparata code, $((2^m,2^{2^m−5m+1},8))$ Goethals-Preparata code, Qubit CSS code
M. Grassl and M. Rotteler, “Quantum Goethals-Preparata codes”, 2008 IEEE International Symposium on Information Theory (2008) arXiv:0801.2150 DOI. Appears in: Goethals code, Preparata code, $((2^m,2^{2^m−5m+1},8))$ Goethals-Preparata code
M. Grassl, P. W. Shor, and B. Zeng, “Generalized concatenation for quantum codes”, 2009 IEEE International Symposium on Information Theory (2009) arXiv:0905.0428 DOI. Appears in: Concatenated code, Concatenated quantum code
M. Grassl and T. A. Gulliver, “On circulant self-dual codes over small fields”, Designs, Codes and Cryptography 52, 57 (2009) DOI. Appears in: Glynn code, Reed-Solomon (RS) code
M. Grassl, P. Shor, G. Smith, J. Smolin, and B. Zeng, “Generalized concatenated quantum codes”, Physical Review A 79, (2009) arXiv:0901.1319 DOI. Appears in: Concatenated quantum code, Perfect quantum code, Modular-qudit CWS code
M. Grassl, “Variations on Encoding Circuits for Stabilizer Quantum Codes”, Lecture Notes in Computer Science 142 (2011) DOI. Appears in: $[[6,2,3]]_{q}$ code
M. Grassl and M. Rötteler, “Nonadditive quantum codes”, Quantum Error Correction 261 (2013) DOI. Appears in: Codeword stabilized (CWS) code, Union stabilizer (USt) code, $((2^m,2^{2^m−5m+1},8))$ Goethals-Preparata code, Modular-qudit CWS code, Modular-qudit USt code
M. Grassl and M. Roetteler, “Leveraging automorphisms of quantum codes for fault-tolerant quantum computation”, 2013 IEEE International Symposium on Information Theory (2013) arXiv:1302.1035 DOI. Appears in: $[[12,2,4]]$ carbon code, Qubit CSS code, $[[15, 7, 3]]$ quantum Hamming code, $[[8, 3, 3]]$ Eight-qubit Gottesman code
M. Grassl, P. W. Shor, G. Smith, J. Smolin, and B. Zeng, “New Constructions of Codes for Asymmetric Channels via Concatenation”, IEEE Transactions on Information Theory 61, 1879 (2015) arXiv:1310.7536 DOI. Appears in: Amplitude-damping (AD) code, Linear binary code, Constantin-Rao (CR) code, $[2^r-1,2^r-r-1,3]$ Hamming code, $q$-ary code
M. Grassl and M. Rotteler, “Quantum MDS codes over small fields”, 2015 IEEE International Symposium on Information Theory (ISIT) 1104 (2015) arXiv:1502.05267 DOI. Appears in: Perfect-tensor code, Galois-qudit stabilizer code, Generalized RS (GRS) code, Glynn code, Quantum maximum-distance-separable (MDS) code, $[[9,1,5]]_3$ quantum Glynn code
M. Grassl, “Classical Information Theory and Classical Error Correction”, Quantum Information 1 (2016) DOI. Appears in: Quantum error-correcting code (QECC)
M. Grassl, S. Lu, and B. Zeng, “Codes for simultaneous transmission of quantum and classical information”, 2017 IEEE International Symposium on Information Theory (ISIT) (2017) arXiv:1701.06963 DOI. Appears in: $[[7, 1:1, 3]]$ hybrid stabilizer code, $[[8, 2:1, 3]]$ hybrid stabilizer code, Hybrid qubit code, Hybrid stabilizer code, Hybrid QECC
M. Grassl, “Algebraic quantum codes: linking quantum mechanics and discrete mathematics”, International Journal of Computer Mathematics: Computer Systems Theory 6, 243 (2020) arXiv:2011.06996 DOI. Appears in: Hermitian Galois-qudit code
M. Grassl, “Entanglement-assisted quantum communication beating the quantum Singleton bound”, Physical Review A 103, (2021) arXiv:2007.01249 DOI. Appears in: EA MDS code, EA qubit stabilizer code
M. Grassl, F. Huber, and A. Winter, “Entropic Proofs of Singleton Bounds for Quantum Error-Correcting Codes”, IEEE Transactions on Information Theory 68, 3942 (2022) arXiv:2010.07902 DOI. Appears in: EA Galois-qudit stabilizer code, EA MDS code, Galois-qudit stabilizer code
M. Grassl, “New quantum codes from CSS codes”, Quantum Information Processing 22, (2023) arXiv:2208.05353 DOI. Appears in: Galois-qudit CSS code
L. Gravina, F. Minganti, and V. Savona, “Critical Schrödinger Cat Qubit”, PRX Quantum 4, (2023) arXiv:2208.04928 DOI. Appears in: Two-component cat code
L. F. Gray, “Toom’s Stability Theorem in Continuous Time”, Perplexing Problems in Probability 331 (1999) DOI. Appears in: Loop toric code, Repetition code
M. A. Graydon, J. Skanes-Norman, and J. J. Wallman, “Clifford groups are not always 2-designs”, (2021) arXiv:2108.04200. Appears in: Modular-qudit stabilizer code, $t$-design
Gray, Frank. "Pulse code communication." United States Patent Number 2632058 (1953).. Appears in: Gray code
D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, “Bell’s theorem without inequalities”, American Journal of Physics 58, 1131 (1990) DOI. Appears in: Quantum repetition code
D. M. Greenberger, M. A. Horne, and A. Zeilinger, “Going Beyond Bell’s Theorem”, (2007) arXiv:0712.0921. Appears in: Quantum repetition code
C. Greene, “Weight Enumeration and the Geometry of Linear Codes”, Studies in Applied Mathematics 55, 119 (1976) DOI. Appears in: Projective geometry code
R. R. Green, "A serial orthogonal decoder," JPL Space Programs Summary, vol. 37–39-IV, pp. 247–253, 1966.. Appears in: $[2^m-1,m,2^{m-1}]$ simplex code
J. H. Griesmer, “A Bound for Error-Correcting Codes”, IBM Journal of Research and Development 4, 532 (1960) DOI. Appears in: Griesmer code
Griffiths, Robert B. "Graph states and graph codes.". Appears in: Cluster-state code, $[[9,1,3]]$ Shor code, Five-qubit perfect code
A. Grimm, N. E. Frattini, S. Puri, S. O. Mundhada, S. Touzard, M. Mirrahimi, S. M. Girvin, S. Shankar, and M. H. Devoret, “Stabilization and operation of a Kerr-cat qubit”, Nature 584, 205 (2020) arXiv:1907.12131 DOI. Appears in: Two-component cat code
A. L. Grimsmo, J. Combes, and B. Q. Baragiola, “Quantum Computing with Rotation-Symmetric Bosonic Codes”, Physical Review X 10, (2020) arXiv:1901.08071 DOI. Appears in: Binomial code, Bosonic rotation code, Cat code, Number-phase code, Bosonic stabilizer code
A. L. Grimsmo and S. Puri, “Quantum Error Correction with the Gottesman-Kitaev-Preskill Code”, PRX Quantum 2, (2021) arXiv:2106.12989 DOI. Appears in: Square-lattice GKP code, Gottesman-Kitaev-Preskill (GKP) code
G. Grinstein, “Can complex structures be generically stable in a noisy world?”, IBM Journal of Research and Development 48, 5 (2004) DOI. Appears in: Loop toric code, Repetition code
A. Grospellier. Constant time decoding of quantum expander codes and application to fault-tolerant quantum computation. PhD thesis, Inria Paris (2019).. Appears in: Quantum expander code
D. Gross, K. Kieling, and J. Eisert, “Potential and limits to cluster-state quantum computing using probabilistic gates”, Physical Review A 74, (2006) arXiv:quant-ph/0605014 DOI. Appears in: Cluster-state code
D. Gross, “Hudson’s theorem for finite-dimensional quantum systems”, Journal of Mathematical Physics 47, (2006) arXiv:quant-ph/0602001 DOI. Appears in: Galois-qudit stabilizer code, Modular-qudit stabilizer code
D. Gross, “Non-negative Wigner functions in prime dimensions”, Applied Physics B 86, 367 (2006) arXiv:quant-ph/0702004 DOI. Appears in: Galois-qudit stabilizer code, Modular-qudit stabilizer code
D. Gross, K. Audenaert, and J. Eisert, “Evenly distributed unitaries: On the structure of unitary designs”, Journal of Mathematical Physics 48, (2007) arXiv:quant-ph/0611002 DOI. Appears in: $t$-design
D. Gross and M. V. den Nest, “The LU-LC conjecture, diagonal local operations and quadratic forms over GF(2)”, (2007) arXiv:0707.4000. Appears in: Qubit stabilizer code
J. A. Gross, “Designing Codes around Interactions: The Case of a Spin”, Physical Review Letters 127, (2021) arXiv:2005.10910 DOI. Appears in: Group-representation code, $((7,2,3))$ Pollatsek-Ruskai code, Clifford spin code
F. Grosshans and P. Grangier, “Continuous Variable Quantum Cryptography Using Coherent States”, Physical Review Letters 88, (2002) arXiv:quant-ph/0109084 DOI. Appears in: Coherent-state c-q code
F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using gaussian-modulated coherent states”, Nature 421, 238 (2003) arXiv:quant-ph/0312016 DOI. Appears in: Coherent-state c-q code
P. Groszkowski, A. D. Paolo, A. L. Grimsmo, A. Blais, D. I. Schuster, A. A. Houck, and J. Koch, “Coherence properties of the 0-πqubit”, New Journal of Physics 20, 043053 (2018) arXiv:1708.02886 DOI. Appears in: Zero-pi qubit code
M. Gschwendtner, R. König, B. Şahinoğlu, and E. Tang, “Quantum error-detection at low energies”, Journal of High Energy Physics 2019, (2019) arXiv:1902.02115 DOI. Appears in: Frustration-free Hamiltonian code, Hamiltonian-based code, Magnon code, Spin code, Symmetry-protected topological (SPT) code
M. Gu, C. Weedbrook, N. C. Menicucci, T. C. Ralph, and P. van Loock, “Quantum computing with continuous-variable clusters”, Physical Review A 79, (2009) arXiv:0903.3233 DOI. Appears in: Analog stabilizer code, Analog-cluster-state code, GKP CV-cluster-state code, Bosonic stabilizer code
S. Gu, C. A. Pattison, and E. Tang, “An efficient decoder for a linear distance quantum LDPC code”, (2022) arXiv:2206.06557. Appears in: Dinur-Hsieh-Lin-Vidick (DHLV) code, Quantum Tanner code
S. Gu, E. Tang, L. Caha, S. H. Choe, Z. He, and A. Kubica, “Single-Shot Decoding of Good Quantum LDPC Codes”, Communications in Mathematical Physics 405, (2024) arXiv:2306.12470 DOI. Appears in: Quantum Tanner code, Single-shot code
S. Gu, Y. Vaknin, A. Retzker, and A. Kubica, “Optimizing quantum error correction protocols with erasure qubits”, (2024) arXiv:2408.00829. Appears in: Rotated surface code
Z.-C. Gu and X.-G. Wen, “Tensor-entanglement-filtering renormalization approach and symmetry-protected topological order”, Physical Review B 80, (2009) arXiv:0903.1069 DOI. Appears in: Symmetry-protected topological (SPT) code
T. Guaita, L. Hackl, and T. Quella, “Representation theory of Gaussian unitary transformations for bosonic and fermionic systems”, (2024) arXiv:2409.11628. Appears in: Fermion code, Bosonic code
V. Guemard, “Lifts of quantum CSS codes”, (2024) arXiv:2404.16736. Appears in: Good QLDPC code, Quantum LDPC (QLDPC) code, Qubit CSS code, Abelian topological code, Lattice stabilizer code
K. Guenda, “Two Families of Quantum Codes Derived from Cyclic Codes”, (2007) arXiv:0711.2050. Appears in: Quantum duadic code
K. GUENDA, “QUANTUM DUADIC AND AFFINE-INVARIANT CODES”, International Journal of Quantum Information 07, 373 (2009) DOI. Appears in: Quantum duadic code
K. Guenda, S. Jitman, and T. A. Gulliver, “Constructions of Good Entanglement-Assisted Quantum Error Correcting Codes”, (2016) arXiv:1606.00134. Appears in: EA Galois-qudit stabilizer code, EA quantum LCD code, Galois-qudit GRS code, Maximal-entanglement EA Galois-qudit stabilizer code
A. Guernut and C. Vuillot, “Fault-Tolerant Constant-Depth Clifford Gates on Toric Codes”, (2024) arXiv:2411.18287. Appears in: Kitaev surface code
L. Guerra and R. Vincenti, “On the Linear Codes Arising from Schubert Varieties”, Designs, Codes and Cryptography 33, 173 (2004) DOI. Appears in: Schubert code
A. Guevara and Y. Hu, “Celestial Quantum Error Correction I: Qubits from Noncommutative Klein Space”, (2023) arXiv:2312.16298. Appears in: Holographic code, Gottesman-Kitaev-Preskill (GKP) code
A. Guevara and Y. Hu, “Celestial Quantum Error Correction II: From Qudits to Celestial CFT”, (2024) arXiv:2412.19653. Appears in: Holographic code, Gottesman-Kitaev-Preskill (GKP) code
S. Guha, Z. Dutton, and J. H. Shapiro, “On quantum limit of optical communications: Concatenated codes and joint-detection receivers”, 2011 IEEE International Symposium on Information Theory Proceedings 274 (2011) arXiv:1102.1963 DOI. Appears in: Concatenated c-q code
S. Guha, “Structured Optical Receivers to Attain Superadditive Capacity and the Holevo Limit”, Physical Review Letters 106, (2011) arXiv:1101.1550 DOI. Appears in: Coherent-state c-q code, BPSK c-q code, Hadamard BPSK c-q code
S. Guha and M. M. Wilde, “Polar coding to achieve the Holevo capacity of a pure-loss optical channel”, 2012 IEEE International Symposium on Information Theory Proceedings 546 (2012) arXiv:1202.0533 DOI. Appears in: Binary PSK (BPSK) code, Polar c-q code
O. Gühne, M. Cuquet, F. E. S. Steinhoff, T. Moroder, M. Rossi, D. Bruß, B. Kraus, and C. Macchiavello, “Entanglement and nonclassical properties of hypergraph states”, Journal of Physics A: Mathematical and Theoretical 47, 335303 (2014) arXiv:1404.6492 DOI. Appears in: Cluster-state code, Qubit stabilizer code, XP stabilizer code
Gui-Liang Feng and T. R. N. Rao, “Improved geometric Goppa codes. I. Basic theory”, IEEE Transactions on Information Theory 41, 1678 (1995) DOI. Appears in: Hyperbolic evaluation code, Reed-Solomon (RS) code
J. Guillaud and M. Mirrahimi, “Repetition Cat Qubits for Fault-Tolerant Quantum Computation”, Physical Review X 9, (2019) arXiv:1904.09474 DOI. Appears in: Asymmetric quantum code, Concatenated cat code, Cat-repetition code, Quantum repetition code, Two-component cat code
J. Guillaud and M. Mirrahimi, “Error rates and resource overheads of repetition cat qubits”, Physical Review A 103, (2021) arXiv:2009.10756 DOI. Appears in: Concatenated cat code, Cat-repetition code, Quantum repetition code, Two-component cat code
J. Guillaud, J. Cohen, and M. Mirrahimi, “Quantum computation with cat qubits”, SciPost Physics Lecture Notes (2023) arXiv:2203.03222 DOI. Appears in: Two-component cat code
S. Gukov and A. Kapustin, “Topological Quantum Field Theory, Nonlocal Operators, and Gapped Phases of Gauge Theories”, (2013) arXiv:1307.4793. Appears in: Two-gauge theory code
M. J. Gullans and D. A. Huse, “Dynamical Purification Phase Transition Induced by Quantum Measurements”, Physical Review X 10, (2020) arXiv:1905.05195 DOI. Appears in: Monitored random-circuit code, Random-circuit code
M. J. Gullans, S. Krastanov, D. A. Huse, L. Jiang, and S. T. Flammia, “Quantum Coding with Low-Depth Random Circuits”, Physical Review X 11, (2021) arXiv:2010.09775 DOI. Appears in: Crystalline-circuit qubit code, Local Haar-random circuit qubit code
T. A. Gulliver, J.-L. Kim, and Y. Lee, “New MDS or Near-MDS Self-Dual Codes”, IEEE Transactions on Information Theory 54, 4354 (2008) DOI. Appears in: Glynn code, Reed-Solomon (RS) code
L. G. Gunderman, “Local-dimension-invariant qudit stabilizer codes”, Physical Review A 101, (2020) arXiv:1910.08122 DOI. Appears in: Qubit stabilizer code, Modular-qudit stabilizer code
L. G. Gunderman, “Degenerate local-dimension-invariant stabilizer codes and an alternative bound for the distance preservation condition”, Physical Review A 105, (2022) arXiv:2110.15274 DOI. Appears in: Qubit stabilizer code, Modular-qudit stabilizer code
L. G. Gunderman, “Transforming collections of Pauli operators into equivalent collections of Pauli operators over minimal registers”, Physical Review A 107, (2023) arXiv:2206.13040 DOI. Appears in: Quantum convolutional code
L. G. Gunderman, “Stabilizer Codes with Exotic Local-dimensions”, Quantum 8, 1249 (2024) arXiv:2303.17000 DOI. Appears in: Analog stabilizer code, Modular-qudit stabilizer code
L. G. Gunderman, “Beyond Integral-Domain Stabilizer Codes”, (2025) arXiv:2501.04888. Appears in: Modular-qudit stabilizer code
U. Güngördü, R. Nepal, and A. A. Kovalev, “Parafermion stabilizer codes”, Physical Review A 90, (2014) arXiv:1409.4724 DOI. Appears in: Majorana stabilizer code, Modular-qudit stabilizer code
A. Günther and G. Nebe, “Automorphisms of doubly even self-dual binary codes”, Bulletin of the London Mathematical Society 41, 769 (2009) arXiv:0810.3787 DOI. Appears in: Group-algebra code
L. Guo and R. Li, “Linear Plotkin bound for entanglement-assisted quantum codes”, Physical Review A 87, (2013) DOI. Appears in: EA qubit stabilizer code
L. Guo, T. Huang, and L. Du, “Engineering Fault-tolerant Bosonic Codes with Quantum Lattice Gates”, (2024) arXiv:2410.17069. Appears in: Bosonic code
H. Gupta, P. Maheshwari, and A. Raina, “Fault-tolerance of [[6, 1, 3]] non-CSS code family generated using measurements on graph states”, (2025) arXiv:2501.12072. Appears in: $[[6,1,3]]$ Six-qubit stabilizer code
P. Gupta, A. Morello, and B. C. Sanders, “Universal transversal gates”, (2024) arXiv:2410.07045. Appears in: Covariant block quantum code
R. S. Gupta et al., “Encoding a magic state with beyond break-even fidelity”, Nature 625, 259 (2024) arXiv:2305.13581 DOI. Appears in: 2D color code, Heavy-hexagon code, $[[4,2,2]]$ Four-qubit code
T. Gur, G. Ramnarayan, and R. Rothblum, Theory of Computing 16, 1 (2020) DOI. Appears in: Locally correctable code (LCC)
R. M. Guralnick and P. H. Tiep, “Decompositions of Small Tensor Powers and Larsen’s Conjecture”, (2005) arXiv:math/0502080. Appears in: $t$-design, Twisted $1$-group code
V. Guruswami and M. Sudan, “Improved decoding of Reed-Solomon and algebraic-geometric codes”, Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280) 28 DOI. Appears in: Alternant code, Binary BCH code, Evaluation AG code, Generalized RS (GRS) code, Reed-Solomon (RS) code
V. Guruswami and M. Sudan, “Improved decoding of Reed-Solomon and algebraic-geometry codes”, IEEE Transactions on Information Theory 45, 1757 (1999) DOI. Appears in: Alternant code, Binary BCH code, Generalized RS (GRS) code
V. Guruswami and A. Sahai, “Multiclass learning, boosting, and error-correcting codes”, Proceedings of the twelfth annual conference on Computational learning theory (1999) DOI. Appears in: Error-correcting output code (ECOC), Hadamard code
V. Guruswami and A. Vardy, “Maximum-likelihood decoding of Reed-Solomon Codes is NP-hard”, (2004) arXiv:cs/0405005. Appears in: Reed-Solomon (RS) code
V. Guruswami, “Iterative Decoding of Low-Density Parity Check Codes (A Survey)”, (2006) arXiv:cs/0610022. Appears in: Low-density parity-check (LDPC) code
V. Guruswami and A. Rudra, “Limits to List Decoding Reed–Solomon Codes”, IEEE Transactions on Information Theory 52, 3642 (2006) DOI. Appears in: Reed-Solomon (RS) code
V. Guruswami and A. Rudra, “Explicit Codes Achieving List Decoding Capacity: Error-correction with Optimal Redundancy”, (2007) arXiv:cs/0511072. Appears in: Folded RS (FRS) code
V. Guruswami and W. Machmouchi, “Explicit interleavers for a Repeat Accumulate Accumulate (RAA) code construction”, 2008 IEEE International Symposium on Information Theory (2008) DOI. Appears in: Repeat-accumulate-accumulate (RAA) code
V. Guruswami and A. Rudra, “Better Binary List Decodable Codes Via Multilevel Concatenation”, IEEE Transactions on Information Theory 55, 19 (2009) DOI. Appears in: Folded RS (FRS) code
V. Guruswami and C. Wang, “Optimal rate list decoding via derivative codes”, (2011) arXiv:1106.3951. Appears in: Multiplicity code
V. Guruswami, “Linear-Algebraic List Decoding of Folded Reed-Solomon Codes”, 2011 IEEE 26th Annual Conference on Computational Complexity 77 (2011) arXiv:1106.0436 DOI. Appears in: Folded RS (FRS) code
V. Guruswami and C. Xing, “List decoding reed-solomon, algebraic-geometric, and gabidulin subcodes up to the singleton bound”, Proceedings of the forty-fifth annual ACM symposium on Theory of Computing (2013) DOI. Appears in: Gabidulin code, Reed-Solomon (RS) code, Subspace code, Subspace design, $t$-design
V. Guruswami and S. Li, “A Deterministic Construction of a Large Distance Code from the Wozencraft Ensemble”, (2023) arXiv:2305.02484. Appears in: Wozencraft ensemble code
V. Guruswami, A. Rudra, and M. Sudan. Essential coding theory. Draft available at this URL (2012).. Appears in: Folded RS (FRS) code
E. J. Gustafson, H. Lamm, F. Lovelace, and D. Musk, “Primitive quantum gates for an SU(2) discrete subgroup: Binary tetrahedral”, Physical Review D 106, (2022) arXiv:2208.12309 DOI. Appears in: Group-based quantum code
L. Guth and A. Lubotzky, “Quantum error correcting codes and 4-dimensional arithmetic hyperbolic manifolds”, Journal of Mathematical Physics 55, (2014) arXiv:1310.5555 DOI. Appears in: Guth-Lubotzky code
W. F. Guthrie, “NIST/SEMATECH e-Handbook of Statistical Methods (NIST Handbook 151)”, (2020) DOI. Appears in: $t$-design
E. Guttentag, A. Nemec, and K. R. Brown, “Robust Syndrome Extraction via BCH Encoding”, (2023) arXiv:2311.16044. Appears in: Quantum data-syndrome (QDS) code, Primitive narrow-sense BCH code
M. J. T. Guy, unpublished.. Appears in: $[24, 12, 8]$ Extended Golay code, Lexicographic code
A. Gyenis, P. S. Mundada, A. Di Paolo, T. M. Hazard, X. You, D. I. Schuster, J. Koch, A. Blais, and A. A. Houck, “Experimental Realization of a Protected Superconducting Circuit Derived from the 0 – π Qubit”, PRX Quantum 2, (2021) arXiv:1910.07542 DOI. Appears in: Zero-pi qubit code
L. Gyongyosi, S. Imre, and H. V. Nguyen, “A Survey on Quantum Channel Capacities”, IEEE Communications Surveys & Tutorials 20, 1149 (2018) arXiv:1801.02019 DOI. Appears in: Qubit code
J. Haah, “Local stabilizer codes in three dimensions without string logical operators”, Physical Review A 83, (2011) arXiv:1101.1962 DOI. Appears in: 3D lattice stabilizer code, Fracton stabilizer code, Haah cubic code (CC), Qudit cubic code, Self-correcting quantum code, Lattice stabilizer code
J. Haah and J. Preskill, “Logical-operator tradeoff for local quantum codes”, Physical Review A 86, (2012) arXiv:1011.3529 DOI. Appears in: Lattice subsystem code
J. Haah, “Commuting Pauli Hamiltonians as Maps between Free Modules”, Communications in Mathematical Physics 324, 351 (2013) arXiv:1204.1063 DOI. Appears in: 3D fermionic surface code, Lattice stabilizer code
J. Haah, Lattice Quantum Codes and Exotic Topological Phases of Matter, California Institute of Technology, 2013 DOI. Appears in: Lattice stabilizer code
J. Haah, “Lattice quantum codes and exotic topological phases of matter”, (2013) arXiv:1305.6973. Appears in: Quantum convolutional code, Lattice stabilizer code
J. Haah, “Bifurcation in entanglement renormalization group flow of a gapped spin model”, Physical Review B 89, (2014) arXiv:1310.4507 DOI. Appears in: Haah cubic code (CC)
J. Haah, “An Invariant of Topologically Ordered States Under Local Unitary Transformations”, Communications in Mathematical Physics 342, 771 (2016) arXiv:1407.2926 DOI. Appears in: Abelian quantum-double stabilizer code, Topological code, Abelian topological code
J. Haah, M. B. Hastings, D. Poulin, and D. Wecker, “Magic state distillation with low space overhead and optimal asymptotic input count”, Quantum 1, 31 (2017) arXiv:1703.07847 DOI. Appears in: Square-octagon (4.8.8) color code, Dodecahedron code, Doubled color code, Cycle code, Petersen cycle code, Qubit CSS code, $[[23, 1, 7]]$ Quantum Golay code, Qubit stabilizer code, $[[15,1,3]]$ quantum Reed-Muller code
J. Haah, “Algebraic Methods for Quantum Codes on Lattices”, Revista Colombiana de Matemáticas 50, 299 (2017) arXiv:1607.01387 DOI. Appears in: 2D lattice stabilizer code, Quantum convolutional code, Kitaev surface code, Lattice stabilizer code
J. Haah, “Towers of generalized divisible quantum codes”, Physical Review A 97, (2018) arXiv:1709.08658 DOI. Appears in: Square-octagon (4.8.8) color code, $[[2^r-1,1,3]]$ simplex code, Doubled color code, Generalized quantum divisible code, Quantum divisible code, $[[k+4,k,2]]$ H code, Triorthogonal code, Qubit CSS code, Random stabilizer code, $[[3k + 8, k, 2]]$ triorthogonal code
J. Haah and M. B. Hastings, “Codes and Protocols for DistillingT, controlled-S, and Toffoli Gates”, Quantum 2, 71 (2018) arXiv:1709.02832 DOI. Appears in: $[[2^D,D,2]]$ hypercube quantum code, Quantum divisible code, Quantum Reed-Muller code, Triorthogonal code
J. Haah, “Clifford quantum cellular automata: Trivial group in 2D and Witt group in 3D”, Journal of Mathematical Physics 62, (2021) arXiv:1907.02075 DOI. Appears in: Chiral semion Walker-Wang model code, Chiral semion subsystem code, Abelian topological code, Abelian TQD stabilizer code, Walker-Wang model code
J. Haah, “A degeneracy bound for homogeneous topological order”, SciPost Physics 10, (2021) arXiv:2009.13551 DOI. Appears in: 3D surface code, Topological code, Abelian topological code, Lattice stabilizer code
J. Haah, “Classification of translation invariant topological Pauli stabilizer codes for prime dimensional qudits on two-dimensional lattices”, Journal of Mathematical Physics 62, (2021) arXiv:1812.11193 DOI. Appears in: 2D lattice stabilizer code, Abelian quantum-double stabilizer code, Lattice stabilizer code
J. Haah and M. B. Hastings, “Measurement sequences for magic state distillation”, Quantum 5, 383 (2021) arXiv:2007.07929 DOI. Appears in: $[[8,3,2]]$ Smallest interesting color code
J. Haah, L. Fidkowski, and M. B. Hastings, “Nontrivial Quantum Cellular Automata in Higher Dimensions”, Communications in Mathematical Physics 398, 469 (2022) arXiv:1812.01625 DOI. Appears in: 3D bosonization code, Bosonization code, Symmetry-protected topological (SPT) code, Three-fermion (3F) Walker-Wang model code, Lattice stabilizer code, Walker-Wang model code
J. Haah and M. B. Hastings, “Boundaries for the Honeycomb Code”, Quantum 6, 693 (2022) arXiv:2110.09545 DOI. Appears in: Honeycomb Floquet code
J. Haah, “Invertible Subalgebras”, Communications in Mathematical Physics 403, 661 (2023) arXiv:2211.02086 DOI. Appears in: Hamiltonian-based code
J. Haah, “Topological phases of unitary dynamics: Classification in Clifford category”, (2024) arXiv:2205.09141. Appears in: 3D bosonization code, Bosonization code, Symmetry-protected topological (SPT) code, Three-fermion (3F) Walker-Wang model code, Walker-Wang model code
J. Haah, Two generalizations of the cubic code model, KITP Conference: Frontiers of Quantum Information Physics, UCSB, Santa Barbara, CA.. Appears in: Homological rotor code, Qudit cubic code
S. Habib, A. Beemer, and J. Kliewer, “RELDEC: Reinforcement Learning-Based Decoding of Moderate Length LDPC Codes”, (2023) arXiv:2112.13934. Appears in: Low-density parity-check (LDPC) code
E. E. Hach III and C. C. Gerry, “Generation of mixtures of Schrödinger-cat states from a competitive two-photon process”, Physical Review A 49, 490 (1994) DOI. Appears in: Cat code, Two-component cat code
L. Hackl and E. Bianchi, “Bosonic and fermionic Gaussian states from Kähler structures”, SciPost Physics Core 4, (2021) arXiv:2010.15518 DOI. Appears in: Fermion code, Bosonic code
B. Haeupler and A. Shahrasbi, “Synchronization Strings and Codes for Insertions and Deletions—A Survey”, IEEE Transactions on Information Theory 67, 3190 (2021) DOI. Appears in: Editing code
M. Hagiwara and H. Imai, “Quantum Quasi-Cyclic LDPC Codes”, 2007 IEEE International Symposium on Information Theory 806 (2007) arXiv:quant-ph/0701020 DOI. Appears in: Quasi-cyclic quantum code, Quasi-cyclic QLDPC (QC-QLDPC) code
M. Hagiwara, K. Kasai, H. Imai, and K. Sakaniwa, “Spatially Coupled Quasi-Cyclic Quantum LDPC Codes”, (2011) arXiv:1102.3181. Appears in: Quasi-cyclic code, Quantum spatially coupled (SC-QLDPC) code
M. Hagiwara and A. Nakayama, “A Four-Qubits Code that is a Quantum Deletion Error-Correcting Code with the Optimal Length”, (2020) arXiv:2001.08405. Appears in: Block quantum code, Four-qubit single-deletion code, Permutation-invariant (PI) code, PI qubit code
A. Hahn and R. Wolf, “Generalized string-net model for unitary fusion categories without tetrahedral symmetry”, Physical Review B 102, (2020) arXiv:2004.07045 DOI. Appears in: String-net code
F. Hahn, A. Pappa, and J. Eisert, “Quantum network routing and local complementation”, npj Quantum Information 5, (2019) arXiv:1805.04559 DOI. Appears in: Cluster-state code, Qubit stabilizer code
O. Hahn, A. Ferraro, L. Hultquist, G. Ferrini, and L. García-Álvarez, “Quantifying Qubit Magic Resource with Gottesman-Kitaev-Preskill Encoding”, Physical Review Letters 128, (2022) arXiv:2109.13018 DOI. Appears in: Gottesman-Kitaev-Preskill (GKP) code
O. Hahn, G. Ferrini, and R. Takagi, “Bridging magic and non-Gaussian resources via Gottesman-Kitaev-Preskill encoding”, (2024) arXiv:2406.06418. Appears in: Gottesman-Kitaev-Preskill (GKP) code
A. A. E. Hajomer, I. Derkach, R. Filip, U. L. Andersen, V. C. Usenko, and T. Gehring, “Continuous-variable quantum passive optical network”, Light: Science & Applications 13, (2024) arXiv:2402.16044 DOI. Appears in: Multi-edge LDPC code
A. Hajr et al., “High-Coherence Kerr-Cat Qubit in 2D Architecture”, Physical Review X 14, (2024) arXiv:2404.16697 DOI. Appears in: Two-component cat code
S. Hakimi and H. Frank, “Cut-set matrices and linear codes (Corresp.)”, IEEE Transactions on Information Theory 11, 457 (1965) DOI. Appears in: Cycle code
S. Hakimi and J. Bredeson, “Graph theoretic error-correcting codes”, IEEE Transactions on Information Theory 14, 584 (1968) DOI. Appears in: Cycle LDPC code, Cycle code, Petersen cycle code
G. B. Halász, T. H. Hsieh, and L. Balents, “Fracton Topological Phases from Strongly Coupled Spin Chains”, Physical Review Letters 119, (2017) arXiv:1707.02308 DOI. Appears in: Hsieh-Halasz-Balents (HHB) code
T. C. Hales, “An overview of the Kepler conjecture”, (2002) arXiv:math/9811071. Appears in: $D_3$ face-centered cubic (fcc) lattice
T. Hales et al., “A formal proof of the Kepler conjecture”, (2015) arXiv:1501.02155. Appears in: $D_3$ face-centered cubic (fcc) lattice
B. Hall, S. Gicev, and M. Usman, “Artificial neural network syndrome decoding on IBM quantum processors”, Physical Review Research 6, (2024) arXiv:2311.15146 DOI. Appears in: Heavy-hexagon code
E. K. Hall and S. G. Wilson, “Design and analysis of turbo codes on Rayleigh fading channels”, IEEE Journal on Selected Areas in Communications 16, 160 (1998) DOI. Appears in: Binary PSK (BPSK) code, Turbo code
T. Halonen, J. Romero, and J. Melero, editors , “GSM, GPRS and EDGE Performance”, (2003) DOI. Appears in: Convolutional code, Reed-Solomon (RS) code
N. Hamada and M. Deza, “A characterization of νμ + 1 + ε, νμ; t, q-min.hypers and its applications to error-correcting codes and factorial designs”, Journal of Statistical Planning and Inference 22, 323 (1989) DOI. Appears in: Griesmer code, Projective geometry code
N. Hamada, Characterization of minihypers in a finite projective geometry and its applications to error-correcting codes, Bull. Osaka Women's Univ. 24 (1987), 1-24.. Appears in: Griesmer code, Projective geometry code
H. Hämäläinen and S. Rankinen, “Upper bounds for football pool problems and mixed covering codes”, Journal of Combinatorial Theory, Series A 56, 84 (1991) DOI. Appears in: Binary-ternary mixed code, Ternary Golay code
H. Hamalainen, I. Honkala, S. Litsyn, and P. Ostergard, “Football Pools--A Game for Mathematicians”, The American Mathematical Monthly 102, 579 (1995) DOI. Appears in: Covering code
N. Hamilton, “Strongly regular graphs from differences of quadrics”, Discrete Mathematics 256, 465 (2002) DOI. Appears in: Projective two-weight code
J. Hamkins and K. Zeger, “Asymptotically dense spherical codes .II. laminated spherical codes”, IEEE Transactions on Information Theory 43, 1786 (1997) DOI. Appears in: Laminated spherical code
J. Hamkins and K. Zeger, “Asymptotically dense spherical codes. I. Wrapped spherical codes”, IEEE Transactions on Information Theory 43, 1774 (1997) DOI. Appears in: Wrapped spherical code
A. Hamma, P. Zanardi, and X.-G. Wen, “String and membrane condensation on three-dimensional lattices”, Physical Review B 72, (2005) arXiv:cond-mat/0411752 DOI. Appears in: 3D surface code
A. Hamma, C. Castelnovo, and C. Chamon, “Toric-boson model: Toward a topological quantum memory at finite temperature”, Physical Review B 79, (2009) arXiv:0812.4622 DOI. Appears in: Self-correcting quantum code, Kitaev surface code
K. Hammar, A. Orekhov, P. W. Hybelius, A. K. Wisakanto, B. Srivastava, A. F. Kockum, and M. Granath, “Error-rate-agnostic decoding of topological stabilizer codes”, Physical Review A 105, (2022) arXiv:2112.01977 DOI. Appears in: XYZ$^2$ hexagonal stabilizer code
P. C. Hammer, O. J. Marlowe, and A. H. Stroud, “Numerical Integration Over Simplexes and Cones”, Mathematical Tables and Other Aids to Computation 10, 130 (1956) DOI. Appears in: $t$-design
P. C. Hammer and A. H. Stroud, “Numerical Integration Over Simplexes”, Mathematical Tables and Other Aids to Computation 10, 137 (1956) DOI. Appears in: $t$-design
R. W. Hamming, “Error Detecting and Error Correcting Codes”, Bell System Technical Journal 29, 147 (1950) DOI. Appears in: $[2^r,2^r-r-1,4]$ Extended Hamming code, $[7,4,3]$ Hamming code, $[8,4,4]$ extended Hamming code, $[2^r-1,2^r-r-1,3]$ Hamming code
R. W. Hamming, Letter, April 5, 1978.. Appears in: Weight-two code
A. R. Hammons, P. V. Kumar, A. R. Calderbank, N. J. A. Sloane, and P. Sole, “The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes”, IEEE Transactions on Information Theory 40, 301 (1994) DOI. Appears in: Delsarte-Goethals (DG) code, Dual linear code, Goethals code, $[23, 12, 7]$ Golay code, Gray code, $[7,4,3]$ Hamming code, $[2^r-1,2^r-r-1,3]$ Hamming code, Hergert code, Kerdock code, $\Lambda_{24}$ Leech lattice, Octacode, Preparata code, Quaternary linear code over $\mathbb{Z}_4$
A. R. Hammons Jr., P. V. Kumar, A. R. Calderbank, N. J. A. Sloane, and P. Solé, “The Z_4-Linearity of Kerdock, Preparata, Goethals and Related Codes”, (2002) arXiv:math/0207208. Appears in: Delsarte-Goethals (DG) code, Dual linear code, Goethals code, Gray code, Hergert code, Kerdock code, Preparata code, Quaternary linear code over $\mathbb{Z}_4$, Quaternary RM (QRM) code, Reed-Muller (RM) code
Y. S. Han, H.-T. Pai, P.-N. Chen, and T.-Y. Wu, “Maximum-likelihood Soft-decision Decoding for Binary Linear Block Codes Based on Their Supercodes”, (2014) arXiv:1408.1310. Appears in: Linear binary code
R. van Handel and H. Mabuchi, “Optimal error tracking via quantum coding and continuous syndrome measurement”, (2005) arXiv:quant-ph/0511221. Appears in: Finite-dimensional quantum error-correcting code
L. Hanggli and R. Konig, “Oscillator-to-Oscillator Codes Do Not Have a Threshold”, IEEE Transactions on Information Theory 68, 1068 (2022) arXiv:2102.05545 DOI. Appears in: Oscillator-into-oscillator GKP code
D. Hangleiter, M. Kalinowski, D. Bluvstein, M. Cain, N. Maskara, X. Gao, A. Kubica, M. D. Lukin, and M. J. Gullans, “Fault-tolerant compiling of classically hard IQP circuits on hypercubes”, (2024) arXiv:2404.19005. Appears in: 3D surface code, Homological code, $[[2^D,D,2]]$ hypercube quantum code, Quantum repetition code, Concatenated qubit code, Qubit stabilizer code, $[[8,3,2]]$ Smallest interesting color code, Tetrahedral color code
M. Hanks, S. Lee, N. L. Piparo, S. Nishio, W. J. Munro, K. Nemoto, and M. S. Kim, “Faulty States can be used in Cat Code Error Correction”, (2024) arXiv:2412.15134. Appears in: Number-phase code
C. T. Hann, K. Noh, H. Putterman, M. H. Matheny, J. K. Iverson, M. T. Fang, C. Chamberland, O. Painter, and F. G. S. L. Brandão, “Hybrid cat-transmon architecture for scalable, hardware-efficient quantum error correction”, (2024) arXiv:2410.23363. Appears in: Two-component cat code
J. P. Hansen and H. Stichtenoth, “Group codes on certain algebraic curves with many rational points”, Applicable Algebra in Engineering, Communication and Computing 1, 67 (1990) DOI. Appears in: Suzuki-curve code
J. P. Hansen, “Deligne-Lusztig varieties and group codes”, Lecture Notes in Mathematics 63 (1992) DOI. Appears in: Deligne-Lusztig code
J. P. Hansen, “Toric Surfaces and Error-correcting Codes”, Coding Theory, Cryptography and Related Areas 132 (2000) DOI. Appears in: Hansen toric code
J. P. Hansen, “Toric Codes, Multiplicative Structure and Decoding”, (2017) arXiv:1702.06569. Appears in: Toric code, Hansen toric code
J. Hansen, “Codes on the Klein quartic, ideals, and decoding (Corresp.)”, IEEE Transactions on Information Theory 33, 923 (1987) DOI. Appears in: Klein-quartic code
S. H. Hansen, “Canonical bundles of Deligne-Lusztig varieties”, manuscripta mathematica 98, 363 (1999) DOI. Appears in: Deligne-Lusztig code
S. H. Hansen, “Error-Correcting Codes from Higher-Dimensional Varieties”, Finite Fields and Their Applications 7, 530 (2001) DOI. Appears in: Deligne-Lusztig code, Ruled-surface code
Hansen, Johan P. Group codes on algebraic curves. Universität zu Göttingen. SFB Geometrie und Analysis, 1987.. Appears in: Group-algebra code, Hermitian code
S.H. Hansen, The geometry of Deligne-Lusztig varieties: Higher dimensional AG codes, Ph.D. Thesis, University of Aarhus, 1999.. Appears in: Deligne-Lusztig code
L. Hanzo, T. H. Liew, and B. L. Yeap, Turbo Coding, Turbo Equalisation and Space‐Time Coding (Wiley, 2002) DOI. Appears in: Turbo code
L. Hanzo, T. H. Liew, B. L. Yeap, R. Y. S. Tee, and S. X. Ng, Turbo Coding, Turbo Equalisation and Space–Time Coding (Wiley, 2011) DOI. Appears in: Turbo code
Hao Chen, “On the minimum distances of Schubert codes”, IEEE Transactions on Information Theory 46, 1535 (2000) DOI. Appears in: Schubert code
H. Hao, “Investigations on Automorphism Groups of Quantum Stabilizer Codes”, (2021) arXiv:2109.12735. Appears in: $[[23, 1, 7]]$ Quantum Golay code, Five-qubit perfect code, $[[8, 3, 3]]$ Eight-qubit Gottesman code, $[[7,1,3]]$ Steane code
M. Harada, A. Munemasa, and V. D. Tonchev, “A Characterization of Designs Related to an Extremal Doubly-Even Self-Dual Code of Length 48”, Annals of Combinatorics 9, 189 (2005) DOI. Appears in: Combinatorial design, $[48,24,12]$ self-dual code
M. Harada, “Binary extremal self-dual codes of length 60 and related codes”, Designs, Codes and Cryptography 86, 1085 (2017) arXiv:1706.01694 DOI. Appears in: Self-dual linear code
N. Harle, O. Shtanko, and R. Movassagh, “Observing and braiding topological Majorana modes on programmable quantum simulators”, Nature Communications 14, (2023) arXiv:2203.15083 DOI. Appears in: Kitaev chain code
D. Harlow, “The Ryu–Takayanagi Formula from Quantum Error Correction”, Communications in Mathematical Physics 354, 865 (2017) arXiv:1607.03901 DOI. Appears in: Holographic tensor-network code, Three-qutrit code
D. Harlow and H. Ooguri, “Symmetries in quantum field theory and quantum gravity”, (2019) arXiv:1810.05338. Appears in: Pastawski-Yoshida-Harlow-Preskill (HaPPY) code
S. Haroche and J.-M. Raimond, Exploring the Quantum (Oxford University Press, 2006) DOI. Appears in: Two-component cat code
P. de la Harpe and C. Pache, “Spherical designs and finite group representations (some results of E. Bannai)”, European Journal of Combinatorics 25, 213 (2004) DOI. Appears in: Rectified Hessian polyhedron code, Slepian group-orbit code, Spherical design
R. Harper and S. T. Flammia, “Fault-Tolerant Logical Gates in the IBM Quantum Experience”, Physical Review Letters 122, (2019) arXiv:1806.02359 DOI. Appears in: $[[4,2,2]]$ Four-qubit code
J. W. Harrington, Analysis of Quantum Error-Correcting Codes: Symplectic Lattice Codes and Toric Codes, California Institute of Technology, 2004 DOI. Appears in: Kitaev surface code, Lattice stabilizer code
J. Harrington and J. Preskill, “Achievable rates for the Gaussian quantum channel”, Physical Review A 64, (2001) arXiv:quant-ph/0105058 DOI. Appears in: Gottesman-Kitaev-Preskill (GKP) code, Bosonic code
R. J. Harris, N. A. McMahon, G. K. Brennen, and T. M. Stace, “Calderbank-Shor-Steane holographic quantum error-correcting codes”, Physical Review A 98, (2018) arXiv:1806.06472 DOI. Appears in: Planar-perfect-tensor code, Heptagon holographic code
R. J. Harris, E. Coupe, N. A. McMahon, G. K. Brennen, and T. M. Stace, “Decoding holographic codes with an integer optimization decoder”, Physical Review A 102, (2020) arXiv:2008.10206 DOI. Appears in: Pastawski-Yoshida-Harlow-Preskill (HaPPY) code, Surface-code-fragment (SCF) holographic code, Qubit stabilizer code
B. Harrison, D. Nelson, D. Adamiak, and J. Whitfield, “Reducing the qubit requirement of Jordan-Wigner encodings of $N$-mode, $K$-fermion systems from $N$ to $\lceil \log_2 {N \choose K} \rceil$”, (2023) arXiv:2211.04501. Appears in: Jordan-Wigner transformation code
P. Harsha et al., “Limits of Approximation Algorithms: PCPs and Unique Games (DIMACS Tutorial Lecture Notes)”, (2010) arXiv:1002.3864. Appears in: Long code
T. Hartman, D. Mazáč, and L. Rastelli, “Sphere packing and quantum gravity”, Journal of High Energy Physics 2019, (2019) arXiv:1905.01319 DOI. Appears in: Hamiltonian-based code, Sphere packing
C. Hartmann and L. Rudolph, “An optimum symbol-by-symbol decoding rule for linear codes”, IEEE Transactions on Information Theory 22, 514 (1976) DOI. Appears in: Linear $q$-ary code
J. A. Harvey and G. W. Moore, “Moonshine, superconformal symmetry, and quantum error correction”, Journal of High Energy Physics 2020, (2020) arXiv:2003.13700 DOI. Appears in: $[23, 12, 7]$ Golay code, Hexacode
N. ul Hassan, M. Lentmaier, and G. P. Fettweis, “Comparison of LDPC block and LDPC convolutional codes based on their decoding latency”, 2012 7th International Symposium on Turbo Codes and Iterative Information Processing (ISTC) (2012) DOI. Appears in: Spatially coupled LDPC (SC-LDPC) code
S. H. Hassani and R. Urbanke, “Universal polar codes”, 2014 IEEE International Symposium on Information Theory (2014) DOI. Appears in: Polar code
S. H. Hassani, K. Alishahi, and R. L. Urbanke, “Finite-Length Scaling for Polar Codes”, IEEE Transactions on Information Theory 60, 5875 (2014) DOI. Appears in: Error-correcting code (ECC)
B. Hassibi and H. Vikalo, “On the sphere-decoding algorithm I. Expected complexity”, IEEE Transactions on Signal Processing 53, 2806 (2005) DOI. Appears in: Linear STC
F. Hassler, “Majorana Qubits”, (2014) arXiv:1404.0897. Appears in: Fermion code
J. Håstad, “Some optimal inapproximability results”, Journal of the ACM 48, 798 (2001) DOI. Appears in: Long code
T. Hastie and R. Tibshirani, “Classification by pairwise coupling”, The Annals of Statistics 26, (1998) DOI. Appears in: One-versus-one (OVO) code
M. B. Hastings and X.-G. Wen, “Quasiadiabatic continuation of quantum states: The stability of topological ground-state degeneracy and emergent gauge invariance”, Physical Review B 72, (2005) arXiv:cond-mat/0503554 DOI. Appears in: Hamiltonian-based code
M. B. Hastings, “Quantum belief propagation: An algorithm for thermal quantum systems”, Physical Review B 76, (2007) arXiv:0706.4094 DOI. Appears in: Quantum LDPC (QLDPC) code
M. B. Hastings, “Superadditivity of communication capacity using entangled inputs”, Nature Physics 5, 255 (2009) arXiv:0809.3972 DOI. Appears in: Classical-quantum (c-q) code
M. B. Hastings, “Topological Order at Nonzero Temperature”, Physical Review Letters 107, (2011) arXiv:1106.6026 DOI. Appears in: Kitaev surface code, Topological code
M. B. Hastings, “Decoding in Hyperbolic Spaces: LDPC Codes With Linear Rate and Efficient Error Correction”, (2013) arXiv:1312.2546. Appears in: Hyperbolic surface code, Single-shot code
M. B. Hastings and A. Geller, “Reduced Space-Time and Time Costs Using Dislocation Codes and Arbitrary Ancillas”, (2015) arXiv:1408.3379. Appears in: Twist-defect surface code
M. B. Hastings, “How quantum are non-negative wavefunctions?”, Journal of Mathematical Physics 57, (2015) arXiv:1506.08883 DOI. Appears in: Double-semion stabilizer code
M. B. Hastings, “Weight Reduction for Quantum Codes”, (2016) arXiv:1611.03790. Appears in: Distance-balanced code, Quantum locally testable code (QLTC)
M. B. Hastings, “Quantum Codes from High-Dimensional Manifolds”, (2016) arXiv:1608.05089. Appears in: $D$-dimensional twisted toric code, Hypersphere product code, Quantum LDPC (QLDPC) code
M. B. Hastings, “Turning Gate Synthesis Errors into Incoherent Errors”, (2016) arXiv:1612.01011. Appears in: Qubit stabilizer code, Qubit code
M. B. Hastings, “Small Majorana Fermion Codes”, (2017) arXiv:1703.00612. Appears in: Majorana color code, $[[2^{m-1},2^{m-1}-m-1,4]]_{f}$ Hamming Majorana code, Majorana stabilizer code
M. B. Hastings and J. Haah, “Distillation with Sublogarithmic Overhead”, Physical Review Letters 120, (2018) arXiv:1709.03543 DOI. Appears in: $[[2^r-1,1,3]]$ simplex code, Quantum Reed-Muller code
M. B. Hastings and J. Haah, “Dynamically Generated Logical Qubits”, Quantum 5, 564 (2021) arXiv:2107.02194 DOI. Appears in: Bacon-Shor code, Dynamical automorphism (DA) code, Hastings-Haah Floquet code, Honeycomb Floquet code, Kitaev honeycomb code, Ladder Floquet code, Monitored random-circuit code, Subsystem color code, Kitaev surface code
M. B. Hastings, J. Haah, and R. O’Donnell, “Fiber bundle codes: breaking the n ${}^{\text{1/2}}$ polylog( n ) barrier for Quantum LDPC codes”, Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing 1276 (2021) arXiv:2009.03921 DOI. Appears in: Bacon-Shor code, Fiber-bundle code, Homological product code, Hypergraph product (HGP) code
M. B. Hastings, J. Haah, and R. O’Donnell, “Fiber bundle codes: breaking the n ${}^{\text{1/2}}$ polylog( n ) barrier for Quantum LDPC codes”, Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing 1276 (2021) DOI. Appears in: Fiber-bundle code, Lifted-product (LP) code
M. B. Hastings, “On Quantum Weight Reduction”, (2023) arXiv:2102.10030. Appears in: Distance-balanced code
M. B. Hastings, LR codes, private communication, 2014.. Appears in: Two-block group-algebra (2BGA) codes
J. Hastrup and U. L. Andersen, “All-optical cat-code quantum error correction”, (2021) arXiv:2108.12225. Appears in: Two-component cat code
Hatuying Lou and J. Garcia-Frias, “Quantum error-correction using codes with low density generator matrix”, IEEE 6th Workshop on Signal Processing Advances in Wireless Communications, 2005. DOI. Appears in: Low-density generator-matrix (LDGM) code, Quantum LDPC (QLDPC) code
P. Hausladen and W. K. Wootters, “A ‘Pretty Good’ Measurement for Distinguishing Quantum States”, Journal of Modern Optics 41, 2385 (1994) DOI. Appears in: Coherent-state c-q code
V. Havlíček, M. Troyer, and J. D. Whitfield, “Operator locality in the quantum simulation of fermionic models”, Physical Review A 95, (2017) arXiv:1701.07072 DOI. Appears in: Bravyi-Kitaev transformation (BKT) code
M. Hayashi and H. Nagaoka, “A general formula for the classical capacity of a general quantum channel”, Proceedings IEEE International Symposium on Information Theory, arXiv:quant-ph/0206186 DOI. Appears in: Classical-quantum (c-q) code
M. Hayashi, “Error exponent in asymmetric quantum hypothesis testing and its application to classical-quantum channel coding”, Physical Review A 76, (2007) arXiv:quant-ph/0611013 DOI. Appears in: Classical-quantum (c-q) code
M. Hayashi, “Information Spectrum Approach to Second-Order Coding Rate in Channel Coding”, IEEE Transactions on Information Theory 55, 4947 (2009) arXiv:0801.2242 DOI. Appears in: Error-correcting code (ECC)
M. Hayashi, “Universal Coding for Classical-Quantum Channel”, Communications in Mathematical Physics 289, 1087 (2009) arXiv:0805.4092 DOI. Appears in: Classical-quantum (c-q) code
P. Hayden, R. Jozsa, D. Petz, and A. Winter, “Structure of States Which Satisfy Strong Subadditivity of Quantum Entropy with Equality”, Communications in Mathematical Physics 246, 359 (2004) arXiv:quant-ph/0304007 DOI. Appears in: Finite-dimensional quantum error-correcting code
P. Hayden and J. Preskill, “Black holes as mirrors: quantum information in random subsystems”, Journal of High Energy Physics 2007, 120 (2007) arXiv:0708.4025 DOI. Appears in: Dynamically-generated QECC
P. Hayden, M. Horodecki, A. Winter, and J. Yard, “A Decoupling Approach to the Quantum Capacity”, Open Systems & Information Dynamics 15, 7 (2008) arXiv:quant-ph/0702005 DOI. Appears in: Approximate quantum error-correcting code (AQECC), Haar-random qubit code
P. Hayden and A. May, “Summoning information in spacetime, or where and when can a qubit be?”, Journal of Physics A: Mathematical and Theoretical 49, 175304 (2016) arXiv:1210.0913 DOI. Appears in: Codeword stabilized (CWS) code, Hayden-Nezami-Salton-Sanders bosonic code, Spacetime code (STC)
P. Hayden, S. Nezami, G. Salton, and B. C. Sanders, “Spacetime replication of continuous variable quantum information”, New Journal of Physics 18, 083043 (2016) arXiv:1601.02544 DOI. Appears in: Codeword stabilized (CWS) code, Hayden-Nezami-Salton-Sanders bosonic code, Niset-Andersen-Cerf code, Spacetime code (STC)
P. Hayden, S. Nezami, X.-L. Qi, N. Thomas, M. Walter, and Z. Yang, “Holographic duality from random tensor networks”, Journal of High Energy Physics 2016, (2016) arXiv:1601.01694 DOI. Appears in: Holographic tensor-network code, Random stabilizer code
P. Hayden and G. Penington, “Learning the Alpha-bits of black holes”, Journal of High Energy Physics 2019, (2019) arXiv:1807.06041 DOI. Appears in: Approximate quantum error-correcting code (AQECC), Holographic code
P. Hayden and G. Penington, “Approximate Quantum Error Correction Revisited: Introducing the Alpha-Bit”, Communications in Mathematical Physics 374, 369 (2020) arXiv:1706.09434 DOI. Appears in: Approximate quantum error-correcting code (AQECC)
P. Hayden, S. Nezami, S. Popescu, and G. Salton, “Error Correction of Quantum Reference Frame Information”, PRX Quantum 2, (2021) arXiv:1709.04471 DOI. Appears in: Covariant block quantum code, $G$-covariant erasure code, Three-rotor code, W-state code
A. J. F. Hayes, A. Gilchrist, and T. C. Ralph, “Loss-tolerant operations in parity-code linear optics quantum computing”, Physical Review A 77, (2008) arXiv:0707.0903 DOI. Appears in: Quantum parity code (QPC)
A. J. F. Hayes, H. L. Haselgrove, A. Gilchrist, and T. C. Ralph, “Fault tolerance in parity-state linear optical quantum computing”, Physical Review A 82, (2010) arXiv:0908.3932 DOI. Appears in: Quantum parity code (QPC)
X. He, L. Xu, and H. Chen, “New $q$-ary Quantum MDS Codes with Distances Bigger than $\frac{q}{2}$”, (2015) arXiv:1507.08355. Appears in: Constacyclic code, Quantum maximum-distance-separable (MDS) code, Hermitian Galois-qudit code
Y.-H. He and J. McKay, “Sporadic and Exceptional”, (2015) arXiv:1505.06742. Appears in: $3_{21}$ polytope code, Hessian polyhedron code, Witting polytope code
Z. He, L. Robitaille, and X. Tan, “Permutation gates in the third level of the Clifford hierarchy”, (2024) arXiv:2410.11818. Appears in: Qubit code
Z. He, D. Amaro, R. Shaydulin, and M. Pistoia, “Performance of Quantum Approximate Optimization with Quantum Error Detection”, (2024) arXiv:2409.12104. Appears in: $[[2m,2m-2,2]]$ error-detecting code
M. Hebenstreit, R. Jozsa, B. Kraus, S. Strelchuk, and M. Yoganathan, “All Pure Fermionic Non-Gaussian States Are Magic States for Matchgate Computations”, Physical Review Letters 123, (2019) arXiv:1905.08584 DOI. Appears in: Fermion code
R. Heckel, G. Mikutis, and R. N. Grass, “A Characterization of the DNA Data Storage Channel”, (2018) arXiv:1803.03322. Appears in: DNA storage code
A. S. Hedayat, N. J. A. Sloane, and J. Stufken, Orthogonal Arrays (Springer New York, 1999) DOI. Appears in: Mixed code, Orthogonal array (OA), $q$-ary code
A. Hedayat and W. D. Wallis, “Hadamard Matrices and Their Applications”, The Annals of Statistics 6, (1978) DOI. Appears in: Hadamard code
O. Heden, “On the size of the symmetry group of a perfect code”, Discrete Mathematics 311, 1879 (2011) DOI. Appears in: Perfect binary code
O. Heden, F. Pasticci, and T. Westerbäck, “On the symmetry group of extended perfect binary codes of length $n+1$ and rank $n-\log(n+1)+2$”, Advances in Mathematics of Communications 6, 121 (2012) DOI. Appears in: Perfect binary code
C. Heegard and S. B. Wicker, Turbo Coding (Springer US, 1999) DOI. Appears in: Turbo code
B. Heim, K. M. Svore, and M. B. Hastings, “Optimal Circuit-Level Decoding for Surface Codes”, (2016) arXiv:1609.06373. Appears in: Kitaev surface code
M. Hein, J. Eisert, and H. J. Briegel, “Multiparty entanglement in graph states”, Physical Review A 69, (2004) arXiv:quant-ph/0307130 DOI. Appears in: Cluster-state code, Concatenated Steane code
M. Hein, W. Dür, J. Eisert, R. Raussendorf, M. V. den Nest, and H.-J. Briegel, “Entanglement in Graph States and its Applications”, (2006) arXiv:quant-ph/0602096. Appears in: Cluster-state code, XP stabilizer code
M. Heinrich and D. Gross, “Robustness of Magic and Symmetries of the Stabiliser Polytope”, Quantum 3, 132 (2019) arXiv:1807.10296 DOI. Appears in: Qubit stabilizer code
H. J. Helgert, “Noncyclic generalizations of BCH and srivastava codes”, Information and Control 21, 280 (1972) DOI. Appears in: Alternant code, Srivastava code
H. J. Helgert, “Alternant codes”, Information and Control 26, 369 (1974) DOI. Appears in: Alternant code
H. J. Helgert, “Binary primitive alternant codes”, Information and Control 27, 101 (1975) DOI. Appears in: Alternant code
H. Helgert, “Srivastava codes”, IEEE Transactions on Information Theory 18, 292 (1972) DOI. Appears in: Generalized Srivastava code, Srivastava code
H. Helgert, “Decoding of alternant codes (Corresp.)”, IEEE Transactions on Information Theory 23, 513 (1977) DOI. Appears in: Alternant code
T. H. Helleseth, H. G. Schaathun, T. H. Helleseth, and H. G. Schaathun, “On the&lt;tex&gt;$”, IEEE Transactions on Information Theory 50, 3312 (2004) DOI. Appears in: Frameproof (FP) code, Kerdock code
T. Helleseth, “No primitive binary&lt;tex&gt;t&lt;/tex&gt;-error-correcting BCH code with&lt;tex&gt;t &gt; 2&lt;/tex&gt;is quasi-perfect (Corresp.)”, IEEE Transactions on Information Theory 25, 361 (1979) DOI. Appears in: Binary BCH code, Quasi-perfect code
T. Helleseth and P. Vijay Kumar, “The weight hierarchy of the Kasami codes”, Discrete Mathematics 145, 133 (1995) DOI. Appears in: Griesmer code, Kasami code
T. Helleseth and P. V. Kumar, “The algebraic decoding of the Z/sub 4/-linear Goethals code”, IEEE Transactions on Information Theory 41, 2040 (1995) DOI. Appears in: Hergert code
T. Helleseth, C. Li, "Pseudo-Noise Sequences." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI. Appears in: Gold code, Kasami code
W. Helwig, W. Cui, J. I. Latorre, A. Riera, and H.-K. Lo, “Absolute maximal entanglement and quantum secret sharing”, Physical Review A 86, (2012) arXiv:1204.2289 DOI. Appears in: Perfect-tensor code, Approximate secret-sharing code
W. Helwig and W. Cui, “Absolutely Maximally Entangled States: Existence and Applications”, (2013) arXiv:1306.2536. Appears in: Perfect-tensor code, Maximum distance separable (MDS) code, Approximate secret-sharing code, Modular-qudit cluster-state code
W. Helwig, “Absolutely Maximally Entangled Qudit Graph States”, (2013) arXiv:1306.2879. Appears in: Perfect-tensor code, Maximum distance separable (MDS) code, Modular-qudit cluster-state code, Three-qutrit code
B. Hemenway, R. Ostrovsky, and M. Wootters, “Local Correctability of Expander Codes”, (2015) arXiv:1304.8129. Appears in: Expander code, Locally decodable code (LDC)
Heng Tang, Jun Xu, S. Lin, and K. A. S. Abdel-Ghaffar, “Codes on finite geometries”, IEEE Transactions on Information Theory 51, 572 (2005) DOI. Appears in: Finite-geometry LDPC (FG-LDPC) code, Quasi-cyclic LDPC (QC-LDPC) code
Henkel, W. (2000). Analog codes for peak-to-average ratio reduction. ITG FACHBERICHT, 151-156.. Appears in: Analog RS code
R. Henry, “Polynomial Batch Codes for Efficient IT-PIR”, Proceedings on Privacy Enhancing Technologies 2016, 202 (2016) DOI. Appears in: Batch code, Locally decodable code (LDC), Private information retrieval (PIR) code
Henry D. Pfister, private communication, 2022. Appears in: Irregular repeat-accumulate (IRA) code, MacKay-Neal LDPC (MN-LDPC) code
R. Hentschke, F. Marques, F. Lima, L. Carro, A. Susin, and R. Reis, “Analyzing area and performance penalty of protecting different digital modules with Hamming code and triple modular redundancy”, Proceedings. 15th Symposium on Integrated Circuits and Systems Design 95 DOI. Appears in: $[2^r-1,2^r-r-1,3]$ Hamming code
X. Herbert, J. Gross, and M. Newman, “Qutrit codes within representations of SU(3)”, (2023) arXiv:2312.00162. Appears in: $SU(3)$ spin code
F. B. Hergert, “On the delsarte-goethals codes and their formal duals”, Discrete Mathematics 83, 249 (1990) DOI. Appears in: Delsarte-Goethals (DG) code, Dual linear code, Goethals code, Hergert code
F. Hernando, K. Lally, and D. Ruano, “Construction and decoding of matrix-product codes from nested codes”, Applicable Algebra in Engineering, Communication and Computing 20, 497 (2009) DOI. Appears in: Matrix-product code
F. Hernando, G. Quintana-Ortí, and M. Grassl, “Fast Algorithms and Implementations for Computing the Minimum Distance of Quantum Codes”, (2024) arXiv:2408.10743. Appears in: Qubit stabilizer code
M. Herold, E. T. Campbell, J. Eisert, and M. J. Kastoryano, “Cellular-automaton decoders for topological quantum memories”, npj Quantum Information 1, (2015) arXiv:1406.2338 DOI. Appears in: Self-correcting quantum code, Kitaev surface code
M. Herold, M. J. Kastoryano, E. T. Campbell, and J. Eisert, “Cellular automaton decoders of topological quantum memories in the fault tolerant setting”, New Journal of Physics 19, 063012 (2017) arXiv:1511.05579 DOI. Appears in: Kitaev surface code
D. A. Herrera-Martí, A. G. Fowler, D. Jennings, and T. Rudolph, “Photonic implementation for the topological cluster-state quantum computer”, Physical Review A 82, (2010) arXiv:1005.2915 DOI. Appears in: Raussendorf-Bravyi-Harrington (RBH) cluster-state code
I. Hesner, B. Hetényi, and J. R. Wootton, “Using Detector Likelihood for Benchmarking Quantum Error Correction”, (2024) arXiv:2408.02082. Appears in: Kitaev surface code
B. Hetényi and J. R. Wootton, “Creating Entangled Logical Qubits in the Heavy-Hex Lattice with Topological Codes”, PRX Quantum 5, (2024) arXiv:2404.15989 DOI. Appears in: Heavy-hexagon code
S. Heußen, D. F. Locher, and M. Müller, “Measurement-free fault-tolerant quantum error correction in near-term devices”, (2023) arXiv:2307.13296. Appears in: Qubit CSS code
S. Heußen and J. Hilder, “Efficient fault-tolerant code switching via one-way transversal CNOT gates”, (2024) arXiv:2409.13465. Appears in: Qubit stabilizer code, Modular-qudit stabilizer code
M. Heydeman, M. Marcolli, S. Parikh, and I. Saberi, “Nonarchimedean Holographic Entropy from Networks of Perfect Tensors”, (2018) arXiv:1812.04057. Appears in: Perfect-tensor code, Galois-qudit GRS code, Galois-qudit RS code, Holographic tensor-network code
L. Heyfron and E. T. Campbell, “An Efficient Quantum Compiler that reduces $T$ count”, (2018) arXiv:1712.01557. Appears in: Qubit code
O. Higgott and N. P. Breuckmann, “Subsystem Codes with High Thresholds by Gauge Fixing and Reduced Qubit Overhead”, Physical Review X 11, (2021) arXiv:2010.09626 DOI. Appears in: Asymmetric quantum code, Subsystem hyperbolic surface code, Subsystem surface code, 2D hyperbolic surface code
O. Higgott, M. Wilson, J. Hefford, J. Dborin, F. Hanif, S. Burton, and D. E. Browne, “Optimal local unitary encoding circuits for the surface code”, Quantum 5, 517 (2021) arXiv:2002.00362 DOI. Appears in: Kitaev surface code
O. Higgott, “PyMatching: A Python package for decoding quantum codes with minimum-weight perfect matching”, (2021) arXiv:2105.13082. Appears in: Kitaev surface code
O. Higgott and N. P. Breuckmann, “Improved Single-Shot Decoding of Higher-Dimensional Hypergraph-Product Codes”, PRX Quantum 4, (2023) arXiv:2206.03122 DOI. Appears in: 3D surface code, Loop toric code, Homological code, Hypergraph product (HGP) code
O. Higgott, T. C. Bohdanowicz, A. Kubica, S. T. Flammia, and E. T. Campbell, “Improved decoding of circuit noise and fragile boundaries of tailored surface codes”, (2023) arXiv:2203.04948. Appears in: Kitaev surface code, XZZX surface code
O. Higgott and N. P. Breuckmann, “Constructions and Performance of Hyperbolic and Semi-Hyperbolic Floquet Codes”, PRX Quantum 5, (2024) arXiv:2308.03750 DOI. Appears in: Hyperbolic Floquet code
O. Higgott and C. Gidney, “Sparse Blossom: correcting a million errors per core second with minimum-weight matching”, Quantum 9, 1600 (2025) arXiv:2303.15933 DOI. Appears in: Qubit stabilizer code
“High-Performance Embedded Computing”, (2014) DOI. Appears in: Repetition code
P. Hilaire, T. Dessertaine, B. Bourdoncle, A. Denys, G. de Gliniasty, G. Valentí-Rojas, and S. Mansfield, “Enhanced Fault-tolerance in Photonic Quantum Computing: Floquet Code Outperforms Surface Code in Tailored Architecture”, (2024) arXiv:2410.07065. Appears in: Honeycomb Floquet code, Kitaev surface code
Hill, R. (1973). Caps and groups. Colloquio Internazionale sulle Teorie Combinatorie (Rome, 1973), 2, 389-394.. Appears in: Hill projective-cap code
Hill, R. (1973). On the largest size of cap in s53. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, 54(3), 378-384.. Appears in: $[56,6,36]_3$ Hill-cap code
R. Hill, Caps and groups, pp. 389–394 in: Proc. Rome 1973, Atti dei Convegni Lincei, 1976.. Appears in: $[78,6,56]_4$ Hill-cap code
R. Hill. A First Course In Coding Theory. Oxford University Press, 1988.. Appears in: Binary BCH code, $[2^r-1,2^r-r-1,3]$ Hamming code, Primitive narrow-sense BCH code
T. Hillmann, F. Quijandría, A. L. Grimsmo, and G. Ferrini, “Performance of Teleportation-Based Error-Correction Circuits for Bosonic Codes with Noisy Measurements”, PRX Quantum 3, (2022) arXiv:2108.01009 DOI. Appears in: Number-phase code
T. Hillmann and F. Quijandría, “Quantum error correction with dissipatively stabilized squeezed-cat qubits”, Physical Review A 107, (2023) arXiv:2210.13359 DOI. Appears in: Squeezed cat code, Two-component cat code
T. Hillmann, L. Berent, A. O. Quintavalle, J. Eisert, R. Wille, and J. Roffe, “Localized statistics decoding: A parallel decoding algorithm for quantum low-density parity-check codes”, (2024) arXiv:2406.18655. Appears in: Quantum LDPC (QLDPC) code
T. Hillmann, G. Dauphinais, I. Tzitrin, and M. Vasmer, “Single-shot and measurement-based quantum error correction via fault complexes”, (2024) arXiv:2410.12963. Appears in: Cluster-state code, Homological code
R. Hill, "Optimal Linear Codes in: C. Mitchell (Ed.) Crytography and Coding." (1992): 75-104.. Appears in: Anticode, Griesmer code
M. Hirao, H. Nozaki, and K. Tasaka, “Spherical designs and modular forms of the $D_4$ lattice”, (2023) arXiv:2303.09000. Appears in: $D_4$ lattice-shell code, Spherical design
J. W. P. Hirschfeld and L. Storme, “The Packing Problem in Statistics, Coding Theory and Finite Projective Spaces: Update 2001”, Developments in Mathematics 201 (2001) DOI. Appears in: Griesmer code, Maximum distance separable (MDS) code, Projective geometry code
J. W. P. Hirschfeld and J. A. Thas, “Open problems in finite projective spaces”, Finite Fields and Their Applications 32, 44 (2015) DOI. Appears in: Maximum distance separable (MDS) code
J. W. P. Hirschfeld. Rational curves on quadrics over ﬁnite ﬁelds of characteristic two. Rend. Mat. (6), 4:773–795, 1971.. Appears in: Hirschfeld code
M. Hivadi, “On quantum SPC product codes”, Quantum Information Processing 17, (2018) DOI. Appears in: Classical-product code
B. M. Hochwald and T. L. Marzetta, “Unitary space-time modulation for multiple-antenna communications in Rayleigh flat fading”, IEEE Transactions on Information Theory 46, 543 (2000) DOI. Appears in: Spacetime block code (STBC)
B. M. Hochwald, T. L. Marzetta, T. J. Richardson, W. Sweldens, and R. Urbanke, “Systematic design of unitary space-time constellations”, IEEE Transactions on Information Theory 46, 1962 (2000) DOI. Appears in: Spacetime block code (STBC)
B. M. Hochwald and W. Sweldens, “Differential unitary space-time modulation”, IEEE Transactions on Communications 48, 2041 (2000) DOI. Appears in: Spacetime block code (STBC)
A. Hocquenghem, Codes correcteurs d'Erreurs, Chiffres (Paris), vol.2, pp.147-156, 1959.. Appears in: Binary BCH code
G. Hoehn, “Self-dual Codes over the Kleinian Four Group”, (2000) arXiv:math/0005266. Appears in: Hexacode, Lexicographic code, Lattice-based code, Self-dual linear code, Self-dual additive code
G. Hoehn, “Conformal Designs based on Vertex Operator Algebras”, (2007) arXiv:math/0701626. Appears in: $t$-design
A. J. Hoffman and R. R. Singleton, “On Moore Graphs with Diameters 2 and 3”, IBM Journal of Research and Development 4, 497 (1960) DOI. Appears in: Hoffman-Singleton cycle code, Hoffman-Singleton graph-adjacency code
J. Hoffstein, J. Pipher, and J. H. Silverman, “NTRU: A ring-based public key cryptosystem”, Lecture Notes in Computer Science 267 (1998) DOI. Appears in: Low-rank parity-check (LRPC) code, NTRU-GKP code
T. Hoholdt and R. Pellikaan, “On the decoding of algebraic-geometric codes”, IEEE Transactions on Information Theory 41, 1589 (1995) DOI. Appears in: Evaluation AG code
J. A. Holbrook, D. W. Kribs, and R. Laflamme, “Noiseless subsystems and the structure of the commutant in quantum error correction”, (2004) arXiv:quant-ph/0402056. Appears in: Operator-algebra QECC (OAQECC)
T. Høholdt, J.H. Van Lint, and R. Pellikaan, 1998. Algebraic geometry codes. Handbook of coding theory, 1 (Part 1), pp.871-961.. Appears in: Algebraic-geometry (AG) code, Hyperbolic evaluation code, Elliptic code, Evaluation AG code, Polynomial evaluation code, Evaluation code, Generalized RM (GRM) code, Generalized RS (GRS) code, Goppa code, Hermitian code, Hexacode, Klein-quartic code, Norm-trace code, Plane-curve code, Linear $q$-ary code, Residue AG code
A. S. Holevo, “The capacity of the quantum channel with general signal states”, IEEE Transactions on Information Theory 44, 269 (1998) DOI. Appears in: Classical-quantum (c-q) code
A. S. Holevo and R. F. Werner, “Evaluating capacities of Bosonic Gaussian channels”, (1999) arXiv:quant-ph/9912067. Appears in: GKP-surface code, Bosonic code
A. S. Holevo, “Reliability function of general classical-quantum channel”, IEEE Transactions on Information Theory 46, 2256 (2000) arXiv:quant-ph/9907087 DOI. Appears in: Classical-quantum (c-q) code
A. S. Holevo, “The Choi–Jamiolkowski forms of quantum Gaussian channels”, Journal of Mathematical Physics 52, (2011) arXiv:1004.0196 DOI. Appears in: Bosonic code
A. S. Holevo, “Quantum Systems, Channels, Information”, (2019) DOI. Appears in: Bosonic c-q code
A. Holevo, Probabilistic and Statistical Aspects of Quantum Theory (Edizioni della Normale, 2011) DOI. Appears in: Number-phase code
A. S. Holevo, “Bounds for the Quantity of Information Transmitted by a Quantum Communication Channel”, Probl. Peredachi Inf., 9:3 (1973), 3–11; Problems Inform. Transmission, 9:3 (1973), 177–183. Appears in: Classical-quantum (c-q) code
H. D. L. Hollmann, J. H. van Lint, J.-P. Linnartz, and L. M. G. M. Tolhuizen, “On Codes with the Identifiable Parent Property”, Journal of Combinatorial Theory, Series A 82, 121 (1998) DOI. Appears in: Identifiable parent property (IPP) code
Z. Holmes, G. Muraleedharan, R. D. Somma, Y. Subasi, and B. Şahinoğlu, “Quantum algorithms from fluctuation theorems: Thermal-state preparation”, Quantum 6, 825 (2022) arXiv:2203.08882 DOI. Appears in: Spin GKP code
T. Holstein and H. Primakoff, “Field Dependence of the Intrinsic Domain Magnetization of a Ferromagnet”, Physical Review 58, 1098 (1940) DOI. Appears in: Binomial code, Square-lattice GKP code, GNU PI code, Spin cat code, Spin GKP code, Two-component cat code
B. Honary and G. Markarian, “New simple encoder and trellis decoder for Golay codes”, Electronics Letters 29, 2170 (1993) DOI. Appears in: $[24, 12, 8]$ Extended Golay code, $[23, 12, 7]$ Golay code
D. Honciuc Menendez, A. Ray, and M. Vasmer, “Implementing fault-tolerant non-Clifford gates using the [[8,3,2]] color code”, Physical Review A 109, (2024) arXiv:2309.08663 DOI. Appears in: $[[8,3,2]]$ Smallest interesting color code
A. Honecker, M. Picco, and P. Pujol, “Universality Class of the Nishimori Point in the 2D±JRandom-Bond Ising Model”, Physical Review Letters 87, (2001) arXiv:cond-mat/0010143 DOI. Appears in: Toric code
S.-M. Hong, “On symmetrization of 6j-symbols and Levin-Wen Hamiltonian”, (2009) arXiv:0907.2204. Appears in: String-net code
Y. Hong, J. T. Young, A. M. Kaufman, and A. Lucas, “Quantum error correction in a time-dependent transverse-field Ising model”, Physical Review A 106, (2022) arXiv:2205.12998 DOI. Appears in: Transverse-field Ising model (TFIM) code
Y. Hong, M. Marinelli, A. M. Kaufman, and A. Lucas, “Long-range-enhanced surface codes”, Physical Review A 110, (2024) arXiv:2309.11719 DOI. Appears in: Hypergraph product (HGP) code, Long-range enhanced surface code (LRESC)
Y. Hong, E. Durso-Sabina, D. Hayes, and A. Lucas, “Entangling Four Logical Qubits beyond Break-Even in a Nonlocal Code”, Physical Review Letters 133, (2024) arXiv:2406.02666 DOI. Appears in: Long-range enhanced surface code (LRESC)
Y. Hong, “Single-shot preparation of hypergraph product codes via dimension jump”, (2024) arXiv:2410.05171. Appears in: Hypergraph product (HGP) code
Y. Hong, J. Guo, and A. Lucas, “Quantum memory at nonzero temperature in a thermodynamically trivial system”, Nature Communications 16, (2025) arXiv:2403.10599 DOI. Appears in: Expander code, Quantum expander code, Self-correcting quantum code
G. ’t Hooft, “On the phase transition towards permanent quark confinement”, Nuclear Physics B 138, 1 (1978) DOI. Appears in: Modular-qudit code
S. Hoory, N. Linial, and A. Wigderson, “Expander graphs and their applications”, Bulletin of the American Mathematical Society 43, 439 (2006) DOI. Appears in: Expander code, Expander LP code, Good QLDPC code, Left-right Cayley complex code, Quantum expander code, Tanner code
J. E. Hopcroft and J. D. Ullman, “Set Merging Algorithms”, SIAM Journal on Computing 2, 294 (1973) DOI. Appears in: Kitaev surface code
F. Hopfmueller, M. Tremblay, P. St-Jean, B. Royer, and M.-A. Lemonde, “Bosonic Pauli+: Efficient Simulation of Concatenated Gottesman-Kitaev-Preskill Codes”, Quantum 8, 1539 (2024) arXiv:2402.09333 DOI. Appears in: Concatenated GKP code
M. Hopkins and T.-C. Lin, “Explicit Lower Bounds Against $Ω(n)$-Rounds of Sum-of-Squares”, (2022) arXiv:2204.11469. Appears in: Quantum Tanner code
F. Hörmann, H. Bartz, and A.-L. Horlemann, “Distinguishing and Recovering Generalized Linearized Reed–Solomon Codes”, Lecture Notes in Computer Science 1 (2023) arXiv:2304.00627 DOI. Appears in: Linearized RS code
M. Horodecki, J. Oppenheim, and A. Winter, “Quantum State Merging and Negative Information”, Communications in Mathematical Physics 269, 107 (2006) arXiv:quant-ph/0512247 DOI. Appears in: Haar-random qubit code
D. Horsman, A. G. Fowler, S. Devitt, and R. V. Meter, “Surface code quantum computing by lattice surgery”, New Journal of Physics 14, 123011 (2012) arXiv:1111.4022 DOI. Appears in: Kitaev surface code
E. Hostens, J. Dehaene, and B. De Moor, “Stabilizer states and Clifford operations for systems of arbitrary dimensions and modular arithmetic”, Physical Review A 71, (2005) arXiv:quant-ph/0408190 DOI. Appears in: Galois-qudit stabilizer code, Qubit stabilizer code, Modular-qudit stabilizer code, Modular-qudit code
S. K. Houghten, C. W. H. Lam, L. H. Thiel, and J. A. Parker, “The extended quadratic residue code is the only (48,24,12) self-dual doubly-even code”, IEEE Transactions on Information Theory 49, 53 (2003) DOI. Appears in: Divisible code, Self-dual linear code, $[48,24,12]$ self-dual code
M. Houshmand, S. Hosseini-Khayat, and M. M. Wilde, “Minimal-Memory Requirements for Pearl-Necklace Encoders of Quantum Convolutional Codes”, IEEE Transactions on Computers 61, 299 (2012) arXiv:1004.5179 DOI. Appears in: Quantum convolutional code
M. Houshmand, S. Hosseini-Khayat, and M. M. Wilde, “Minimal-Memory, Noncatastrophic, Polynomial-Depth Quantum Convolutional Encoders”, IEEE Transactions on Information Theory 59, 1198 (2013) arXiv:1105.0649 DOI. Appears in: Quantum convolutional code
M. Howard and J. Vala, “Qudit versions of the qubitπ/8gate”, Physical Review A 86, (2012) arXiv:1206.1598 DOI. Appears in: Modular-qudit code
Hsiang-Ku Lin and Leonid Pryadko, private communication, 2024.. Appears in: Two-block group-algebra (2BGA) codes
J.-Y. Hsieh, C.-M. Li, and D.-S. Chuu, “Analytical technique for simplification of the encoder–decoder circuit for a perfect five-qubit error correction”, New Journal of Physics 8, 80 (2006) arXiv:quant-ph/0410004 DOI. Appears in: Five-qubit perfect code
M. H. Hsieh, W. T. Yen, and L. Y. Hsu, “Undetermined states: how to find them and their applications”, The European Physical Journal D 61, 261 (2010) arXiv:0809.3081 DOI. Appears in: Perfect-tensor code
M.-H. Hsieh, I. Devetak, and T. Brun, “General entanglement-assisted quantum error-correcting codes”, Physical Review A 76, (2007) arXiv:0708.2142 DOI. Appears in: Entanglement-assisted (EA) subsystem QECC
M.-H. Hsieh, “Entanglement-assisted Coding Theory”, (2008) arXiv:0807.2080. Appears in: Entanglement-assisted (EA) hybrid QECC
M.-H. Hsieh and M. M. Wilde, “Public and private communication with a quantum channel and a secret key”, Physical Review A 80, (2009) arXiv:0903.3920 DOI. Appears in: Entanglement-assisted (EA) hybrid QECC
M.-H. Hsieh and M. M. Wilde, “Entanglement-Assisted Communication of Classical and Quantum Information”, IEEE Transactions on Information Theory 56, 4682 (2010) arXiv:0811.4227 DOI. Appears in: Entanglement-assisted (EA) hybrid QECC
M.-H. Hsieh, W.-T. Yen, and L.-Y. Hsu, “High Performance Entanglement-Assisted Quantum LDPC Codes Need Little Entanglement”, IEEE Transactions on Information Theory 57, 1761 (2011) arXiv:0906.5532 DOI. Appears in: EA FG-QLDPC code, EA QC-QLDPC code
M.-H. Hsieh and F. Le Gall, “NP-hardness of decoding quantum error-correction codes”, Physical Review A 83, (2011) arXiv:1009.1319 DOI. Appears in: Qubit stabilizer code
T. H. Hsieh and G. B. Halász, “Fractons from partons”, Physical Review B 96, (2017) arXiv:1703.02973 DOI. Appears in: Hsieh-Halasz (HH) code
P.-S. Hsin, R. Kobayashi, and G. Zhu, “Non-Abelian Self-Correcting Quantum Memory”, (2024) arXiv:2405.11719. Appears in: Loop toric code, Cubic theory code, Dihedral $G=D_m$ quantum-double code, Self-correcting quantum code
P.-S. Hsin, R. Kobayashi, and G. Zhu, “Classifying Logical Gates in Quantum Codes via Cohomology Operations and Symmetry”, (2024) arXiv:2411.15848. Appears in: Qubit CSS code
P. S. Hsin, private communication, 2024.. Appears in: Dijkgraaf-Witten gauge theory code, Two-gauge theory code
C.-H. Hsu and A. Anastasopoulos, “Capacity-Achieving Codes with Bounded Graphical Complexity on Noisy Channels”, (2005) arXiv:cs/0509062. Appears in: Hsu-Anastasopoulos LDPC (HA-LDPC) code
A. T. Hu and A. B. Khesin, “Improved graph formalism for quantum circuit simulation”, Physical Review A 105, (2022) arXiv:2109.10210 DOI. Appears in: Qubit stabilizer code
C. Hu, S. Yang, and S. S.-T. Yau, “Weight enumerators for nonbinary asymmetric quantum codes and their applications”, Advances in Applied Mathematics 121, 102085 (2020) DOI. Appears in: Qubit code
D. Hu, W. Tang, M. Zhao, Q. Chen, S. Yu, and C. H. Oh, “Graphical nonbinary quantum error-correcting codes”, Physical Review A 78, (2008) arXiv:0801.0831 DOI. Appears in: $((5,6,2))$ qubit code, Modular-qudit CWS code, Modular-qudit USt code, $((5+2r,3\times 2^{2r+1},2))$ Rains code, Small-distance block quantum code
F. N. Hu, W. Henkel, and M. J. Zhao, “Analog Codes for Gross Error Correction in Signal Transmission”, Advanced Materials Research 341–342, 514 (2011) DOI. Appears in: Analog RS code
J. Y.-C. Hu, D. Wu, and H. Liu, “Provably Optimal Memory Capacity for Modern Hopfield Models: Transformer-Compatible Dense Associative Memories as Spherical Codes”, (2024) arXiv:2410.23126. Appears in: Spherical code
J. Hu, Q. Liang, N. Rengaswamy, and R. Calderbank, “CSS Codes that are Oblivious to Coherent Noise”, 2021 IEEE International Symposium on Information Theory (ISIT) (2021) DOI. Appears in: Constant-excitation (CE) code, Qubit CSS code
J. Hu, Q. Liang, and R. Calderbank, “Divisible Codes for Quantum Computation”, (2022) arXiv:2204.13176. Appears in: $[2^m,m+1,2^{m-1}]$ First-order RM code, Quantum divisible code, Concatenated qubit code, Qubit CSS code, Five-qubit perfect code, $[[7,1,3]]$ Steane code
J. Hu, Q. Liang, N. Rengaswamy, and R. Calderbank, “Mitigating Coherent Noise by Balancing Weight-2 Z-Stabilizers”, IEEE Transactions on Information Theory 68, 1795 (2022) arXiv:2011.00197 DOI. Appears in: Constant-excitation (CE) code, $[[10,1,4]]_{G}$ tenfold code, Qubit CSS code, Five-qubit perfect code
J. Hu, Q. Liang, and R. Calderbank, “Designing the Quantum Channels Induced by Diagonal Gates”, Quantum 6, 802 (2022) arXiv:2109.13481 DOI. Appears in: Quantum divisible code, Qubit CSS code
L. Hu et al., “Quantum error correction and universal gate set operation on a binomial bosonic logical qubit”, Nature Physics 15, 503 (2019) arXiv:1805.09072 DOI. Appears in: Binomial code
X.-Yu. Hu and E. Eleftheriou, “Binary representation of cycle Tanner-graph GF(2/sup b/) codes”, 2004 IEEE International Conference on Communications (IEEE Cat. No.04CH37577) (2004) DOI. Appears in: $q$-ary LDPC code
Y. Hu, Y. Wan, and Y.-S. Wu, “Twisted quantum double model of topological phases in two dimensions”, Physical Review B 87, (2013) arXiv:1211.3695 DOI. Appears in: Dijkgraaf-Witten gauge theory code, String-net code, Twisted quantum double (TQD) code, Abelian TQD stabilizer code
Y. Hu and Y. Zou, “Petz map recovery for long-range entangled quantum many-body states”, Physical Review B 110, (2024) arXiv:2408.00857 DOI. Appears in: Approximate quantum error-correcting code (AQECC), Topological code
C. Huang and L. Xu, “STAR : An Efficient Coding Scheme for Correcting Triple Storage Node Failures”, IEEE Transactions on Computers 57, 889 (2008) DOI. Appears in: Star code
C. Huang, M. Chen, and J. Li, “Pyramid Codes”, ACM Transactions on Storage 9, 1 (2013) DOI. Appears in: Pyramid code
E. Huang, A. Pesah, C. T. Chubb, M. Vasmer, and A. Dua, “Tailoring Three-Dimensional Topological Codes for Biased Noise”, PRX Quantum 4, (2023) arXiv:2211.02116 DOI. Appears in: 3D lattice stabilizer code, 3D surface code, Asymmetric quantum code, Clifford-deformed surface code (CDSC), Qubit stabilizer code, Rotated surface code
H.-Y. Huang, R. Kueng, G. Torlai, V. V. Albert, and J. Preskill, “Provably efficient machine learning for quantum many-body problems”, Science 377, (2022) arXiv:2106.12627 DOI. Appears in: Topological code
K. Huang, D. G. M. Mitchell, L. Wei, X. Ma, and D. J. Costello, “Performance comparison of non-binary LDPC block and spatially coupled codes”, 2014 IEEE International Symposium on Information Theory (2014) DOI. Appears in: $q$-ary protograph LDPC code
S.-J. Huang and Y. Chen, “Generating logical magic states with the aid of non-Abelian topological order”, (2025) arXiv:2502.00998. Appears in: Quantum-double code, Modular-qudit surface code
S. Huang, T. Jochym-O’Connor, and T. J. Yoder, “Homomorphic Logical Measurements”, (2022) arXiv:2211.03625. Appears in: Qubit CSS code, Kitaev surface code
S. Huang and S. Puri, “Improved Noisy Syndrome Decoding of Quantum LDPC Codes with Sliding Window”, (2023) arXiv:2311.03307. Appears in: Quantum LDPC (QLDPC) code
T.-H. Huang and Y.-L. Ueng, “A Binary BP Decoding Using Posterior Adjustment for Quantum LDPC Codes”, ICASSP 2024 - 2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (2024) DOI. Appears in: Quantum LDPC (QLDPC) code
C. Huang, H. Simitci, Y. Xu, A. Ogus, B. Calder, P. Gopalan, J. Li, and S. Yekhanin. Erasure coding in Windows Azure Storage. In Proc. USENIX Annual Technical Conference (ATC), pgs. 15-26, Boston, Massachusetts, June 2012.. Appears in: Locally recoverable code (LRC)
Huaxiong Wang, Chaoping Xing, and R. Safavi-Naini, “Linear authentication codes: bounds and constructions”, IEEE Transactions on Information Theory 49, 866 (2003) DOI. Appears in: Gabidulin code, Subspace code
F. Huber, C. Eltschka, J. Siewert, and O. Gühne, “Bounds on absolutely maximally entangled states from shadow inequalities, and the quantum MacWilliams identity”, Journal of Physics A: Mathematical and Theoretical 51, 175301 (2018) arXiv:1708.06298 DOI. Appears in: Perfect-tensor code
F. Huber and M. Grassl, “Quantum Codes of Maximal Distance and Highly Entangled Subspaces”, Quantum 4, 284 (2020) arXiv:1907.07733 DOI. Appears in: Perfect-tensor code, Quantum maximum-distance-separable (MDS) code
M. HUBER, “CODING THEORY AND ALGEBRAIC COMBINATORICS”, Selected Topics in Information and Coding Theory 121 (2010) arXiv:0811.1254 DOI. Appears in: Combinatorial design, $[24, 12, 8]$ Extended Golay code, $[23, 12, 7]$ Golay code, Pless symmetry code, Quadratic-residue (QR) code, Ternary Golay code
W. C. Huffman and V. Pless, Fundamentals of Error-Correcting Codes (Cambridge University Press, 2003) DOI. Appears in: Binary BCH code, Binary duadic code, Binary quadratic-residue (QR) code, Cross-interleaved RS (CIRS) code, Dodecacode, Extended GRS code, Generalized RM (GRM) code, Generalized RS (GRS) code, Goppa code, $[2^r-1,2^r-r-1,3]$ Hamming code, Hexacode, Maximum distance separable (MDS) code, Primitive narrow-sense BCH code, Narrow-sense RS code, Nearly perfect code, Perfect code, Pless symmetry code, Bose–Chaudhuri–Hocquenghem (BCH) code, $q$-ary duadic code, $q$-ary Hamming code, Quadratic-residue (QR) code, Reed-Muller (RM) code, Self-dual linear code, Self-dual additive code, Hermitian qubit code
W. C. Huffman, J.-L. Kim, and P. Solé, Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI. Appears in: Evaluation AG code, Frameproof (FP) code, Kerdock code, Preparata code, Universally optimal $q$-ary code
Huffman, D. A. "A graph-theoretic formulation of binary group codes." Summaries of papers presented at ICMCI, part 3 (1964): 29-30.. Appears in: Cycle code
W. C. Huffman, J.-L. Kim, and P. Solé, "Basics of coding theory." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI. Appears in: Binary code, Dual linear code, Maximum distance separable (MDS) code, $q$-ary code
B. L. Hughes, “Differential space-time modulation”, IEEE Transactions on Information Theory 46, 2567 (2000) DOI. Appears in: Spacetime block code (STBC), Multi-channel group-orbit code
D. Hughes and S. Waldron, “Spherical (t,t)-designs with a small number of vectors”, Linear Algebra and its Applications 608, 84 (2021) DOI. Appears in: Pentakis dodecahedron code, Spherical design
Hui Jin and R. J. McEliece, “Coding theorems for turbo code ensembles”, IEEE Transactions on Information Theory 48, 1451 (2002) DOI. Appears in: Turbo code
Hui Jin, Aamod Khandekar, and Robert McEliece. "Irregular repeat-accumulate codes." Proc. 2nd Int. Symp. Turbo codes and related topics. 2000.. Appears in: Irregular repeat-accumulate (IRA) code
Hui Jin, Aamod Khandekar, and Robert J. McEliece. "Serial concatenation of interleaved convolutional codes forming turbo-like codes." United States Patent Number 7116710B1 (2023).. Appears in: Irregular repeat-accumulate (IRA) code
M.-X. Huo and Y. Li, “Learning time-dependent noise to reduce logical errors: real time error rate estimation in quantum error correction”, New Journal of Physics 19, 123032 (2017) arXiv:1710.03636 DOI. Appears in: Qubit stabilizer code
N. Hussami, S. B. Korada, and R. Urbanke, “Performance of polar codes for channel and source coding”, 2009 IEEE International Symposium on Information Theory (2009) DOI. Appears in: Polar code
A. Hutter, J. R. Wootton, and D. Loss, “Efficient Markov chain Monte Carlo algorithm for the surface code”, Physical Review A 89, (2014) arXiv:1302.2669 DOI. Appears in: Kitaev surface code, Toric code
J. Huxford and S. H. Simon, “Excitations in the higher-lattice gauge theory model for topological phases. I. Overview”, Physical Review B 108, (2023) arXiv:2202.08294 DOI. Appears in: Two-gauge theory code
J. Huxford and S. H. Simon, “Excitations in the higher-lattice gauge theory model for topological phases. II. The (2+1) -dimensional case”, Physical Review B 108, (2023) arXiv:2204.05341 DOI. Appears in: Quantum-double code
J. Huxford, D. X. Nguyen, and Y. B. Kim, “Twisted Lattice Gauge Theory: Membrane Operators, Three-loop Braiding and Topological Charge”, (2024) arXiv:2401.13042. Appears in: Dijkgraaf-Witten gauge theory code
J. Huxford and S. H. Simon, “Excitations in the higher-lattice gauge theory model for topological phases. III. The (3+1)-dimensional case”, Physical Review B 109, (2024) arXiv:2206.09941 DOI. Appears in: Two-gauge theory code
Y. Hwang and J. Heo, “On the relation between a graph code and a graph state”, (2015) arXiv:1511.05647. Appears in: Cluster-state code, Graph quantum code, Group-based cluster-state code, Modular-qudit cluster-state code, $[[9,1,3]]$ Shor code, Five-qubit perfect code
S. I. Mrutu, A. Sam, and N. H. Mvungi, “Forward Error Correction Convolutional Codes for RTAs’ Networks: An Overview”, International Journal of Computer Network and Information Security 6, 19 (2014) DOI. Appears in: Convolutional code
A. V. Iampolskaia, A. N. Skorobogatov, and E. A. Sorokin, “Formula for the number of [9,3] MDS codes”, IEEE Transactions on Information Theory 41, 1667 (1995) DOI. Appears in: Maximum distance separable (MDS) code, Projective geometry code
Ian Teixeira, private communication, 2024. Appears in: Five-qubit perfect code
B. Ide, M. G. Gowda, P. J. Nadkarni, and G. Dauphinais, “Fault-tolerant logical measurements via homological measurement”, (2024) arXiv:2410.02753. Appears in: Qubit CSS code
Y. Ihara. "Some remarks on the number of rational points of algebraic curves over finite fields." J. Fac. Sci. Univ. Tokyo Sect. IA Math., 28:721-724 (1982),1981.. Appears in: Tsfasman-Vladut-Zink (TVZ) code
K. A. S. Immink. Codes for mass data storage systems. Shannon Foundation Publisher, 2004.. Appears in: Balanced code
T. Inada, W. Jang, Y. Iiyama, K. Terashi, R. Sawada, J. Tanaka, and S. Asai, “Measurement-Free Ultrafast Quantum Error Correction by Using Multi-Controlled Gates in Higher-Dimensional State Space”, (2021) arXiv:2109.00086. Appears in: Qubit CSS code
P. Indyk, “Deterministic superimposed coding with applications to pattern matching”, Proceedings 38th Annual Symposium on Foundations of Computer Science 18, 127 DOI. Appears in: Superimposed code
I. Ingemarsson, “Group Codes for the Gaussian Channel”, Lecture Notes in Control and Information Sciences 73 DOI. Appears in: Slepian group-orbit code
I. Ingemarsson, “Optimized permutation modulation”, IEEE Transactions on Information Theory 36, 1098 (1990) DOI. Appears in: Permutation spherical code
International Organization for Standardization, Information Technology: Automatic Identification and Data Capture Techniques-QR Code 2005 Bar Code Symbology Specification, 2nd ed., IEC18004 (ISO, 2006).. Appears in: Reed-Solomon (RS) code
International Telecommunication Union-T, Recommendation V.21: 300 bits per second duplex modem standardized for use in the general switched telephone network, 1984. Appears in: Binary PSK (BPSK) code
International Telecommunication Union-T, Recommendation V.23: 600/1200-baud modem standardized for use in the general switched telephone network, 1988. Appears in: Binary PSK (BPSK) code
International Telecommunication Union-T, Recommendation V.24: List of definitions for interchange circuits between data terminal equipment (DTE) and data circuit-terminating equipment (DCE), 1988. Appears in: Quadrature PSK (QPSK) code
International Telecommunication Union-T, Recommendation V.27ter: 4800/2400 Bits Per Second Modem Standardized For Use in the General Switched Telephone Network, 1984. Appears in: Phase-shift keying (PSK) code
International Telecommunication Union-T, Recommendation V.29: 9600 Bits Per Second Modem Standardized For Use on Point-to-Point 4-Wire Leased Telephone-Tpe Circuits, 1993. Appears in: Quadrature-amplitude modulation (QAM) code
L. B. Ioffe and M. V. Feigel’man, “Possible realization of an ideal quantum computer in Josephson junction array”, Physical Review B 66, (2002) arXiv:cond-mat/0205186 DOI. Appears in: Zero-pi qubit code
L. Ioffe and M. Mézard, “Asymmetric quantum error-correcting codes”, Physical Review A 75, (2007) arXiv:quant-ph/0606107 DOI. Appears in: Asymmetric quantum code, Galois-qudit BCH code, Subsystem Galois-qudit stabilizer code
A. deMarti iOlius, J. E. Martinez, P. Fuentes, and P. M. Crespo, “Performance enhancement of surface codes via recursive minimum-weight perfect-match decoding”, Physical Review A 108, (2023) arXiv:2212.11632 DOI. Appears in: Toric code
A. deMarti iOlius and J. E. Martinez, “The closed-branch decoder for quantum LDPC codes”, (2024) arXiv:2402.01532. Appears in: Quantum LDPC (QLDPC) code
A. deMarti iOlius, I. E. Martinez, J. Roffe, and J. E. Martinez, “An almost-linear time decoding algorithm for quantum LDPC codes under circuit-level noise”, (2024) arXiv:2409.01440. Appears in: Quantum LDPC (QLDPC) code
A. deMarti iOlius, P. Fuentes, R. Orús, P. M. Crespo, and J. Etxezarreta Martinez, “Decoding algorithms for surface codes”, Quantum 8, 1498 (2024) arXiv:2307.14989 DOI. Appears in: Kitaev surface code
J. T. Iosue, K. Sharma, M. J. Gullans, and V. V. Albert, “Continuous-Variable Quantum State Designs: Theory and Applications”, Physical Review X 14, (2024) arXiv:2211.05127 DOI. Appears in: Number-phase code, $t$-design
J. T. Iosue, T. C. Mooney, A. Ehrenberg, and A. V. Gorshkov, “Projective toric designs, quantum state designs, and mutually unbiased bases”, Quantum 8, 1546 (2024) arXiv:2311.13479 DOI. Appears in: $t$-design
M. Ippoliti, M. J. Gullans, S. Gopalakrishnan, D. A. Huse, and V. Khemani, “Entanglement Phase Transitions in Measurement-Only Dynamics”, Physical Review X 11, (2021) arXiv:2004.09560 DOI. Appears in: Dynamically-generated QECC, Quantum LDPC (QLDPC) code
M. Iqbal et al., “Non-Abelian topological order and anyons on a trapped-ion processor”, Nature 626, 505 (2024) arXiv:2305.03766 DOI. Appears in: Dihedral $G=D_m$ quantum-double code
M. Iqbal et al., “Qutrit Toric Code and Parafermions in Trapped Ions”, (2024) arXiv:2411.04185. Appears in: Modular-qudit surface code
Y. Ishai, E. Kushilevitz, R. Ostrovsky, and A. Sahai, “Batch codes and their applications”, Proceedings of the thirty-sixth annual ACM symposium on Theory of computing (2004) DOI. Appears in: Batch code, Locally decodable code (LDC)
“Is quantum mechanics useful?”, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences 353, 367 (1995) DOI. Appears in: Quantum error-correcting code (QECC)
T. Itogawa, Y. Takada, Y. Hirano, and K. Fujii, “Even more efficient magic state distillation by zero-level distillation”, (2024) arXiv:2403.03991. Appears in: Kitaev surface code
J. S. Ivan, K. K. Sabapathy, and R. Simon, “Operator-sum representation for bosonic Gaussian channels”, Physical Review A 84, (2011) arXiv:1012.4266 DOI. Appears in: Bosonic code
K. Ivanov and R. L. Urbanke, “Capacity-achieving codes: a review on double transitivity”, (2020) arXiv:2010.15453. Appears in: Pless symmetry code, Linear $q$-ary code, Quadratic-residue (QR) code
K. Ivanov and R. Urbanke, “Polar Codes Do Not Have Many Affine Automorphisms”, (2022) arXiv:2112.12495. Appears in: Polar code
J. K. Iverson and J. Preskill, “Coherence in logical quantum channels”, New Journal of Physics 22, 073066 (2020) arXiv:1912.04319 DOI. Appears in: Toric code
P. Iyer and D. Poulin, “Hardness of decoding quantum stabilizer codes”, (2013) arXiv:1310.3235. Appears in: Qubit stabilizer code
S. Izumi, M. Takeoka, M. Fujiwara, N. D. Pozza, A. Assalini, K. Ema, and M. Sasaki, “Displacement receiver for phase-shift-keyed coherent states”, Physical Review A 86, (2012) arXiv:1208.1815 DOI. Appears in: PSK c-q code
S. Izumi, M. Takeoka, K. Ema, and M. Sasaki, “Quantum receivers with squeezing and photon-number-resolving detectors forM-ary coherent state discrimination”, Physical Review A 87, (2013) arXiv:1302.2691 DOI. Appears in: PSK c-q code
S. Izumi, J. S. Neergaard-Nielsen, S. Miki, H. Terai, and U. L. Andersen, “Experimental Demonstration of a Quantum Receiver Beating the Standard Quantum Limit at Telecom Wavelength”, Physical Review Applied 13, (2020) arXiv:2001.05902 DOI. Appears in: PSK c-q code
S. Izumi, J. S. Neergaard-Nielsen, and U. L. Andersen, “Adaptive Generalized Measurement for Unambiguous State Discrimination of Quaternary Phase-Shift-Keying Coherent States”, PRX Quantum 2, (2021) arXiv:2009.02558 DOI. Appears in: PSK c-q code
M. V. Jabir, I. A. Burenkov, N. F. R. Annafianto, A. Battou, and S. V. Polyakov, “Experimental demonstration of the near-quantum optimal receiver”, OSA Continuum 3, 3324 (2020) DOI. Appears in: Coherent FSK (CFSK) c-q code
M. V. Jabir, N. F. R. Annafianto, I. A. Burenkov, A. Battou, and S. V. Polyakov, “Energy and bandwidth efficiency optimization of quantum-enabled optical communication channels”, npj Quantum Information 8, (2022) DOI. Appears in: Coherent FSK (CFSK) c-q code
M. V. Jabir, N. F. R. Annafianto, I. A. Burenkov, M. Dagenais, A. Battou, and S. V. Polyakov, “Versatile quantum-enabled telecom receiver”, AVS Quantum Science 5, (2023) DOI. Appears in: PSK c-q code
T. Jackson, M. Grassl, and B. Zeng, “Concatenated codes for amplitude damping”, 2016 IEEE International Symposium on Information Theory (ISIT) (2016) arXiv:1601.07423 DOI. Appears in: Amplitude-damping (AD) code, Concatenated qubit code
R. Jahangir, N. Arshed, and A. H. Toor, “Quantum capacity of an amplitude-damping channel with memory”, Quantum Information Processing 14, 765 (2014) arXiv:1207.5612 DOI. Appears in: Amplitude-damping (AD) code
A. Jahn, M. Gluza, F. Pastawski, and J. Eisert, “Majorana dimers and holographic quantum error-correcting codes”, Physical Review Research 1, (2019) arXiv:1905.03268 DOI. Appears in: Pastawski-Yoshida-Harlow-Preskill (HaPPY) code, Majorana stabilizer code
A. Jahn and J. Eisert, “Holographic tensor network models and quantum error correction: a topical review”, Quantum Science and Technology 6, 033002 (2021) arXiv:2102.02619 DOI. Appears in: Holographic code
A. Jain, A. R. Kalra, and S. Prakash, “A Normal Form for Single-Qudit Clifford+$T$ Operators”, (2020) arXiv:2011.07970. Appears in: Modular-qudit code
A. Jain and S. Prakash, “Qutrit and ququint magic states”, Physical Review A 102, (2020) arXiv:2003.07164 DOI. Appears in: Modular-qudit stabilizer code
A. Jain, P. Iyer, S. D. Bartlett, and J. Emerson, “Improved quantum error correction with randomized compiling”, Physical Review Research 5, (2023) arXiv:2303.06846 DOI. Appears in: Concatenated Steane code
S. P. Jain, J. T. Iosue, A. Barg, and V. V. Albert, “Quantum spherical codes”, Nature Physics (2024) arXiv:2302.11593 DOI. Appears in: Clifford subgroup-orbit QSC, Dodecahedron code, Hessian QSC, Quantum spherical code (QSC), Spherical design
S. P. Jain and V. V. Albert, “High-distance codes with transversal Clifford and T-gates”, (2024) arXiv:2408.12752. Appears in: CSS-T code, Quantum quadratic-residue (QR) code, Quantum divisible code, Triorthogonal code
S. P. Jain, E. R. Hudson, W. C. Campbell, and V. V. Albert, “Absorption-Emission Codes for Atomic and Molecular Quantum Information Platforms”, Physical Review Letters 133, (2024) arXiv:2311.12324 DOI. Appears in: Æ code
H. Janwa and O. Moreno, “McEliece public key cryptosystems using algebraic-geometric codes”, Designs, Codes and Cryptography 8, (1996) DOI. Appears in: Generalized RS (GRS) code, Goppa code
H. Janwa and O. Moreno, Designs, Codes and Cryptography 8, 293 (1996) DOI. Appears in: Residue AG code
D. Jaramillo, M. V. Pinto, and R. H. Villarreal, “Evaluation codes and their basic parameters”, (2020) arXiv:1907.13217. Appears in: Polynomial evaluation code, Hansen toric code
S. Javed, F. Garcia-Herrero, B. Vasic, and M. F. Flanagan, “Low-Complexity Linear Programming Based Decoding of Quantum LDPC codes”, (2024) arXiv:2311.18488. Appears in: Quantum LDPC (QLDPC) code
A. Jayashankar and P. Mandayam, “Quantum Error Correction: Noise-adapted Techniques and Applications”, (2022) arXiv:2208.00365. Appears in: Approximate quantum error-correcting code (AQECC)
H. Jeong and M. S. Kim, “Efficient quantum computation using coherent states”, Physical Review A 65, (2002) arXiv:quant-ph/0109077 DOI. Appears in: Coherent-state repetition code, Quantum repetition code, Two-component cat code
H. Jeong and T. C. Ralph, “Schrödinger Cat States for Quantum Information Processing”, Quantum Information with Continuous Variables of Atoms and Light 159 (2007) DOI. Appears in: Two-component cat code
F. G. Jeronimo, D. Quintana, S. Srivastava, and M. Tulsiani, “Unique Decoding of Explicit $ε$-balanced Codes Near the Gilbert-Varshamov Bound”, (2020) arXiv:2011.05500. Appears in: Ta-Shma zigzag code
F. G. Jeronimo, T. Mittal, R. O’Donnell, P. Paredes, and M. Tulsiani, “Explicit Abelian Lifts and Quantum LDPC Codes”, (2021) arXiv:2112.01647. Appears in: Abelian LP code, Expander LP code, Quasi-cyclic LDPC (QC-LDPC) code
Z. Ji, J. Chen, Z. Wei, and M. Ying, “The LU-LC conjecture is false”, (2008) arXiv:0709.1266. Appears in: Cluster-state code, Qubit stabilizer code
Z. Jia, D. Kaszlikowski, and S. Tan, “Boundary and domain wall theories of 2d generalized quantum double model”, Journal of High Energy Physics 2023, (2023) arXiv:2207.03970 DOI. Appears in: Hopf-algebra quantum-double code
Z. Jia, S. Tan, D. Kaszlikowski, and L. Chang, “On Weak Hopf Symmetry and Weak Hopf Quantum Double Model”, Communications in Mathematical Physics 402, 3045 (2023) arXiv:2302.08131 DOI. Appears in: Multi-fusion string-net code, Hopf-algebra quantum-double code
Z. Jia, “Weak Hopf non-invertible symmetry-protected topological spin liquid and lattice realization of (1+1)D symmetry topological field theory”, (2024) arXiv:2412.15336. Appears in: Hopf-algebra cluster-state code
Z. Jia, “Generalized cluster states from Hopf algebras: non-invertible symmetry and Hopf tensor network representation”, Journal of High Energy Physics 2024, (2024) arXiv:2405.09277 DOI. Appears in: Hopf-algebra cluster-state code
L. Jiang, J. M. Taylor, A. S. Sørensen, and M. D. Lukin, “Distributed quantum computation based on small quantum registers”, Physical Review A 76, (2007) arXiv:0709.4539 DOI. Appears in: Quantum repetition code
L. Jiang, J. M. Taylor, K. Nemoto, W. J. Munro, R. Van Meter, and M. D. Lukin, “Quantum repeater with encoding”, Physical Review A 79, (2009) arXiv:0809.3629 DOI. Appears in: Qubit CSS code
Y. Jiang, I. Dumer, A. A. Kovalev, and L. P. Pryadko, “Duality and free energy analyticity bounds for few-body Ising models with extensive homology rank”, Journal of Mathematical Physics 60, (2019) arXiv:1805.00644 DOI. Appears in: 2D hyperbolic surface code
Z. Jiang and E. G. Rieffel, “Non-commuting two-local Hamiltonians for quantum error suppression”, Quantum Information Processing 16, (2017) arXiv:1511.01997 DOI. Appears in: $[[4,1,1,2]]$ Four-qubit subsystem code, Bravyi-Bacon-Shor (BBS) code, $[[6,2,3,2]]$ BBS code, Commuting-projector Hamiltonian code, Subsystem qubit stabilizer code
Z. Jiang, J. McClean, R. Babbush, and H. Neven, “Majorana Loop Stabilizer Codes for Error Mitigation in Fermionic Quantum Simulations”, Physical Review Applied 12, (2019) arXiv:1812.08190 DOI. Appears in: Bravyi-Kitaev superfast (BKSF) code, Majorana loop stabilizer code (MLSC)
Z. Jiang, A. Kalev, W. Mruczkiewicz, and H. Neven, “Optimal fermion-to-qubit mapping via ternary trees with applications to reduced quantum states learning”, Quantum 4, 276 (2020) arXiv:1910.10746 DOI. Appears in: Bravyi-Kitaev transformation (BKT) code, Jordan-Wigner transformation code, Ternary-tree fermion-into-qubit code
Jie Huang and Jinkang Zhu, “Linear time encoding of cycle GF(2/sup P)/ codes through graph analysis”, IEEE Communications Letters 10, 369 (2006) DOI. Appears in: Cycle LDPC code
Jimbo, Masakazu, and Keisuke Shiromoto. "Quantum jump codes and related combinatorial designs." Information Security, Coding Theory and Related Combinatorics. IOS Press, 2011. 285-311.. Appears in: Jump code
A. Jimenez Felstrom and K. S. Zigangirov, “Time-varying periodic convolutional codes with low-density parity-check matrix”, IEEE Transactions on Information Theory 45, 2181 (1999) DOI. Appears in: LDPC convolutional code (LDPC-CC), Spatially coupled LDPC (SC-LDPC) code
Jim Harrington and Ben W. Reichardt, “Addressable multi-qubit logic via permutations,” Talk at Southwest Quantum Information and Technology (SQuInT) (2011).. Appears in: $[[15, 7, 3]]$ quantum Hamming code
L. Jin, S. Ling, J. Luo, and C. Xing, “Application of Classical Hermitian Self-Orthogonal MDS Codes to Quantum MDS Codes”, IEEE Transactions on Information Theory 56, 4735 (2010) DOI. Appears in: Galois-qudit GRS code
L. Jin and C. Xing, “A Construction of New Quantum MDS Codes”, (2020) arXiv:1311.3009. Appears in: Galois-qudit GRS code, Quantum maximum-distance-separable (MDS) code
J. Jing, J. Zhang, Y. Yan, F. Zhao, C. Xie, and K. Peng, “Experimental Demonstration of Tripartite Entanglement and Controlled Dense Coding for Continuous Variables”, Physical Review Letters 90, (2003) arXiv:quant-ph/0210132 DOI. Appears in: Analog repetition code
M.-H. Jing, Y. Chang, C.-D. Lee, J.-H. Chen, and Z.-H. Chen, “A Result on Zetterberg Codes”, IEEE Communications Letters 14, 662 (2010) DOI. Appears in: Zetterberg code
Jin, Hui, Aamod Khandekar, and Robert McEliece. "Irregular repeat-accumulate codes." Proc. 2nd Int. Symp. Turbo codes and related topics. 2000.. Appears in: Irregular repeat-accumulate (IRA) code
H. Jin, T. Richardson, V. Novichkov, "Error Correction of Algebraic Block Codes". U.S. Patent, Number US8751902B2 2002. Appears in: Quasi-cyclic LDPC (QC-LDPC) code
S. Jitman, S. Ling, H. Liu, and X. Xie, “Abelian Codes in Principal Ideal Group Algebras”, IEEE Transactions on Information Theory 59, 3046 (2013) DOI. Appears in: Cyclic linear $q$-ary code, Self-dual linear code
T. Jochym-O’Connor and R. Laflamme, “Using Concatenated Quantum Codes for Universal Fault-Tolerant Quantum Gates”, Physical Review Letters 112, (2014) arXiv:1309.3310 DOI. Appears in: Concatenated Steane code, $[[15,1,3]]$ quantum Reed-Muller code, $[[7,1,3]]$ Steane code
T. Jochym-O’Connor and S. D. Bartlett, “Stacked codes: Universal fault-tolerant quantum computation in a two-dimensional layout”, Physical Review A 93, (2016) arXiv:1509.04255 DOI. Appears in: Doubled color code
T. Jochym-O’Connor, A. Kubica, and T. J. Yoder, “Disjointness of Stabilizer Codes and Limitations on Fault-Tolerant Logical Gates”, Physical Review X 8, (2018) arXiv:1710.07256 DOI. Appears in: Concatenated Steane code, Homological rotor code, Qubit stabilizer code, $[[15,1,3]]$ quantum Reed-Muller code, $[[7,1,3]]$ Steane code
T. Jochym-O’Connor, “Fault-tolerant gates via homological product codes”, Quantum 3, 120 (2019) arXiv:1807.09783 DOI. Appears in: Homological product code
T. Jochym-O’Connor and T. J. Yoder, “Four-dimensional toric code with non-Clifford transversal gates”, Physical Review Research 3, (2021) arXiv:2010.02238 DOI. Appears in: $(1,3)$ 4D toric code, Loop toric code, $D_4$ hyper-diamond lattice
T. Johnsen, S. Manshadi, and N. Monzavi, “A determination of the parameters of a large class of Goppa codes”, IEEE Transactions on Information Theory 40, 1678 (1994) DOI. Appears in: Evaluation AG code
S. J. Johnson and S. R. Weller, “Regular low-density parity-check codes from combinatorial designs”, Proceedings 2001 IEEE Information Theory Workshop (Cat. No.01EX494) DOI. Appears in: Algebraic LDPC code, Combinatorial design
S. J. Johnson and S. R. Weller, “Construction of low-density parity-check codes from Kirkman triple systems”, GLOBECOM’01. IEEE Global Telecommunications Conference (Cat. No.01CH37270) DOI. Appears in: Algebraic LDPC code, Combinatorial design
S. J. Johnson and S. R. Weller, “Codes for iterative decoding from partial geometries”, Proceedings IEEE International Symposium on Information Theory, DOI. Appears in: Algebraic LDPC code
S. J. Johnson and S. R. Weller, “Resolvable 2-designs for regular low-density parity-check codes”, IEEE Transactions on Communications 51, 1413 (2003) DOI. Appears in: Algebraic LDPC code, Combinatorial design
S. Johnson, “A new upper bound for error-correcting codes”, IEEE Transactions on Information Theory 8, 203 (1962) DOI. Appears in: Nearly perfect code
T. Johnson-Freyd, “(3+1)D topological orders with only a $\mathbb{Z}_2$-charged particle”, (2020) arXiv:2011.11165. Appears in: Homological code, Chen-Hsin invertible-order code, Abelian topological code
T. Johnson-Freyd and M. Yu, “Topological Orders in (4+1)-Dimensions”, SciPost Physics 13, (2022) arXiv:2104.04534 DOI. Appears in: Topological code
T. Johnson-Freyd, “On the Classification of Topological Orders”, Communications in Mathematical Physics 393, 989 (2022) arXiv:2003.06663 DOI. Appears in: Topological code
E. E. Johnson. An Efficient Golay Codec For MIL-STD-188-141A and FED-STD-1045. Department of Electrical and Computer Engineering, New Mexico State University, 1991.. Appears in: $[24, 12, 8]$ Extended Golay code
Johnson, Sarah J. "Introducing low-density parity-check codes." University of Newcastle, Australia 1 (2006): 2006.. Appears in: Low-density parity-check (LDPC) code, Repeat-accumulate (RA) code
M. T. Johnsson, N. R. Mukty, D. Burgarth, T. Volz, and G. K. Brennen, “Geometric Pathway to Scalable Quantum Sensing”, Physical Review Letters 125, (2020) arXiv:1908.01120 DOI. Appears in: Permutation-invariant (PI) code
S. L. Johnsson and C.-T. Ho, “Optimum broadcasting and personalized communication in hypercubes”, IEEE Transactions on Computers 38, 1249 (1989) DOI. Appears in: Gray code
J. T. Joichi, D. E. White, and S. G. Williamson, “Combinatorial Gray Codes”, SIAM Journal on Computing 9, 130 (1980) DOI. Appears in: Gray code
B. D. M. Jones, N. Linden, and P. Skrzypczyk, “The Hadamard gate cannot be replaced by a resource state in universal quantum computation”, Quantum 8, 1470 (2024) arXiv:2312.03515 DOI. Appears in: Qubit stabilizer code
C. Jones, “Multilevel distillation of magic states for quantum computing”, Physical Review A 87, (2013) arXiv:1210.3388 DOI. Appears in: $[[k+4,k,2]]$ H code
C. Jones, P. Brooks, and J. Harrington, “Gauge color codes in two dimensions”, Physical Review A 93, (2016) arXiv:1512.04193 DOI. Appears in: Doubled color code
C. Jones, P. Naaijkens, D. Penneys, and D. Wallick, “Local topological order and boundary algebras”, (2023) arXiv:2307.12552. Appears in: String-net code
C. Jones, “Improved accuracy for decoding surface codes with matching synthesis”, (2024) arXiv:2408.12135. Appears in: Kitaev surface code
J. Joo, E. Alba, J. J. García-Ripoll, and T. P. Spiller, “Generating and verifying graph states for fault-tolerant topological measurement-based quantum computing in two-dimensional optical lattices”, Physical Review A 88, (2013) arXiv:1207.0253 DOI. Appears in: Kitaev surface code
P. Jordan and E. P. Wigner, “Über das Paulische Äquivalenzverbot”, The Collected Works of Eugene Paul Wigner 109 (1993) DOI. Appears in: Jordan-Wigner transformation code
S. P. Jordan, E. Farhi, and P. W. Shor, “Error-correcting codes for adiabatic quantum computation”, Physical Review A 74, (2006) arXiv:quant-ph/0512170 DOI. Appears in: Quantum repetition code, $[[4,2,2]]$ Four-qubit code
S. P. Jordan, N. Shutty, M. Wootters, A. Zalcman, A. Schmidhuber, R. King, S. V. Isakov, and R. Babbush, “Optimization by Decoded Quantum Interferometry”, (2024) arXiv:2408.08292. Appears in: Reed-Solomon (RS) code
A. Joshi, K. Noh, and Y. Y. Gao, “Quantum information processing with bosonic qubits in circuit QED”, Quantum Science and Technology 6, 033001 (2021) arXiv:2008.13471 DOI. Appears in: Bosonic code
Joshi, G., Rhim, J. B., Sun, J., & Wang, D. (2010). Fountain codes. In Global telecommunications conference (GLOBECOM 2010) (pp. 7–12). IEEE.. Appears in: Fountain code, Tornado code
P. Jouzdani, E. Novais, and E. R. Mucciolo, “Fidelity of the surface code in the presence of a bosonic bath”, Physical Review A 88, (2013) arXiv:1304.2975 DOI. Appears in: Toric code
D. Joyner, “Toric codes over finite fields”, (2003) arXiv:math/0208155. Appears in: Hansen toric code
R. Jozsa and A. Miyake, “Matchgates and classical simulation of quantum circuits”, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464, 3089 (2008) arXiv:0804.4050 DOI. Appears in: Fermion code
D. Julin, “Two improved block codes (Corresp.)”, IEEE Transactions on Information Theory 11, 459 (1965) DOI. Appears in: Julin-Golay code
M. Junge, R. Renner, D. Sutter, M. M. Wilde, and A. Winter, “Universal Recovery Maps and Approximate Sufficiency of Quantum Relative Entropy”, Annales Henri Poincaré 19, 2955 (2018) arXiv:1509.07127 DOI. Appears in: Approximate quantum error-correcting code (AQECC)
D. Jungnickel, Graphs, Networks and Algorithms (Springer Berlin Heidelberg, 2008) DOI. Appears in: Petersen cycle code
D. Jungnickel and V. D. Tonchev, “The classification of antipodal two-weight linear codes”, Finite Fields and Their Applications 50, 372 (2018) DOI. Appears in: Projective geometry code, Two-weight code
J. Justesen, “Class of constructive asymptotically good algebraic codes”, IEEE Transactions on Information Theory 18, 652 (1972) DOI. Appears in: Justesen code
J. Justesen, K. J. Larsen, H. E. Jensen, A. Havemose, and T. Hoholdt, “Construction and decoding of a class of algebraic geometry codes”, IEEE Transactions on Information Theory 35, 811 (1989) DOI. Appears in: Evaluation AG code, Plane-curve code
Y. Kabashima and D. Saad, “Statistical mechanics of low-density parity-check codes”, Journal of Physics A: Mathematical and General 37, R1 (2004) DOI. Appears in: Low-density parity-check (LDPC) code
G. A. Kabatiansky, V. I. Levenshtein, “On Bounds for Packings on a Sphere and in Space”, Probl. Peredachi Inf., 14:1 (1978), 3–25; Problems Inform. Transmission, 14:1 (1978), 1–17. Appears in: Sphere packing, Spherical code, Universally optimal code
X. Kai and S. Zhu, “New Quantum MDS Codes From Negacyclic Codes”, IEEE Transactions on Information Theory 59, 1193 (2013) DOI. Appears in: Constacyclic code, Quantum maximum-distance-separable (MDS) code, Hermitian Galois-qudit code
X. Kai, S. Zhu, and P. Li, “Constacyclic Codes and Some New Quantum MDS Codes”, IEEE Transactions on Information Theory 60, 2080 (2014) DOI. Appears in: Constacyclic code, Quantum maximum-distance-separable (MDS) code, Hermitian Galois-qudit code
J. Kaidi, Z. Komargodski, K. Ohmori, S. Seifnashri, and S.-H. Shao, “Higher central charges and topological boundaries in 2+1-dimensional TQFTs”, SciPost Physics 13, (2022) arXiv:2107.13091 DOI. Appears in: Topological code, Abelian topological code, Twisted quantum double (TQD) code, Abelian TQD stabilizer code
S. Kak, “Unary Coding for Neural Network Learning”, (2010) arXiv:1009.4495. Appears in: Unary code
G. Kalachev and S. Sadov, “A linear-algebraic and lattice-theoretical look at the Cleaning Lemma of quantum coding theory”, Linear Algebra and its Applications 649, 96 (2022) arXiv:2204.04699 DOI. Appears in: Qubit stabilizer code
G. Kalachev and P. Panteleev, “Two-sided Robustly Testable Codes”, (2023) arXiv:2206.09973. Appears in: Tensor-product code
Kalachev, G. V., and Panteleev, P. A. (2020). On the minimum distance in one class of quantum LDPC codes. Intelligent systems. Theory and applications, 24(4), 87-117.. Appears in: Two-block group-algebra (2BGA) codes
J. G. Kalbfleisch and R. G. Stanton, “A Combinatorial Problem in Matching”, Journal of the London Mathematical Society s1-44, 60 (1969) DOI. Appears in: Maximum distance separable (MDS) code, $q$-ary Hamming code
P. Kallquist, "Decoding of Zetterberg codes," in Proc. Fourth Joint Swedish-Soviet Workshop on Inform. Theory, Gotland, Sweden, Aug. 27-Sept. 1, 1989, p. 305-300. Appears in: Zetterberg code
A. R. Kalra, D. Valluri, and M. Mosca, “Synthesis and Arithmetic of Single Qutrit Circuits”, (2024) arXiv:2311.08696. Appears in: Modular-qudit code
A. R. Kalra, M. Saikia, D. Valluri, S. Winnick, and J. Yard, “Multi-qutrit exact synthesis”, (2024) arXiv:2405.08147. Appears in: Modular-qudit code
A. R. Kalra and S. Prakash, “Invariant Theory and Magic State Distillation”, (2025) arXiv:2501.10163. Appears in: Self-dual linear code, Hermitian qubit code
J. F. Kam, S. Gicev, K. Modi, A. Southwell, and M. Usman, “Detrimental non-Markovian errors for surface code memory”, (2024) arXiv:2410.23779. Appears in: Rotated surface code
D. M. Kane, “Small Designs for Path Connected Spaces and Path Connected Homogeneous Spaces”, (2012) arXiv:1112.4900. Appears in: $t$-design
W. M. Kantor, “Spreads, Translation Planes and Kerdock Sets. I”, SIAM Journal on Algebraic Discrete Methods 3, 151 (1982) DOI. Appears in: Preparata code
W. M. Kantor, “Spreads, Translation Planes and Kerdock Sets. II”, SIAM Journal on Algebraic Discrete Methods 3, 308 (1982) DOI. Appears in: Preparata code
W. Kantor, “On the inequivalence of generalized Preparata codes”, IEEE Transactions on Information Theory 29, 345 (1983) DOI. Appears in: Kerdock code, Nordstrom-Robinson (NR) code, Preparata code, Self-dual linear code
E. Kapit, “Hardware-Efficient and Fully Autonomous Quantum Error Correction in Superconducting Circuits”, Physical Review Letters 116, (2016) arXiv:1510.06117 DOI. Appears in: Very small logical qubit (VSLQ) code
U. S. Kapshikar, “The Diagonal Distance of CWS Codes”, (2021) arXiv:2107.11286. Appears in: Codeword stabilized (CWS) code, Qubit code
U. Kapshikar and S. Kundu, “On the Hardness of the Minimum Distance Problem of Quantum Codes”, IEEE Transactions on Information Theory 69, 6293 (2023) arXiv:2203.04262 DOI. Appears in: Qubit stabilizer code
A. Kapustin and N. Saulina, “Topological boundary conditions in abelian Chern–Simons theory”, Nuclear Physics B 845, 393 (2011) arXiv:1008.0654 DOI. Appears in: Abelian topological code, Abelian TQD stabilizer code
A. Kapustin and R. Thorngren, “Topological Field Theory on a Lattice, Discrete Theta-Angles and Confinement”, (2013) arXiv:1308.2926. Appears in: Two-gauge theory code
A. Kapustin, “Symmetry Protected Topological Phases, Anomalies, and Cobordisms: Beyond Group Cohomology”, (2014) arXiv:1403.1467. Appears in: Topological code
A. Kapustin and R. Thorngren, “Higher symmetry and gapped phases of gauge theories”, (2015) arXiv:1309.4721. Appears in: Dijkgraaf-Witten gauge theory code, Two-gauge theory code
M. Karácsony, L. Oroszlány, and Z. Zimborás, “Efficient qudit based scheme for photonic quantum computing”, (2023) arXiv:2302.07357. Appears in: One-hot quantum code
M. Kargarian, “Entanglement properties of topological color codes”, Physical Review A 78, (2008) arXiv:0809.4276 DOI. Appears in: 2D color code, Kitaev surface code
M. Kargarian, “Finite temperature topological order in 2D topological color codes”, (2009) arXiv:0904.4492. Appears in: Topological code
M. Kargarian, H. Bombin, and M. A. Martin-Delgado, “Topological color codes and two-body quantum lattice Hamiltonians”, New Journal of Physics 12, 025018 (2010) arXiv:0906.4127 DOI. Appears in: 2D color code, Hamiltonian-based code, Abelian quantum-double stabilizer code
M. Karlin, “New binary coding results by circulants”, IEEE Transactions on Information Theory 15, 81 (1969) DOI. Appears in: Karlin double circulant code
D. Karliner, R. Salama, and A. Ta-Shma, “The Plane Test Is a Local Tester for Multiplicity Codes”, (2022) DOI. Appears in: Locally testable code (LTC), Multiplicity code
D. Karliner and A. Ta-Shma, “Improved Local Testing for Multiplicity Codes”, (2022) DOI. Appears in: Locally testable code (LTC), Multiplicity code
J. Karlof and C. Downey, “Odd Group Codes for The Gaussian Channel”, SIAM Journal on Applied Mathematics 34, 715 (1978) DOI. Appears in: Slepian group-orbit code
K. Karplus and H. Krit, “A semi-systolic decoder for the PDSC-73 error-correcting code”, Discrete Applied Mathematics 33, 109 (1991) DOI. Appears in: Regular binary Tanner code
T. Karzig et al., “Scalable designs for quasiparticle-poisoning-protected topological quantum computation with Majorana zero modes”, Physical Review B 95, (2017) arXiv:1610.05289 DOI. Appears in: Honeycomb Floquet code, Majorana stabilizer code, Majorana box qubit
K. KASAI and K. SAKANIWA, “Spatially-Coupled MacKay-Neal Codes and Hsu-Anastasopoulos Codes”, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E94-A, 2161 (2011) arXiv:1102.4612 DOI. Appears in: Dual linear code, Hsu-Anastasopoulos LDPC (HA-LDPC) code, Low-density generator-matrix (LDGM) code, MacKay-Neal LDPC (MN-LDPC) code, Multi-edge LDPC code
K. Kasai, M. Hagiwara, H. Imai, and K. Sakaniwa, “Quantum Error Correction Beyond the Bounded Distance Decoding Limit”, IEEE Transactions on Information Theory 58, 1223 (2012) arXiv:1007.1778 DOI. Appears in: Quasi-cyclic QLDPC (QC-QLDPC) code
T. Kasami, Shu Lin, and W. Peterson, “New generalizations of the Reed-Muller codes--I: Primitive codes”, IEEE Transactions on Information Theory 14, 189 (1968) DOI. Appears in: Generalized RM (GRM) code
Kasami, Tadao. Weight distribution formula for some class of cyclic codes. Champaign, IL, USA: University of Illinois, 1966.. Appears in: Kasami code
Kasami, T. "A topological approach to construction of group codes." J. Inst. Elec. Commun. Engrs.(Japan) 44 (1961): 1316-1321.. Appears in: Cycle code
R. Kashaev, “A simple model of 4d-TQFT”, (2014) arXiv:1405.5763. Appears in: $G$-enriched Walker-Wang model code
R. Kashaev, “On realizations of Pachner moves in 4D”, (2015) arXiv:1504.01979. Appears in: $G$-enriched Walker-Wang model code
S. Kasi, J. Kaewell, S. Hamidi-Rad, and K. Jamieson, “Decoding Polar Codes via Noisy Quantum Gates: Quantum Circuits and Insights”, (2022) arXiv:2210.10854. Appears in: Polar code
W. Kassem, Optimal Lattice Codes for the Gaussian Channel, Ph.D Thesis, McMaster Univ., Hamilton, Ontario, 1981,doi:10.1109/18.651040. Appears in: Lattice-based code
M. J. Kastoryano, L. B. Kristensen, C.-F. Chen, and A. Gilyén, “A little bit of self-correction”, (2024) arXiv:2408.14970. Appears in: Symmetry-protected topological (SPT) code, Symmetry-protected self-correcting quantum code
K. Kato, M. Osaki, M. Sasaki, and O. Hirota, “Quantum detection and mutual information for QAM and PSK signals”, IEEE Transactions on Communications 47, 248 (1999) DOI. Appears in: PSK c-q code
K. Kato and F. G. S. L. Brandão, “Locality of edge states and entanglement spectrum from strong subadditivity”, Physical Review B 99, (2019) arXiv:1804.05457 DOI. Appears in: Topological code
J. Katz and L. Trevisan, “On the efficiency of local decoding procedures for error-correcting codes”, Proceedings of the thirty-second annual ACM symposium on Theory of computing (2000) DOI. Appears in: Locally decodable code (LDC)
H. G. Katzgraber, H. Bombin, and M. A. Martin-Delgado, “Error Threshold for Color Codes and Random Three-Body Ising Models”, Physical Review Letters 103, (2009) arXiv:0902.4845 DOI. Appears in: Square-octagon (4.8.8) color code, Honeycomb (6.6.6) color code, Union-Jack color code
H. G. Katzgraber, H. Bombin, R. S. Andrist, and M. A. Martin-Delgado, “Topological color codes on Union Jack lattices: a stable implementation of the whole Clifford group”, Physical Review A 81, (2010) arXiv:0910.0573 DOI. Appears in: Union-Jack color code
T. Kaufman and S. Litsyn, “Almost Orthogonal Linear Codes are Locally Testable”, 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS’05) 317 DOI. Appears in: Linear binary code, Binary linear LTC, Goppa code, Bose–Chaudhuri–Hocquenghem (BCH) code, Linear $q$-ary code, $q$-ary linear LTC
T. Kaufman and D. Ron, “Testing Polynomials over General Fields”, SIAM Journal on Computing 36, 779 (2006) DOI. Appears in: Binary linear LTC, Reed-Muller (RM) code
T. Kaufman and M. Sudan, “Sparse Random Linear Codes are Locally Decodable and Testable”, 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS’07) 590 (2007) DOI. Appears in: Linear binary code, Binary linear LTC, Linear $q$-ary code, $q$-ary linear LTC
T. Kaufman and M. Viderman, “Locally Testable vs. Locally Decodable Codes”, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques 670 (2010) DOI. Appears in: Locally correctable code (LCC), Locally decodable code (LDC), Locally testable code (LTC)
T. Kaufman, D. Kazhdan, and A. Lubotzky, “Isoperimetric Inequalities for Ramanujan Complexes and Topological Expanders”, (2014) arXiv:1409.1397. Appears in: High-dimensional expander (HDX) code
T. Kaufman and R. J. Tessler, “New Cosystolic Expanders from Tensors Imply Explicit Quantum LDPC Codes with $Ω(\sqrt{n}\log^kn)$ Distance”, (2020) arXiv:2008.09495. Appears in: Tensor-product HDX code
A. Kaufmann and I. Arad, “A blockBP decoder for the surface code”, (2024) arXiv:2402.04834. Appears in: Kitaev surface code
Kauko Lindström. "The nonexistence of unknown nearly perfect binary codes." PhD diss., Turun yliopisto, 1975.. Appears in: Nearly perfect code
W. Kautz and R. Singleton, “Nonrandom binary superimposed codes”, IEEE Transactions on Information Theory 10, 363 (1964) DOI. Appears in: Superimposed code
S. Kawabata, “Quantum Interleaver: Quantum Error Correction for Burst Error”, Journal of the Physical Society of Japan 69, 3540 (2000) arXiv:quant-ph/0002020 DOI. Appears in: Block quantum code, Qubit stabilizer code
S. Kawabata, “Quantum Interleaver: Quantum Error Correction for Burst Error”, Journal of the Physical Society of Japan 69, 3540 (2000) DOI. Appears in: Block quantum code
S. Kawabata, “Information-theoretical approach to control of quantum-mechanical systems”, Physical Review A 68, (2003) arXiv:quant-ph/0409187 DOI. Appears in: Finite-dimensional quantum error-correcting code
A. Kay and R. Colbeck, “Quantum Self-Correcting Stabilizer Codes”, (2008) arXiv:0810.3557. Appears in: Self-correcting quantum code
A. Kay, “Nonequilibrium Reliability of Quantum Memories”, Physical Review Letters 102, (2009) arXiv:0807.0287 DOI. Appears in: 2D lattice stabilizer code, Self-correcting quantum code
A. Kay, “Capabilities of a Perturbed Toric Code as a Quantum Memory”, Physical Review Letters 107, (2011) arXiv:1107.3940 DOI. Appears in: 2D lattice stabilizer code
K. Keane and A. N. Korotkov, “Simplified quantum error detection and correction for superconducting qubits”, Physical Review A 86, (2012) arXiv:1205.1836 DOI. Appears in: Quantum repetition code
P. Keevash, “The existence of designs II”, (2018) arXiv:1802.05900. Appears in: Combinatorial design, $t$-design
P. Keevash, A. Sah, and M. Sawhney, “The existence of subspace designs”, (2023) arXiv:2212.00870. Appears in: Subspace design, $t$-design
P. Keevash, “The existence of designs”, (2024) arXiv:1401.3665. Appears in: Combinatorial design, $t$-design
P. Keevash, “A short proof of the existence of designs”, (2024) arXiv:2411.18291. Appears in: Combinatorial design, $t$-design
C. A. Kelley, D. Sridhara, and J. Rosenthal, “Tree-Based Construction of LDPC Codes Having Good Pseudocodeword Weights”, IEEE Transactions on Information Theory 53, 1460 (2007) DOI. Appears in: Algebraic LDPC code
C. A. Kelley and D. Sridhara, “Eigenvalue bounds on the pseudocodeword weight of expander codes”, (2007) arXiv:0708.2462. Appears in: Regular binary Tanner code
C. A. Kelley, “On codes designed via algebraic lifts of graphs”, 2008 46th Annual Allerton Conference on Communication, Control, and Computing (2008) DOI. Appears in: Algebraic LDPC code, Protograph LDPC code
C. A. Kelley and J. L. Walker, “LDPC codes from voltage graphs”, 2008 IEEE International Symposium on Information Theory (2008) DOI. Appears in: Algebraic LDPC code, Protograph LDPC code, $q$-ary protograph LDPC code
C. A. Kelley, “Minimum distance and pseudodistance lower bounds for generalised LDPC codes”, International Journal of Information and Coding Theory 1, 313 (2010) DOI. Appears in: Regular binary Tanner code
C. A. Kelley, "Codes over Graphs." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI. Appears in: Cycle LDPC code, $[7,4,3]$ Hamming code, Incidence-matrix projective code, Low-density parity-check (LDPC) code, Tanner code, Tanner-Sridhara-Fuja (TSF) code
J. Kelly et al., “State preservation by repetitive error detection in a superconducting quantum circuit”, Nature 519, 66 (2015) arXiv:1411.7403 DOI. Appears in: Quantum repetition code
J. Kempe, “Approaches to Quantum Error Correction”, (2006) arXiv:quant-ph/0612185. Appears in: Quantum error-correcting code (QECC)
J. D. Kene and K. D. Kulat, “Soft Output Decoding Algorithm for Turbo Codes Implementation in Mobile Wi-Max Environment”, Procedia Technology 6, 666 (2012) DOI. Appears in: Turbo code
Kennedy, Robert S. "A near-optimum receiver for the binary coherent state quantum channel." Quarterly Progress Report 108 (1973): 219-225.. Appears in: BPSK c-q code
Kepler, Johannes. The six-cornered snowflake. Paul Dry Books, 2010.. Appears in: $D_3$ face-centered cubic (fcc) lattice
Keqin Feng, “Quantum codes [[6, 2, 3]]/sub p/ and [[7, 3, 3]]/sub p/ (p ≥ 3) exist”, IEEE Transactions on Information Theory 48, 2384 (2002) DOI. Appears in: $[[6,2,3]]_{q}$ code, $[[7,3,3]]_{q}$ code, Graph quantum code
Keqin Feng, San Ling, and Chaoping Xing, “Asymptotic bounds on quantum codes from algebraic geometry codes”, IEEE Transactions on Information Theory 52, 986 (2006) DOI. Appears in: Block quantum code
A. M. Kerdock, “A class of low-rate nonlinear binary codes”, Information and Control 20, 182 (1972) DOI. Appears in: Kerdock code
O. Kern and G. Alber, “Suppressing decoherence of quantum algorithms by jump codes”, The European Physical Journal D 36, 241 (2005) arXiv:quant-ph/0506037 DOI. Appears in: Jump code
R. Kershner, “The Number of Circles Covering a Set”, American Journal of Mathematics 61, 665 (1939) DOI. Appears in: $A_2$ triangular lattice
M. S. Kesselring, F. Pastawski, J. Eisert, and B. J. Brown, “The boundaries and twist defects of the color code and their applications to topological quantum computation”, Quantum 2, 101 (2018) arXiv:1806.02820 DOI. Appears in: 2D color code, $[[4,2,2]]$ Four-qubit code, Stellated color code, Three-fermion (3F) subsystem code, Triangular surface code, Twist-defect color code, Twist-defect surface code
M. S. Kesselring, J. C. Magdalena de la Fuente, F. Thomsen, J. Eisert, S. D. Bartlett, and B. J. Brown, “Anyon Condensation and the Color Code”, PRX Quantum 5, (2024) arXiv:2212.00042 DOI. Appears in: 2D color code, Dynamical automorphism (DA) code, Floquet color code, $[[4,2,2]]$ Four-qubit code, Kitaev surface code, Abelian topological code
H. Kesten and B. P. Stigum, “A Limit Theorem for Multidimensional Galton-Watson Processes”, The Annals of Mathematical Statistics 37, 1211 (1966) DOI. Appears in: Repetition code
A. Ketkar, A. Klappenecker, S. Kumar, and P. K. Sarvepalli, “Nonbinary stabilizer codes over finite fields”, (2005) arXiv:quant-ph/0508070. Appears in: Perfect-tensor code, $[[6,2,3]]_{q}$ code, $[[7,3,3]]_{q}$ code, Quantum quadratic-residue (QR) code, Galois-qudit stabilizer code, True Galois-qudit stabilizer code, Hermitian Galois-qudit code
J. D. Key and A. Wagner, “On an infinite class of Steiner systems constructed from affine spaces”, Archiv der Mathematik 47, 376 (1986) DOI. Appears in: Combinatorial design
J. D. Key and P. Seneviratne, “Partial permutation decoding for MacDonald codes”, Applicable Algebra in Engineering, Communication and Computing 27, 399 (2016) DOI. Appears in: $q$-ary simplex code
C. W. von Keyserlingk, F. J. Burnell, and S. H. Simon, “Three-dimensional topological lattice models with surface anyons”, Physical Review B 87, (2013) arXiv:1208.5128 DOI. Appears in: Chiral semion Walker-Wang model code, Walker-Wang model code
A. K. Khandani and P. Kabal, “Shaping multidimensional signal spaces. I. Optimum shaping, shell mapping”, IEEE Transactions on Information Theory 39, 1799 (1993) DOI. Appears in: Lattice-shell code
A. D. Khandekar, Graph-Based Codes and Iterative Decoding, California Institute of Technology, 2003 DOI. Appears in: Irregular repeat-accumulate (IRA) code
A. B. Khesin, J. Z. Lu, and P. W. Shor, “Universal graph representation of stabilizer codes”, (2024) arXiv:2411.14448. Appears in: Dodecahedron code, $[2^r-1,2^r-r-1,3]$ Hamming code, Hypercube code, Icosahedron code, $[[m 2^m / (m+1), 2^m / (m+1)]]$ Khesin-Lu-Shor code, $[[16,4,3]]$ dodecahedral code, $[[54,6,5]]$ five-covered icosahedral code, Qubit stabilizer code, $[[9,1,3]]$ Shor code, Five-qubit perfect code, $[[7,1,3]]$ Steane code
A. B. Khesin, J. Z. Lu, and P. W. Shor, “Graphical quantum Clifford-encoder compilers from the ZX calculus”, (2024) arXiv:2301.02356. Appears in: Qubit stabilizer code, Qubit code
A. B. Khesin and A. Li, “Equivalence Classes of Quantum Error-Correcting Codes”, (2024) arXiv:2406.12083. Appears in: Qubit CSS code
K. Khodjasteh and D. A. Lidar, “Quantum computing in the presence of spontaneous emission by a combined dynamical decoupling and quantum-error-correction strategy”, Physical Review A 68, (2003) arXiv:quant-ph/0301105 DOI. Appears in: $[[2m,2m-2,2]]$ error-detecting code
A. S. Kholevo, “On Asymptotically Optimal Hypothesis Testing in Quantum Statistics”, Theory of Probability & Its Applications 23, 411 (1979) DOI. Appears in: Coherent-state c-q code
H. M. Kiah, G. J. Puleo, and O. Milenkovic, “Codes for DNA Storage Channels”, (2015) arXiv:1410.8837. Appears in: DNA storage code
H. M. Kiah, G. J. Puleo, and O. Milenkovic, “Codes for DNA Sequence Profiles”, (2015) arXiv:1502.00517. Appears in: DNA storage code
A. Kiayias and M. Yung, “Cryptographic Hardness Based on the Decoding of Reed-Solomon Codes”, Lecture Notes in Computer Science 232 (2002) DOI. Appears in: Reed-Solomon (RS) code
T. Kibe, P. Mandayam, and A. Mukhopadhyay, “Holographic spacetime, black holes and quantum error correcting codes: a review”, The European Physical Journal C 82, (2022) arXiv:2110.14669 DOI. Appears in: Holographic code
H.-S. Kim, I. H. Kim, and D. Ranard, “Learning State Preparation Circuits for Quantum Phases of Matter”, (2024) arXiv:2410.23544. Appears in: Topological code
H. Kim, W. Choi, and Y. Kwon, “Implementation of Magic State Injection within Heavy-Hexagon Architecture”, (2024) arXiv:2412.15751. Appears in: Heavy-hexagon code
I. H. Kim, “3D local qupit quantum code without string logical operator”, (2012) arXiv:1202.0052. Appears in: Fracton stabilizer code, Qudit cubic code
I. H. Kim, “Local non-CSS quantum error correcting code on a three-dimensional lattice”, (2013) arXiv:1012.0859. Appears in: 3D surface code
I. H. Kim, B. Shi, K. Kato, and V. V. Albert, “Chiral Central Charge from a Single Bulk Wave Function”, Physical Review Letters 128, (2022) arXiv:2110.06932 DOI. Appears in: Topological code
I. H. Kim and D. Ranard, “Classifying 2D topological phases: mapping ground states to string-nets”, (2024) arXiv:2405.17379. Appears in: String-net code, Topological code
I. Kim, E. Tang, and J. Preskill, “The ghost in the radiation: robust encodings of the black hole interior”, Journal of High Energy Physics 2020, (2020) arXiv:2003.05451 DOI. Appears in: Kim-Preskill-Tang (KPT) code, SYK code
J.-L. Kim, U. N. Peled, I. Perepelitsa, V. Pless, and S. Friedland, “Explicit Construction of Families of LDPC Codes With No&lt;tex&gt;$4$&lt;/tex&gt;-Cycles”, IEEE Transactions on Information Theory 50, 2378 (2004) DOI. Appears in: Lazebnik-Ustimenko (LU) code
J.-L. Kim and J. Walker, “Nonbinary quantum error-correcting codes from algebraic curves”, Discrete Mathematics 308, 3115 (2008) DOI. Appears in: Galois-qudit CSS code
J. Kim and V. Pless, Designs, Codes and Cryptography 30, 187 (2003) DOI. Appears in: Combinatorial design, Dodecacode
J. Kim, X. Cao, and E. Altman, “Low-rank Sachdev-Ye-Kitaev models”, Physical Review B 101, (2020) arXiv:1910.10173 DOI. Appears in: SYK code
J. Kim, E. Altman, and X. Cao, “Dirac fast scramblers”, Physical Review B 103, (2021) arXiv:2010.10545 DOI. Appears in: SYK code
J. Kim, H. Jung, and J. Ha, “Low-Complexity Decoding Algorithm Utilizing Degeneracy for Quantum LDPC Codes”, MILCOM 2023 - 2023 IEEE Military Communications Conference (MILCOM) 115 (2023) DOI. Appears in: Quantum LDPC (QLDPC) code
J. Kim, E. Altman, and J. Y. Lee, “Error Threshold of SYK Codes from Strong-to-Weak Parity Symmetry Breaking”, (2024) arXiv:2410.24225. Appears in: SYK code
Y. Kim, J. Kang, and Y. Kwon, “Design of Quantum error correcting code for biased error on heavy-hexagon structure”, (2022) arXiv:2211.14038. Appears in: Heavy-hexagon code, XY surface code, XZZX surface code
Y. Kim, M. Sevior, and M. Usman, “Magic State Injection on IBM Quantum Processors Above the Distillation Threshold”, (2024) arXiv:2412.01446. Appears in: Heavy-hexagon code
A. Kirillov Jr, “String-net model of Turaev-Viro invariants”, (2011) arXiv:1106.6033. Appears in: String-net code
A. Kissinger and J. van de Wetering, “Reducing the number of non-Clifford gates in quantum circuits”, Physical Review A 102, (2020) arXiv:1903.10477 DOI. Appears in: Qubit code
A. Kissinger and J. van de Wetering, “Simulating quantum circuits with ZX-calculus reduced stabiliser decompositions”, Quantum Science and Technology 7, 044001 (2022) arXiv:2109.01076 DOI. Appears in: Qubit code
A. Kissinger, “Phase-free ZX diagrams are CSS codes (...or how to graphically grok the surface code)”, (2022) arXiv:2204.14038. Appears in: Qubit CSS code
A. Y. Kitaev, “Quantum computations: algorithms and error correction”, Russian Mathematical Surveys 52, 1191 (1997) DOI. Appears in: Approximate quantum error-correcting code (AQECC), Qubit CSS code, Kitaev surface code, Toric code
A. Y. Kitaev, “Quantum computations: algorithms and error correction”, Russian Mathematical Surveys 52, 1191 (1997) DOI. Appears in: Qubit code
A. Y. Kitaev, “Unpaired Majorana fermions in quantum wires”, Physics-Uspekhi 44, 131 (2001) arXiv:cond-mat/0010440 DOI. Appears in: Jordan-Wigner transformation code, Kitaev chain code, Majorana stabilizer code, Majorana box qubit
A. Yu. Kitaev, “Quantum Error Correction with Imperfect Gates”, Quantum Communication, Computing, and Measurement 181 (1997) DOI. Appears in: Kitaev surface code, Toric code
A. Yu. Kitaev, “Fault-tolerant quantum computation by anyons”, Annals of Physics 303, 2 (2003) arXiv:quant-ph/9707021 DOI. Appears in: $[[4,2,2]]_{G}$ four group-qudit code, Hopf-algebra quantum-double code, Quantum-double code, Abelian quantum-double stabilizer code, Dihedral $G=D_m$ quantum-double code, Modular-qudit surface code, Kitaev surface code, Topological code
A. Kitaev, A. Shen, and M. Vyalyi, Classical and Quantum Computation (American Mathematical Society, 2002) DOI. Appears in: Approximate quantum error-correcting code (AQECC), Circuit-to-Hamiltonian approximate code, Quantum error-correcting code (QECC), Quantum low-weight check (QLWC) code, Qubit code, Unary code
A. Kitaev, “Protected qubit based on a superconducting current mirror”, (2006) arXiv:cond-mat/0609441. Appears in: Kitaev current-mirror qubit code, Square-lattice GKP code, Zero-pi qubit code
A. Kitaev and J. Preskill, “Topological Entanglement Entropy”, Physical Review Letters 96, (2006) arXiv:hep-th/0510092 DOI. Appears in: Topological code
A. Kitaev, “Anyons in an exactly solved model and beyond”, Annals of Physics 321, 2 (2006) arXiv:cond-mat/0506438 DOI. Appears in: Honeycomb Floquet code, Kitaev honeycomb code, Majorana stabilizer code, Matching code, Abelian quantum-double stabilizer code, Qubit stabilizer code, $\mathbb{Z}_q^{(1)}$ subsystem code, Topological code
A. Kitaev and C. Laumann, “Topological phases and quantum computation”, (2009) arXiv:0904.2771. Appears in: Kitaev chain code
A. Kitaev and L. Kong, “Models for Gapped Boundaries and Domain Walls”, Communications in Mathematical Physics 313, 351 (2012) arXiv:1104.5047 DOI. Appears in: Abelian topological code, Twist-defect surface code
Kitaev, Alexei. "A simple model of quantum holography (part 2)." Entanglement in Strongly-Correlated Quantum Matter (2015): 38.. Appears in: SYK code
Kitaev, Alexei Yu. "Protected qubit based on superconducting current mirror." United States Patent Number 7858966B2 (2006).. Appears in: Kitaev current-mirror qubit code
J. Kittler, R. Ghaderi, T. Windeatt, and J. Matas, “Face verification using error correcting output codes”, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001 DOI. Appears in: Error-correcting output code (ECOC)
M. Kiyota, “An inequality for finite permutation groups”, Journal of Combinatorial Theory, Series A 27, 119 (1979) DOI. Appears in: Code in permutations
A. Klappenecker and M. Roetteler, “Beyond Stabilizer Codes I: Nice Error Bases”, (2001) arXiv:quant-ph/0010082. Appears in: Knill code
A. Klappenecker and M. Roetteler, “Beyond Stabilizer Codes II: Clifford Codes”, (2001) arXiv:quant-ph/0010076. Appears in: Knill code
A. Klappenecker and M. Roetteler, “Constructions of Mutually Unbiased Bases”, (2003) arXiv:quant-ph/0309120. Appears in: $t$-design
A. Klappenecker and M. Roetteler, “Mutually Unbiased Bases are Complex Projective 2-Designs”, (2005) arXiv:quant-ph/0502031. Appears in: $t$-design
A. Klappenecker and P. K. Sarvepalli, “Clifford Code Constructions of Operator Quantum Error Correcting Codes”, (2006) arXiv:quant-ph/0604161. Appears in: Subsystem Galois-qudit CSS code, Subsystem Galois-qudit stabilizer code, Knill code, Subsystem QECC, Subsystem CSS code
A. Klappenecker and P. K. Sarvepalli, “On subsystem codes beating the quantum Hamming or Singleton bound”, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, 2887 (2007) arXiv:quant-ph/0703213 DOI. Appears in: Subsystem Galois-qudit stabilizer code
A. Klappenecker, “Algebraic quantum coding theory”, Quantum Error Correction 307 (2013) DOI. Appears in: Galois-qudit BCH code, True Galois-qudit stabilizer code, Quantum maximum-distance-separable (MDS) code
Klappenecker, Andreas, and Martin Rötteler. "On the structure of nonstabilizer Clifford codes." Quantum Information & Computation 4.2 (2004): 152-160.. Appears in: Knill code
R. Klesse and S. Frank, “Quantum Error Correction in Spatially Correlated Quantum Noise”, Physical Review Letters 95, (2005) arXiv:quant-ph/0505153 DOI. Appears in: Qubit code
R. Klesse, “A random-coding based proof for the quantum coding theorem”, (2007) arXiv:0712.2558. Appears in: Haar-random qubit code
R. Klesse, “Approximate quantum error correction, random codes, and quantum channel capacity”, Physical Review A 75, (2007) arXiv:quant-ph/0701102 DOI. Appears in: Haar-random qubit code
V. Kliuchnikov, A. Bocharov, and K. M. Svore, “Asymptotically Optimal Topological Quantum Compiling”, Physical Review Letters 112, (2014) arXiv:1310.4150 DOI. Appears in: Fibonacci string-net code
V. Kliuchnikov and S. Schönnenbeck, “Stabilizer operators and Barnes-Wall lattices”, (2024) arXiv:2404.17677. Appears in: Barnes-Wall (BW) lattice, Qubit stabilizer code, Modular-qudit stabilizer code, Real-Clifford subgroup-orbit code
T. Klove and M. Miller, “The Detection of Errors After Error-Correction Decoding”, IEEE Transactions on Communications 32, 511 (1984) DOI. Appears in: Repetition code
T. Kløve, Codes for Error Detection (WORLD SCIENTIFIC, 2007) DOI. Appears in: $q$-ary code
Kløve, Torleiv. Error correcting codes for the asymmetric channel. Department of Pure Mathematics, University of Bergen, 1981.. Appears in: Constantin-Rao (CR) code, $[2^r-1,2^r-r-1,3]$ Hamming code, $q$-ary code
C. Knapp, M. Beverland, D. I. Pikulin, and T. Karzig, “Modeling noise and error correction for Majorana-based quantum computing”, Quantum 2, 88 (2018) arXiv:1806.01275 DOI. Appears in: Fermion code
S. Knerr, L. Personnaz, and G. Dreyfus, “Handwritten digit recognition by neural networks with single-layer training”, IEEE Transactions on Neural Networks 3, 962 (1992) DOI. Appears in: One-versus-one (OVO) code
E. Knill, “Group Representations, Error Bases and Quantum Codes”, (1996) arXiv:quant-ph/9608049. Appears in: Galois-qudit CSS code, Group-representation code, Knill code
E. Knill, “Non-binary Unitary Error Bases and Quantum Codes”, (1996) arXiv:quant-ph/9608048. Appears in: Knill code
E. Knill and R. Laflamme, “Concatenated Quantum Codes”, (1996) arXiv:quant-ph/9608012. Appears in: Concatenated quantum code
E. Knill, R. Laflamme, and W. Zurek, “Threshold Accuracy for Quantum Computation”, (1996) arXiv:quant-ph/9610011. Appears in: $[[15,1,3]]$ quantum Reed-Muller code
E. Knill and R. Laflamme, “Theory of quantum error-correcting codes”, Physical Review A 55, 900 (1997) DOI. Appears in: Finite-dimensional quantum error-correcting code
E. Knill, R. Laflamme, and W. H. Zurek, “Resilient quantum computation: error models and thresholds”, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 454, 365 (1998) arXiv:quant-ph/9702058 DOI. Appears in: Concatenated Steane code, Concatenated qubit code, Qubit code
E. Knill, R. Laflamme, and L. Viola, “Theory of Quantum Error Correction for General Noise”, Physical Review Letters 84, 2525 (2000) arXiv:quant-ph/9604034 DOI. Appears in: Finite-dimensional quantum error-correcting code, Quantum maximum-distance-separable (MDS) code
E. Knill, R. Laflamme, and G. Milburn, “Efficient Linear Optics Quantum Computation”, (2000) arXiv:quant-ph/0006088. Appears in: Quantum parity code (QPC), Quantum repetition code
E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics”, Nature 409, 46 (2001) DOI. Appears in: Dual-rail quantum code, Concatenated bosonic code, $[[7,1,3]]$ Steane code
E. Knill, “Fermionic Linear Optics and Matchgates”, (2001) arXiv:quant-ph/0108033. Appears in: Fermion code
E. Knill, R. Laflamme, R. Martinez, and C. Negrevergne, “Benchmarking Quantum Computers: The Five-Qubit Error Correcting Code”, Physical Review Letters 86, 5811 (2001) arXiv:quant-ph/0101034 DOI. Appears in: Five-qubit perfect code
E. Knill, “Bounds on the probability of success of postselected nonlinear sign shifts implemented with linear optics”, Physical Review A 68, (2003) arXiv:quant-ph/0307015 DOI. Appears in: Dual-rail quantum code
E. Knill, “Scalable Quantum Computation in the Presence of Large Detected-Error Rates”, (2004) arXiv:quant-ph/0312190. Appears in: Bosonic rotation code, Square-lattice GKP code, Number-phase code, Qubit stabilizer code, Two-component cat code
E. Knill, “Fault-Tolerant Postselected Quantum Computation: Schemes”, (2004) arXiv:quant-ph/0402171. Appears in: $[[6,4,2]]$ error-detecting code
E. Knill, “Fault-Tolerant Postselected Quantum Computation: Threshold Analysis”, (2004) arXiv:quant-ph/0404104. Appears in: $[[6,4,2]]$ error-detecting code
E. Knill, “Quantum computing with realistically noisy devices”, Nature 434, 39 (2005) arXiv:quant-ph/0410199 DOI. Appears in: Bosonic rotation code, Square-lattice GKP code, Number-phase code, Concatenated qubit code, Qubit stabilizer code, $[[4,2,2]]$ Four-qubit code, $[[6,2,2]]$ $C_6$ code, Two-component cat code
E. Knill, private communication, ca. 1998.. Appears in: Qubit code
D. Knuth, “Efficient balanced codes”, IEEE Transactions on Information Theory 32, 51 (1986) DOI. Appears in: Balanced code
F. Kobayashi, H. Manabe, G. A. L. White, T. Farrelly, K. Modi, and T. M. Stace, “Tensor-network decoders for process tensor descriptions of non-Markovian noise”, (2024) arXiv:2412.13739. Appears in: Qubit stabilizer code
R. Kobayashi and G. Zhu, “Cross-Cap Defects and Fault-Tolerant Logical Gates in the Surface Code and the Honeycomb Floquet Code”, PRX Quantum 5, (2024) arXiv:2310.06917 DOI. Appears in: Honeycomb Floquet code, Projective-plane surface code
A. F. Kockum, A. Soro, L. García-Álvarez, P. Vikstål, T. Douce, G. Johansson, and G. Ferrini, “Lecture notes on quantum computing”, (2024) arXiv:2311.08445. Appears in: Bosonic code
R. Koenig, G. Kuperberg, and B. W. Reichardt, “Quantum computation with Turaev–Viro codes”, Annals of Physics 325, 2707 (2010) arXiv:1002.2816 DOI. Appears in: Fibonacci string-net code, String-net code
R. Koetter and A. Vardy, “Algebraic soft-decision decoding of reed-solomon codes”, IEEE Transactions on Information Theory 49, 2809 (2003) DOI. Appears in: Generalized RS (GRS) code, Reed-Solomon (RS) code
R. Koetter and F. R. Kschischang, “Coding for Errors and Erasures in Random Network Coding”, IEEE Transactions on Information Theory 54, 3579 (2008) DOI. Appears in: Gabidulin code, Maximum-rank distance (MRD) code, Reed-Solomon (RS) code, Subspace code
R. Koetter and F. Kschischang, “Coding for Errors and Erasures in Random Network Coding”, (2008) arXiv:cs/0703061. Appears in: Maximum-rank distance (MRD) code
J. B. Kogut, “An introduction to lattice gauge theory and spin systems”, Reviews of Modern Physics 51, 659 (1979) DOI. Appears in: Quantum-double code
T. Kohler and T. Cubitt, “Toy models of holographic duality between local Hamiltonians”, Journal of High Energy Physics 2019, (2019) arXiv:1810.08992 DOI. Appears in: Hamiltonian-based code, Holographic tensor-network code
P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits”, Reviews of Modern Physics 79, 135 (2007) arXiv:quant-ph/0512071 DOI. Appears in: Dual-rail quantum code
X. C. Kolesnikow, R. W. Bomantara, A. C. Doherty, and A. L. Grimsmo, “Gottesman-Kitaev-Preskill State Preparation Using Periodic Driving”, Physical Review Letters 132, (2024) arXiv:2303.03541 DOI. Appears in: Square-lattice GKP code
L. Kollros, “An Attempt to determine the twenty-seven Lines upon a Surface of the third Order, and to divide such Surfaces into Species in Reference to the Reality of the Lines upon the Surface”, Gesammelte Mathematische Abhandlungen 198 (1953) DOI. Appears in: 120-cell code, 24-cell code, 600-cell code
A. V. KOLUSHOV and V. A. YUDIN, “On Korkin-Zolotarev’s construction”, Discrete Mathematics and Applications 4, (1994) DOI. Appears in: $3_{21}$ polytope code, Spherical sharp configuration, Witting polytope code
A. V. Kolushov, V. A. Yudin, А. В. Колущов, and В. А. Удин, “Extremal dispositions of points on the sphere”, Analysis Mathematica 23, 25 (1997) DOI. Appears in: Universally optimal spherical code
A. Kómár, O. Landon-Cardinal, and K. Temme, “Necessity of an energy barrier for self-correction of Abelian quantum doubles”, Physical Review A 93, (2016) arXiv:1601.01324 DOI. Appears in: Self-correcting quantum code
D. Komoto and K. Kasai, “Explicit Construction of Classical and Quantum Quasi-Cyclic Low-Density Parity-Check Codes with Column Weight 2 and Girth 12”, (2025) arXiv:2501.13444. Appears in: Quasi-cyclic LDPC (QC-LDPC) code, Quasi-cyclic QLDPC (QC-QLDPC) code
D. Komoto and K. Kasai, “Quantum Error Correction near the Coding Theoretical Bound”, (2025) arXiv:2412.21171. Appears in: Quasi-cyclic QLDPC (QC-QLDPC) code
L. Kong and X.-G. Wen, “Braided fusion categories, gravitational anomalies, and the mathematical framework for topological orders in any dimensions”, (2014) arXiv:1405.5858. Appears in: Topological code
L. Kong, X.-G. Wen, and H. Zheng, “Boundary-bulk relation in topological orders”, Nuclear Physics B 922, 62 (2017) arXiv:1702.00673 DOI. Appears in: Topological code
L. Kong and Z.-W. Liu, “Charge-conserving unitaries typically generate optimal covariant quantum error-correcting codes”, (2021) arXiv:2102.11835. Appears in: Covariant block quantum code, Random quantum code
L. Kong and Z.-W. Liu, “Near-Optimal Covariant Quantum Error-Correcting Codes from Random Unitaries with Symmetries”, PRX Quantum 3, (2022) arXiv:2112.01498 DOI. Appears in: Covariant block quantum code, Random quantum code
L. Kong and Z.-H. Zhang, “An invitation to topological orders and category theory”, (2022) arXiv:2205.05565. Appears in: Topological code
R. König, B. W. Reichardt, and G. Vidal, “Exact entanglement renormalization for string-net models”, Physical Review B 79, (2009) arXiv:0806.4583 DOI. Appears in: Quantum-double code, String-net code, Kitaev surface code
R. König and F. Pastawski, “Generating topological order: No speedup by dissipation”, Physical Review B 90, (2014) arXiv:1310.1037 DOI. Appears in: Qubit stabilizer code, Toric code
S. Konno et al., “Logical states for fault-tolerant quantum computation with propagating light”, Science 383, 289 (2024) arXiv:2309.02306 DOI. Appears in: Square-lattice GKP code
P. Koopman, “32-bit cyclic redundancy codes for Internet applications”, Proceedings International Conference on Dependable Systems and Networks DOI. Appears in: Cyclic redundancy check (CRC) code
P. Koopman and T. Chakravarty, “Cyclic redundancy code (CRC) polynomial selection for embedded networks”, International Conference on Dependable Systems and Networks, 2004 (2004) DOI. Appears in: Cyclic redundancy check (CRC) code
A. Koottandavida et al., “Erasure detection of a dual-rail qubit encoded in a double-post superconducting cavity”, (2023) arXiv:2311.04423. Appears in: Dual-rail quantum code
S. Kopparty and S. Saraf, “Local list-decoding and testing of random linear codes from high error”, Proceedings of the forty-second ACM symposium on Theory of computing 417 (2010) DOI. Appears in: Balanced code, Locally testable code (LTC)
S. Kopparty, S. Saraf, and S. Yekhanin, “High-rate codes with sublinear-time decoding”, Journal of the ACM 61, 1 (2014) DOI. Appears in: Multiplicity code, $q$-ary linear LCC
S. Kopparty, Theory of Computing 11, 149 (2015) DOI. Appears in: Multiplicity code
S. Kopparty, “Some remarks on multiplicity codes”, (2015) arXiv:1505.07547. Appears in: Multiplicity code
S. Kopparty and S. Saraf, “Guest Column”, ACM SIGACT News 47, 46 (2016) DOI. Appears in: Locally decodable code (LDC)
S. Kopparty, O. Meir, N. Ron-Zewi, and S. Saraf, “High-Rate Locally Correctable and Locally Testable Codes with Sub-Polynomial Query Complexity”, Journal of the ACM 64, 1 (2017) DOI. Appears in: Kopparty-Meir-Ron-Zewi-Saraf (KMRS) code
S. B. Korada, E. Sasoglu, and R. Urbanke, “Polar Codes: Characterization of Exponent, Bounds, and Constructions”, IEEE Transactions on Information Theory 56, 6253 (2010) DOI. Appears in: Polar code
S. B. Korada, A. Montanari, E. Telatar, and R. Urbanke, “An empirical scaling law for polar codes”, 2010 IEEE International Symposium on Information Theory (2010) DOI. Appears in: Polar code
S. B. Korada and R. L. Urbanke, “Polar Codes are Optimal for Lossy Source Coding”, IEEE Transactions on Information Theory 56, 1751 (2010) DOI. Appears in: Polar code
G. Korchmáros and P. Speziali, “Hermitian codes with automorphism group isomorphic to PGL(2,q) with q odd”, Finite Fields and Their Applications 44, 1 (2017) DOI. Appears in: Hermitian code
V. Korepin and J. Terilla, “Thermodynamic interpretation of quantum error correcting criterion”, (2004) arXiv:quant-ph/0202054. Appears in: Finite-dimensional quantum error-correcting code
J. Korevaar and J. L. H. Meyers, “Spherical faraday cage for the case of equal point charges and chebyshev-type quadrature on the sphere”, Integral Transforms and Special Functions 1, 105 (1993) DOI. Appears in: Spherical design
A. Korkine and G. Zolotareff, “Sur les formes quadratiques positives quaternaires”, Mathematische Annalen 5, 581 (1872) DOI. Appears in: $D_4$ hyper-diamond lattice
A. Korkine and G. Zolotareff, “Sur les formes quadratiques”, Mathematische Annalen 6, 366 (1873) DOI. Appears in: $E_8$ Gosset lattice-shell code
S. B. Korolev, E. N. Bashmakova, and T. Yu. Golubeva, “Error correction using squeezed Fock states”, Quantum Information Processing 23, (2024) arXiv:2312.16000 DOI. Appears in: Squeezed fock-state code
V. A. Kotelnikov, “The theory of optimum noise immunity,” PhD Thesis, Molotov Energy Institute, Moscow, Jan. 1947. Appears in: Sphere packing
P. K. Kothari and P. Manohar, “An Exponential Lower Bound for Linear 3-Query Locally Correctable Codes”, (2023) arXiv:2311.00558. Appears in: Locally correctable code (LCC)
R. Kotter. A unified description of an error locating procedure for linear codes. In D. Yorgov, editor, Proc. 3rd International Workshop on Algebraic and Combinatorial Coding Theory, pages 113–117, Voneshta Voda, Bulgaria, June 1992. Hermes.. Appears in: Linear $q$-ary code
D. A. Kottwitz, “The densest packing of equal circles on a sphere”, Acta Crystallographica Section A Foundations of Crystallography 47, 158 (1991) DOI. Appears in: Annealing-based spherical code
Y. Kou, S. Lin, and M. P. C. Fossorier, “Low-density parity-check codes based on finite geometries: a rediscovery and new results”, IEEE Transactions on Information Theory 47, 2711 (2001) DOI. Appears in: Finite-geometry LDPC (FG-LDPC) code, Quasi-cyclic LDPC (QC-LDPC) code
N. Koukoulekidis, F. Šimkovic IV, M. Leib, and F. R. F. Pereira, “Small Quantum Codes from Algebraic Extensions of Generalized Bicycle Codes”, (2024) arXiv:2401.07583. Appears in: Generalized bicycle (GB) code, Quantum LDPC (QLDPC) code
S. Koutsioumpas, D. Banfield, and A. Kay, “The Smallest Code with Transversal T”, (2022) arXiv:2210.14066. Appears in: $[[2^r-1,1,3]]$ simplex code, $k$-orthogonal code, $[[15,1,3]]$ quantum Reed-Muller code
A. A. Kovalev, I. Dumer, and L. P. Pryadko, “Design of additive quantum codes via the code-word-stabilized framework”, Physical Review A 84, (2011) arXiv:1108.5490 DOI. Appears in: Codeword stabilized (CWS) code, Cyclic quantum code, $[[13,1,5]]$ cyclic code, Five-qubit perfect code, $[[7,1,3]]$ Steane code, Twisted XZZX toric code, XZZX surface code
A. A. Kovalev and L. P. Pryadko, “Improved quantum hypergraph-product LDPC codes”, 2012 IEEE International Symposium on Information Theory Proceedings 348 (2012) arXiv:1202.0928 DOI. Appears in: Cyclic linear binary code, Hypergraph product (HGP) code, Repetition code, Rotated surface code, $[[5,1,2]]$ rotated surface code, Toric code
A. A. Kovalev and L. P. Pryadko, “Fault tolerance of quantum low-density parity check codes with sublinear distance scaling”, Physical Review A 87, (2013) arXiv:1208.2317 DOI. Appears in: 2D lattice stabilizer code, Hypergraph product (HGP) code, Quantum LDPC (QLDPC) code, Qubit CSS code, Qubit stabilizer code, 2D hyperbolic surface code
A. A. Kovalev and L. P. Pryadko, “Quantum Kronecker sum-product low-density parity-check codes with finite rate”, Physical Review A 88, (2013) arXiv:1212.6703 DOI. Appears in: Two-block group-algebra (2BGA) codes, Generalized bicycle (GB) code, Subsystem modular-qudit CSS code, Five-qubit perfect code, Twisted XZZX toric code, Two-block CSS code
A. A. Kovalev and L. P. Pryadko, “Spin glass reflection of the decoding transition for quantum error correcting codes”, (2014) arXiv:1311.7688. Appears in: 2D lattice stabilizer code, Quantum LDPC (QLDPC) code, Qubit stabilizer code
A. A. Kovalev, S. Prabhakar, I. Dumer, and L. P. Pryadko, “Numerical and analytical bounds on threshold error rates for hypergraph-product codes”, Physical Review A 97, (2018) arXiv:1804.01950 DOI. Appears in: Hypergraph product (HGP) code, 2D hyperbolic surface code
V. Y. Krachkovsky, “Reed-solomon codes for correcting phased error bursts”, IEEE Transactions on Information Theory 49, 2975 (2003) DOI. Appears in: Folded RS (FRS) code
I. Krasikov and S. Litsyn, “Linear programming bounds for doubly-even self-dual codes”, IEEE Transactions on Information Theory 43, 1238 (1997) DOI. Appears in: Divisible code, Self-dual linear code
Krasnopeev, A., and Yu L. Sagalovich. "The Kerdock codes and separating systems." Eight International Workshop on Algebraic and Combinatorial Coding Theory. Vol. 7. No. 7.2. 2002.. Appears in: Frameproof (FP) code, Kerdock code
S. Krastanov and L. Jiang, “Deep Neural Network Probabilistic Decoder for Stabilizer Codes”, Scientific Reports 7, (2017) arXiv:1705.09334 DOI. Appears in: Qubit stabilizer code
I. Kremsky, M.-H. Hsieh, and T. A. Brun, “Classical enhancement of quantum-error-correcting codes”, Physical Review A 78, (2008) arXiv:0802.2414 DOI. Appears in: Entanglement-assisted (EA) hybrid QECC, EA qubit stabilizer code, Hybrid qubit code, Hybrid stabilizer code, Hybrid QECC, Union stabilizer (USt) code, Qubit stabilizer code, Qubit code, $[[9,1,3]]$ Shor code
D. W. Kribs, “A quantum computing primer for operator theorists”, (2004) arXiv:math/0404553. Appears in: Subsystem QECC
D. W. Kribs, “A brief introduction to operator quantum error correction”, (2005) arXiv:math/0506491. Appears in: Subsystem QECC
D. W. Kribs, R. Laflamme, D. Poulin, and M. Lesosky, “Operator quantum error correction”, (2006) arXiv:quant-ph/0504189. Appears in: Subsystem QECC
D. W. Kribs and R. W. Spekkens, “Quantum error-correcting subsystems are unitarily recoverable subsystems”, Physical Review A 74, (2006) arXiv:quant-ph/0608045 DOI. Appears in: Subsystem QECC
D. W. Kribs, A. Pasieka, and K. Zyczkowski, “Entropy of a quantum error correction code”, (2008) arXiv:0811.1621. Appears in: Finite-dimensional quantum error-correcting code, Perfect quantum code
D. W. Kribs and S. Plosker, “Private quantum codes: introduction and connection with higher rank numerical ranges”, Linear and Multilinear Algebra 62, 639 (2013) arXiv:1407.1350 DOI. Appears in: Finite-dimensional quantum error-correcting code
D. W. Kribs, J. Levick, M. I. Nelson, R. Pereira, and M. Rahaman, “Quantum Complementarity and Operator Structures”, (2019) arXiv:1811.10425. Appears in: Operator-algebra QECC (OAQECC)
D. W. Kribs, N. Cao, C.-K. Li, Y.-T. Poon, B. Zeng, and M. Nelson, “Higher Rank Matricial Ranges and Hybrid Quantum Error Correction”, (2019) arXiv:1911.12744. Appears in: Hybrid QECC
D. Kribs, R. Laflamme, and D. Poulin, “Unified and Generalized Approach to Quantum Error Correction”, Physical Review Letters 94, (2005) arXiv:quant-ph/0412076 DOI. Appears in: Subsystem QECC
D. Kribs and D. Poulin, “Operator quantum error correction”, Quantum Error Correction 163 (2013) DOI. Appears in: Subsystem QECC
S. Krinner et al., “Realizing repeated quantum error correction in a distance-three surface code”, Nature 605, 669 (2022) arXiv:2112.03708 DOI. Appears in: $[[9,1,3]]$ Surface-17 code
L. Krippner, W. J. Munro, and M. D. Reid, “Transient macroscopic quantum superposition states in degenerate parametric oscillation: Calculations in the large-quantum-noise limit using the positivePrepresentation”, Physical Review A 50, 4330 (1994) DOI. Appears in: Cat code, Two-component cat code
A. Krishna and J.-P. Tillich, “Towards Low Overhead Magic State Distillation”, Physical Review Letters 123, (2019) arXiv:1811.08461 DOI. Appears in: Prime-qudit RS code, Prime-qudit triorthogonal code
A. Krishna and D. Poulin, “Fault-Tolerant Gates on Hypergraph Product Codes”, Physical Review X 11, (2021) arXiv:1909.07424 DOI. Appears in: Hypergraph product (HGP) code
A. Krishna, I. L. Navon, and M. Wootters, “Viderman’s algorithm for quantum LDPC codes”, (2023) arXiv:2310.07868. Appears in: Hypergraph product (HGP) code
D. S. Krotov and S. V. Avgustinovich, “On the Number of $1$-Perfect Binary Codes: A Lower Bound”, IEEE Transactions on Information Theory 54, 1760 (2008) arXiv:math/0608278 DOI. Appears in: Perfect code, Perfect binary code
D. Krotov and P. Sole, “The punctured Dodecacode is uniformly packed”, 2019 IEEE International Symposium on Information Theory (ISIT) 1912 (2019) DOI. Appears in: Dodecacode
D. Krotov and P. Sole, “The punctured Dodecacode is uniformly packed”, 2019 IEEE International Symposium on Information Theory (ISIT) 1912 (2019) DOI. Appears in: Dodecacode, Uniformly packed code
D. S. Krotov, “Lower bounds for the number of m-quasigroups of order four and of the number of perfect binary codes”, Diskretn. Anal. Issled. Oper., Ser. 1, 7:2 (2000), 47–53. Appears in: Perfect code, Perfect binary code
H. Krovi, S. Guha, Z. Dutton, and M. P. da Silva, “Optimal measurements for symmetric quantum states with applications to optical communication”, Physical Review A 92, (2015) arXiv:1507.04737 DOI. Appears in: Coherent-state c-q code
A. Kruckenhauser et al., “Dark spin-cats as biased qubits”, (2024) arXiv:2408.04421. Appears in: Spin cat code, Spin code
F. R. Kschischang, P. G. de Buda, and S. Pasupathy, “Block coset codes for M-ary phase shift keying”, IEEE Journal on Selected Areas in Communications 7, 900 (1989) DOI. Appears in: Linear code over $G$
F. R. Kschischang, B. J. Frey, and H.-A. Loeliger, “Factor graphs and the sum-product algorithm”, IEEE Transactions on Information Theory 47, 498 (2001) DOI. Appears in: Low-density parity-check (LDPC) code
F. R. Kschischang, "Network Codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI. Appears in: Subspace code
A. M. Kubica, The ABCs of the Color Code: A Study of Topological Quantum Codes as Toy Models for Fault-Tolerant Quantum Computation and Quantum Phases Of Matter, California Institute of Technology, 2018 DOI. Appears in: 2D color code, 3D color code, Color code, Homological code
A. Kubica, B. Yoshida, and F. Pastawski, “Unfolding the color code”, New Journal of Physics 17, 083026 (2015) arXiv:1503.02065 DOI. Appears in: 2D color code, 3D color code, 3D surface code, Ball color code, Color code, Homological code, $[[2^D,D,2]]$ hypercube quantum code, Abelian quantum-double stabilizer code, Concatenated qubit code, Qubit CSS code, $[[8,3,2]]$ Smallest interesting color code, Kitaev surface code
A. Kubica and M. E. Beverland, “Universal transversal gates with color codes: A simplified approach”, Physical Review A 91, (2015) arXiv:1410.0069 DOI. Appears in: Color code, $[[15,1,3]]$ quantum Reed-Muller code, $[[15, 7, 3]]$ quantum Hamming code, Tetrahedral color code
A. Kubica and B. Yoshida, “Ungauging quantum error-correcting codes”, (2018) arXiv:1805.01836. Appears in: 3D subsystem color code, Fracton stabilizer code, Majorana color code, Majorana subsystem stabilizer code, Subsystem modular-qudit stabilizer code, Raussendorf-Bravyi-Harrington (RBH) cluster-state code, Symmetry-protected topological (SPT) code, Subsystem color code, Symmetry-protected self-correcting quantum code, Lattice stabilizer code, Two-gauge theory code
A. Kubica, M. E. Beverland, F. Brandão, J. Preskill, and K. M. Svore, “Three-Dimensional Color Code Thresholds via Statistical-Mechanical Mapping”, Physical Review Letters 120, (2018) arXiv:1708.07131 DOI. Appears in: Tetrahedral color code
A. Kubica and J. Preskill, “Cellular-Automaton Decoders with Provable Thresholds for Topological Codes”, Physical Review Letters 123, (2019) arXiv:1809.10145 DOI. Appears in: Homological code
A. Kubica and R. Demkowicz-Dobrzański, “Using Quantum Metrological Bounds in Quantum Error Correction: A Simple Proof of the Approximate Eastin-Knill Theorem”, Physical Review Letters 126, (2021) arXiv:2004.11893 DOI. Appears in: Covariant block quantum code
A. Kubica and M. Vasmer, “Single-shot quantum error correction with the three-dimensional subsystem toric code”, Nature Communications 13, (2022) arXiv:2106.02621 DOI. Appears in: 3D subsystem surface code, Single-shot code
A. Kubica, A. Haim, Y. Vaknin, H. Levine, F. Brandão, and A. Retzker, “Erasure Qubits: Overcoming the T1 Limit in Superconducting Circuits”, Physical Review X 13, (2023) arXiv:2208.05461 DOI. Appears in: Amplitude-damping (AD) code, Dual-rail quantum code
E. Kubischta and I. Teixeira, “Family of Quantum Codes with Exotic Transversal Gates”, Physical Review Letters 131, (2023) arXiv:2305.07023 DOI. Appears in: Group-representation code, $((7,2,3))$ Pollatsek-Ruskai code, Icosahedron code
E. Kubischta and I. Teixeira, “Quantum Codes from Twisted Unitary t -Groups”, Physical Review Letters 133, (2024) arXiv:2402.01638 DOI. Appears in: $((7,2,3))$ Pollatsek-Ruskai code, $((5,3,2))_3$ qutrit code, $t$-design, Twisted $1$-group code
E. Kubischta and I. Teixeira, “Quantum Codes and Irreducible Products of Characters”, (2024) arXiv:2403.08999. Appears in: Group-representation code, Small-distance block quantum code, Twisted $1$-group code
E. Kubischta and I. Teixeira, “Permutation-Invariant Quantum Codes with Transversal Generalized Phase Gates”, (2024) arXiv:2310.17652. Appears in: Binary dihedral PI code, PI qubit code
E. Kubischta and I. Teixeira, “Classification of the Subgroups of the Two-Qubit Clifford Group”, (2024) arXiv:2409.14624. Appears in: Qubit code
E. Kubischta and I. Teixeira, “Flexible Fault Tolerant Gate Gadgets”, (2024) arXiv:2409.11616. Appears in: Qubit code
E. Kubischta, I. Teixeira, and J. M. Silvester, “Quantum Weight Enumerators for Real Codes with $X$ and $Z$ Exactly Transversal”, (2024) arXiv:2306.12526. Appears in: Five-qubit perfect code
S. Kudekar, T. J. Richardson, and R. L. Urbanke, “Threshold Saturation via Spatial Coupling: Why Convolutional LDPC Ensembles Perform So Well over the BEC”, IEEE Transactions on Information Theory 57, 803 (2011) DOI. Appears in: Spatially coupled LDPC (SC-LDPC) code
S. Kudekar, T. Richardson, and R. Urbanke, “Spatially Coupled Ensembles Universally Achieve Capacity under Belief Propagation”, (2012) arXiv:1201.2999. Appears in: Low-density parity-check (LDPC) code, Spatially coupled LDPC (SC-LDPC) code
S. Kudekar, T. Richardson, and R. L. Urbanke, “Spatially Coupled Ensembles Universally Achieve Capacity Under Belief Propagation”, IEEE Transactions on Information Theory 59, 7761 (2013) DOI. Appears in: Spatially coupled LDPC (SC-LDPC) code
S. Kudekar, S. Kumar, M. Mondelli, H. D. Pfister, E. Şaşoğlu, and R. Urbanke, “Reed-Muller Codes Achieve Capacity on Erasure Channels”, (2016) arXiv:1601.04689. Appears in: Linear $q$-ary code, Reed-Muller (RM) code
M. Kudra et al., “Robust Preparation of Wigner-Negative States with Optimized SNAP-Displacement Sequences”, PRX Quantum 3, (2022) arXiv:2111.07965 DOI. Appears in: Binomial code, Square-lattice GKP code
R. Kueng and D. Gross, “Qubit stabilizer states are complex projective 3-designs”, (2015) arXiv:1510.02767. Appears in: Qubit stabilizer code, Modular-qudit stabilizer code, $t$-design
K. I. Kugel’ and D. I. Khomskiĭ, “The Jahn-Teller effect and magnetism: transition metal compounds”, Soviet Physics Uspekhi 25, 231 (1982) DOI. Appears in: Bacon-Shor code, Compass code, Hamiltonian-based code
A. Kulkarni and P. K. Sarvepalli, “Decoding the three-dimensional toric codes and welded codes on cubic lattices”, Physical Review A 100, (2019) arXiv:1808.03092 DOI. Appears in: 3D surface code
H. D. Kumar, “On the Fourier Transform Approach to Quantum Error Control”, (2012) arXiv:1208.4907. Appears in: Galois-qudit USt code
P. Kumar, “A Class of Quantum Double Subsystem Codes”, (2011) DOI. Appears in: Subsystem QECC, Quantum-double code
S. Kumar, A. J. Young, N. Macris, and H. D. Pfister, “Threshold Saturation for Spatially Coupled LDPC and LDGM Codes on BMS Channels”, IEEE Transactions on Information Theory 60, 7389 (2014) arXiv:1309.7543 DOI. Appears in: Spatially coupled LDPC (SC-LDPC) code
S. Kumar and H. D. Pfister, “Reed-Muller Codes Achieve Capacity on Erasure Channels”, (2015) arXiv:1505.05123. Appears in: Linear $q$-ary code, Reed-Muller (RM) code
S. Kumar, R. Calderbank, and H. D. Pfister, “Reed-muller codes achieve capacity on the quantum erasure channel”, 2016 IEEE International Symposium on Information Theory (ISIT) 1750 (2016) DOI. Appears in: Quantum Reed-Muller code
S. Kundu and B. W. Reichardt, “Majorana qubit codes that also correct odd-weight errors”, (2023) arXiv:2311.01779. Appears in: Majorana box qubit
C.-F. Kung, K.-Y. Kuo, and C.-Y. Lai, “Efficient Approximate Degenerate Ordered Statistics Decoding for Quantum Codes via Reliable Subset Reduction”, (2024) arXiv:2412.21118. Appears in: Quantum LDPC (QLDPC) code
K.-Y. Kuo and C.-Y. Lai, “Comparison of 2D topological codes and their decoding performances”, 2022 IEEE International Symposium on Information Theory (ISIT) (2022) arXiv:2202.06612 DOI. Appears in: Kitaev surface code, Honeycomb (6.6.6) color code, Twisted XZZX toric code, XZZX surface code
K.-Y. Kuo and C.-Y. Lai, “Exploiting degeneracy in belief propagation decoding of quantum codes”, npj Quantum Information 8, (2022) arXiv:2104.13659 DOI. Appears in: Kitaev surface code, Toric code, Honeycomb (6.6.6) color code, Twisted XZZX toric code, XZZX surface code
K.-Y. Kuo and Y. Ouyang, “Degenerate quantum erasure decoding”, (2024) arXiv:2411.13509. Appears in: Qubit stabilizer code
K.-Y. Kuo and C.-Y. Lai, “Fault-Tolerant Belief Propagation for Practical Quantum Memory”, (2024) arXiv:2409.18689. Appears in: Rotated surface code, Twisted XZZX toric code
Kuo, Kao-Yueh, and Chung-Chin Lu. "On the hardness of decoding quantum stabilizer codes under the depolarizing channel." 2012 International Symposium on Information Theory and its Applications. IEEE, 2012.. Appears in: Qubit stabilizer code
G. Kuperberg, “The capacity of hybrid quantum memory”, (2003) arXiv:quant-ph/0203105. Appears in: Hybrid QECC
G. Kuperberg, “Numerical cubature from Archimedes’ hat-box theorem”, (2004) arXiv:math/0405366. Appears in: $t$-design
G. Kuperberg and N. Weaver, “A von Neumann algebra approach to quantum metrics”, (2010) arXiv:1005.0353. Appears in: Classical-quantum (c-q) code, Error-correcting code (ECC), Operator-algebra QECC (OAQECC)
G. Kuperberg, S. Lovett, and R. Peled, “Probabilistic existence of regular combinatorial structures”, (2017) arXiv:1302.4295. Appears in: Orthogonal array (OA), $t$-design
S. Kurz, “Divisible Codes”, (2023) arXiv:2112.11763. Appears in: Divisible code, Self-dual linear code
S. Kushnarev and H. J. Asghar, “The Qudit Cirq Library: An Extension of Google’s Cirq Library for Qudits”, (2025) arXiv:2501.07812. Appears in: Modular-qudit code
T. Kuwahara, R. Nasu, G. Tanaka, and A. Tsuchiya, “Quantum Error Correction Realized by the Renormalization Group in Scalar Field Theories”, Progress of Theoretical and Experimental Physics 2024, (2024) arXiv:2401.17795 DOI. Appears in: Renormalization group (RG) cat code
P. G. Kwiat, “Hyper-entangled states”, Journal of Modern Optics 44, 2173 (1997) DOI. Appears in: Hybrid qudit-oscillator code
H. Kwon and M. S. Kim, “Fluctuation Theorems for a Quantum Channel”, Physical Review X 9, (2019) arXiv:1810.03150 DOI. Appears in: Approximate quantum error-correcting code (AQECC)
S. Kwon, S. Watabe, and J.-S. Tsai, “Autonomous quantum error correction in a four-photon Kerr parametric oscillator”, npj Quantum Information 8, (2022) arXiv:2203.09234 DOI. Appears in: Bosonic rotation code
D. K. Kythe and P. K. Kythe, “Algebraic and Stochastic Coding Theory”, (2017) DOI. Appears in: Tanner code
Kyungjoo Noh, Leung code as quantum polar code, 2017.. Appears in: Quantum polar code, $[[4,2,2]]$ Four-qubit code
G. G. La Guardia, “Constructions of new families of nonbinary quantum codes”, Physical Review A 80, (2009) DOI. Appears in: Galois-qudit BCH code
G. G. La Guardia and R. Palazzo Jr., “Constructions of new families of nonbinary CSS codes”, Discrete Mathematics 310, 2935 (2010) DOI. Appears in: Galois-qudit BCH code
G. G. La Guardia, “New Quantum MDS Codes”, IEEE Transactions on Information Theory 57, 5551 (2011) DOI. Appears in: Constacyclic code, Cyclic linear $q$-ary code, Quantum maximum-distance-separable (MDS) code, Hermitian Galois-qudit code
G. G. La Guardia, “Asymmetric quantum Reed-Solomon and generalized Reed-Solomon codes”, Quantum Information Processing 11, 591 (2011) DOI. Appears in: Asymmetric quantum code, Galois-qudit RS code
G. G. La Guardia, “New families of asymmetric quantum BCH codes”, Quantum Information and Computation 11, 239 (2011) DOI. Appears in: Asymmetric quantum code, Galois-qudit BCH code, Subsystem Galois-qudit stabilizer code
G. G. La Guardia, “Quantum Codes Derived from Cyclic Codes”, International Journal of Theoretical Physics 56, 2479 (2017) arXiv:1705.00239 DOI. Appears in: Galois-qudit BCH code
Laborde, J. M., & SCHÜTZENBERGER, M. (1983). Une nouvelle famille de codes binaires, parfaits, non linéaires. Comptes rendus des séances de l'Académie des sciences. Série 1, Mathématique, 297(1), 67-70.. Appears in: Perfect code
F. Lacerda, J. M. Renes, and V. B. Scholz, “Coherent state constellations for Bosonic Gaussian channels”, 2016 IEEE International Symposium on Information Theory (ISIT) 2499 (2016) DOI. Appears in: Coherent-state constellation code, Modulation scheme, Concatenated bosonic code, $t$-design
F. Lacerda, J. M. Renes, and V. B. Scholz, “Coherent-state constellations and polar codes for thermal Gaussian channels”, Physical Review A 95, (2017) arXiv:1603.05970 DOI. Appears in: Coherent-state constellation code, Modulation scheme, Concatenated bosonic code, $t$-design
D. Lachance-Quirion et al., “Autonomous quantum error correction of Gottesman-Kitaev-Preskill states”, (2023) arXiv:2310.11400. Appears in: Square-lattice GKP code
G. Lachaud, “Number of points of plane sections and linear codes defined on algebraic varieties”, Arithmetic, Geometry, and Coding Theory DOI. Appears in: Projective RM (PRM) code
G. Lachaud, “The parameters of projective Reed–Müller codes”, Discrete Mathematics 81, 217 (1990) DOI. Appears in: Projective RM (PRM) code
Lachaud, G. (1985). Les codes géométriques de Goppa. Sem. Bourbaki, 37, 1984-85.. Appears in: Evaluation code
M. Lachmann, M. E. J. Newman, and C. Moore, “The physical limits of communication or Why any sufficiently advanced technology is indistinguishable from noise”, American Journal of Physics 72, 1290 (2004) arXiv:cond-mat/9907500 DOI. Appears in: Bosonic c-q code
N. Lacroix et al., “Scaling and logic in the color code on a superconducting quantum processor”, (2024) arXiv:2412.14256. Appears in: Honeycomb (6.6.6) color code
S. Laendner and O. Milenkovic, “LDPC Codes Based on Latin Squares: Cycle Structure, Stopping Set, and Trapping Set Analysis”, IEEE Transactions on Communications 55, 303 (2007) DOI. Appears in: Algebraic LDPC code
J. D. Lafferty and D. N. Rockmore, “Spectral techniques for expander codes”, Proceedings of the twenty-ninth annual ACM symposium on Theory of computing - STOC ’97 160 (1997) DOI. Appears in: Regular binary Tanner code
R. Laflamme, C. Miquel, J. P. Paz, and W. H. Zurek, “Perfect Quantum Error Correction Code”, (1996) arXiv:quant-ph/9602019. Appears in: Five-qubit perfect code
M. Laforest, D. Simon, J.-C. Boileau, J. Baugh, M. J. Ditty, and R. Laflamme, “Using error correction to determine the noise model”, Physical Review A 75, (2007) arXiv:quant-ph/0610038 DOI. Appears in: Quantum repetition code
La Guardia, G. G., R. Palazzo, and C. Lavor. "Nonbinary quantum Reed-Solomon codes." Int. J. Pure Applied Math 65.1 (2010): 55-63.. Appears in: Asymmetric quantum code, Galois-qudit RS code
C.-Y. Lai and C.-C. Lu, “A Construction of Quantum Stabilizer Codes Based on Syndrome Assignment by Classical Parity-Check Matrices”, IEEE Transactions on Information Theory 57, 7163 (2011) arXiv:0712.0103 DOI. Appears in: Quantum quadratic-residue (QR) code, Galois-qudit quantum RM code, $[[23, 1, 7]]$ Quantum Golay code, $[[7,1,3]]$ Steane code
C.-Y. Lai, T. A. Brun, and M. M. Wilde, “Dualities and identities for entanglement-assisted quantum codes”, Quantum Information Processing 13, 957 (2013) arXiv:1010.5506 DOI. Appears in: EA qubit code, EA qubit stabilizer code
C.-Y. Lai, T. A. Brun, and M. M. Wilde, “Duality in Entanglement-Assisted Quantum Error Correction”, IEEE Transactions on Information Theory 59, 4020 (2013) arXiv:1302.4150 DOI. Appears in: EA quantum turbo code, Maximal-entanglement EA Galois-qudit stabilizer code
C.-Y. Lai and T. A. Brun, “Entanglement increases the error-correcting ability of quantum error-correcting codes”, Physical Review A 88, (2013) arXiv:1008.2598 DOI. Appears in: EA MDS code
E. Lake, S. Balasubramanian, and S. Choi, “Exact Quantum Algorithms for Quantum Phase Recognition: Renormalization Group and Error Correction”, (2023) arXiv:2211.09803. Appears in: 2D lattice stabilizer code
H. L. J. A. K. Lal, “On Expanders Graphs: Parameters and Applications”, (2004) arXiv:cs/0406048. Appears in: Expander code
L. Lami and M. M. Wilde, “Exact solution for the quantum and private capacities of bosonic dephasing channels”, Nature Photonics 17, 525 (2023) arXiv:2205.05736 DOI. Appears in: Bosonic code
T. Lan, L. Kong, and X.-G. Wen, “Classification of (3+1)D Bosonic Topological Orders: The Case When Pointlike Excitations Are All Bosons”, Physical Review X 8, (2018) arXiv:1704.04221 DOI. Appears in: Topological code
T. Lan and X.-G. Wen, “Classification of 3+1D Bosonic Topological Orders (II): The Case When Some Pointlike Excitations Are Fermions”, Physical Review X 9, (2019) arXiv:1801.08530 DOI. Appears in: Topological code
A. M. Lance, T. Symul, W. P. Bowen, B. C. Sanders, and P. K. Lam, “Tripartite Quantum State Sharing”, Physical Review Letters 92, (2004) arXiv:quant-ph/0311015 DOI. Appears in: Analog repetition code
A. J. Landahl, J. T. Anderson, and P. R. Rice, “Fault-tolerant quantum computing with color codes”, (2011) arXiv:1108.5738. Appears in: 2D color code, Truncated trihexagonal (4.6.12) color code, Square-octagon (4.8.8) color code, Honeycomb (6.6.6) color code
A. J. Landahl and C. Cesare, “Complex instruction set computing architecture for performing accurate quantum $Z$ rotations with less magic”, (2013) arXiv:1302.3240. Appears in: Quantum divisible code
A. J. Landahl and C. Ryan-Anderson, “Quantum computing by color-code lattice surgery”, (2014) arXiv:1407.5103. Appears in: Square-octagon (4.8.8) color code
A. J. Landahl, “The surface code on the rhombic dodecahedron”, (2020) arXiv:2010.06628. Appears in: $[[14,3,3]]$ Rhombic dodecahedron surface code, Twist-defect surface code
A. J. Landahl and B. C. A. Morrison, “Logical fermions for fault-tolerant quantum simulation”, (2023) arXiv:2110.10280. Appears in: Fermion-into-qubit code, Twist-defect surface code
H. Landau, “How does a porcupine separate its quills?”, IEEE Transactions on Information Theory 17, 157 (1971) DOI. Appears in: Permutation spherical code
L. A. Landau, S. Plugge, E. Sela, A. Altland, S. M. Albrecht, and R. Egger, “Towards Realistic Implementations of a Majorana Surface Code”, Physical Review Letters 116, (2016) arXiv:1509.05345 DOI. Appears in: Majorana surface code
L. J. Landau and R. F. Streater, “On Birkhoff’s theorem for doubly stochastic completely positive maps of matrix algebras”, Linear Algebra and its Applications 193, 107 (1993) DOI. Appears in: Single-spin code
I. N. Landjev, “Linear codes over finite fields and finite projective geometries”, Discrete Mathematics 213, 211 (2000) DOI. Appears in: Algebraic-geometry (AG) code, Anticode, Griesmer code, Maximum distance separable (MDS) code, Projective geometry code
I. N. Landjev, “The Geometric Approach to Linear Codes”, Developments in Mathematics 247 (2001) DOI. Appears in: Griesmer code, Projective geometry code, Linear $q$-ary code
O. Landon-Cardinal and D. Poulin, “Local Topological Order Inhibits Thermal Stability in 2D”, Physical Review Letters 110, (2013) arXiv:1209.5750 DOI. Appears in: 2D lattice stabilizer code, Self-correcting quantum code
O. Landon-Cardinal, B. Yoshida, D. Poulin, and J. Preskill, “Perturbative instability of quantum memory based on effective long-range interactions”, Physical Review A 91, (2015) arXiv:1501.04112 DOI. Appears in: 3D surface code, Self-correcting quantum code
P. Landrock and O. Manz, “Classical codes as ideals in group algebras”, Designs, Codes and Cryptography 2, 273 (1992) DOI. Appears in: Generalized RM (GRM) code, Group-algebra code
N. Lang and H. P. Büchler, “Strictly local one-dimensional topological quantum error correction with symmetry-constrained cellular automata”, SciPost Physics 4, (2018) arXiv:1711.08196 DOI. Appears in: Kitaev chain code
R. Lang and P. W. Shor, “Nonadditive quantum error correcting codes adapted to the ampltitude damping channel”, (2007) arXiv:0712.2586. Appears in: Amplitude-damping (AD) code, Self-complementary qubit code
M. Lange, P. Havström, B. Srivastava, V. Bergentall, K. Hammar, O. Heuts, E. van Nieuwenburg, and M. Granath, “Data-driven decoding of quantum error correcting codes using graph neural networks”, (2023) arXiv:2307.01241. Appears in: Quantum LDPC (QLDPC) code
A. Lapidoth, A Foundation in Digital Communication (Cambridge University Press, 2017) DOI. Appears in: Linear binary code, Binary PSK (BPSK) code, Modulation scheme, Single parity-check (SPC) code, Quadrature-amplitude modulation (QAM) code
M. V. Larsen, C. Chamberland, K. Noh, J. S. Neergaard-Nielsen, and U. L. Andersen, “Fault-Tolerant Continuous-Variable Measurement-based Quantum Computation Architecture”, PRX Quantum 2, (2021) arXiv:2101.03014 DOI. Appears in: GKP-surface code, Rotated surface code
W. Laskowski, M. Markiewicz, T. Paterek, and M. Żukowski, “Correlation-tensor criteria for genuine multiqubit entanglement”, Physical Review A 84, (2011) arXiv:1110.4108 DOI. Appears in: Tensor-network code
M. Lassen, M. Sabuncu, A. Huck, J. Niset, G. Leuchs, N. J. Cerf, and U. L. Andersen, “Quantum optical coherence can survive photon losses using a continuous-variable quantum erasure-correcting code”, Nature Photonics 4, 700 (2010) arXiv:1006.3941 DOI. Appears in: Niset-Andersen-Cerf code
“Latin Squares and their Applications”, (2015) DOI. Appears in: Finite-geometry LDPC (FG-LDPC) code, Quasi-cyclic LDPC (QC-LDPC) code
H.-K. Lau and M. B. Plenio, “Universal Quantum Computing with Arbitrary Continuous-Variable Encoding”, Physical Review Letters 117, (2016) arXiv:1605.09278 DOI. Appears in: Dual-rail quantum code, Concatenated bosonic code, Single-mode bosonic code
T. Lau and C. Tan, “A New Technique in Rank Metric Code-Based Encryption”, Cryptography 2, 32 (2018) DOI. Appears in: Gabidulin code
K. Laubscher, D. Loss, and J. R. Wootton, “Universal quantum computation in the surface code using non-Abelian islands”, Physical Review A 100, (2019) arXiv:1811.06738 DOI. Appears in: Quantum-double code, Kitaev surface code
W. de Launey and D. Flannery, Algebraic Design Theory (American Mathematical Society, 2011) DOI. Appears in: Combinatorial design
A. Lavasani, G. Zhu, and M. Barkeshli, “Universal logical gates with constant overhead: instantaneous Dehn twists for hyperbolic quantum codes”, Quantum 3, 180 (2019) arXiv:1901.11029 DOI. Appears in: String-net code
A. Lavasani, Y. Alavirad, and M. Barkeshli, “Topological Order and Criticality in (2+1)D Monitored Random Quantum Circuits”, Physical Review Letters 127, (2021) arXiv:2011.06595 DOI. Appears in: Monitored random-circuit code, Topological code
A. Lavasani, M. J. Gullans, V. V. Albert, and M. Barkeshli, “On stability of k-local quantum phases of matter”, (2024) arXiv:2405.19412. Appears in: Commuting-projector Hamiltonian code, Hamiltonian-based code, Quantum LDPC (QLDPC) code, Topological code
A. Lavasani and S. Vijay, “The Stability of Gapped Quantum Matter and Error-Correction with Adiabatic Noise”, (2024) arXiv:2402.14906. Appears in: 2D lattice stabilizer code
M. Lavrauw, L. Storme, and G. Van de Voorde (2010). Linear codes from projective spaces. In A. Bruen & D. Wehlau (Eds.), Contemporary Mathematics (Vol. 523, pp. 185–202). Providence, RI, USA: American Mathematical Society (AMS).. Appears in: Incidence-matrix projective code
D. Layden, S. Zhou, P. Cappellaro, and L. Jiang, “Ancilla-Free Quantum Error Correction Codes for Quantum Metrology”, Physical Review Letters 122, (2019) arXiv:1811.01450 DOI. Appears in: Binomial code, Chebyshev code, Error-corrected sensing code
F. Lazaro, G. Liva, and G. Bauch, “Inactivation Decoding of LT and Raptor Codes: Analysis and Code Design”, IEEE Transactions on Communications 1 (2017) arXiv:1706.05814 DOI. Appears in: Raptor (RAPid TORnado) code
F. Lazebnik and V. A. Ustimenko, “Explicit construction of graphs with an arbitrary large girth and of large size”, Discrete Applied Mathematics 60, 275 (1995) DOI. Appears in: Lazebnik-Ustimenko (LU) code
LDPC coding for OFDMA PHY. 802.16REVe Sponsor Ballot Recirculation comment, July 2004. IEEE C802.16e04/141r2. Appears in: Quasi-cyclic LDPC (QC-LDPC) code
S. Le Goff, A. Glavieux, and C. Berrou, “Turbo-codes and high spectral efficiency modulation”, Proceedings of ICC/SUPERCOMM’94 - 1994 International Conference on Communications DOI. Appears in: Quadrature-amplitude modulation (QAM) code, Turbo code
W. Lechner, P. Hauke, and P. Zoller, “A quantum annealing architecture with all-to-all connectivity from local interactions”, Science Advances 1, (2015) DOI. Appears in: Lechner-Hauke-Zoller (LHZ) code
D. Lee and B. Yoshida, “Randomly Monitored Quantum Codes”, (2024) arXiv:2402.00145. Appears in: Bacon-Shor code, Concatenated Steane code, Haar-random qubit code, Pastawski-Yoshida-Harlow-Preskill (HaPPY) code, Concatenated qubit code, Qubit stabilizer code, Qubit code, Modular-qudit stabilizer code, $[[15,1,3]]$ quantum Reed-Muller code, Five-qubit perfect code, Subsystem qubit stabilizer code, Toric code, Honeycomb (6.6.6) color code
H.-W. Lee and J. Kim, “Quantum teleportation and Bell’s inequality using single-particle entanglement”, Physical Review A 63, (2000) arXiv:quant-ph/0007106 DOI. Appears in: Single-mode bosonic code
J. Y. Lee, C.-M. Jian, and C. Xu, “Quantum Criticality Under Decoherence or Weak Measurement”, PRX Quantum 4, (2023) arXiv:2301.05238 DOI. Appears in: 2D lattice stabilizer code
J. Lee, N. Kang, S.-H. Lee, H. Jeong, L. Jiang, and S.-W. Lee, “Fault-tolerant quantum computation by hybrid qubits with bosonic cat-code and single photons”, (2023) arXiv:2401.00450. Appears in: Hybrid cat code, Concatenated bosonic code, Raussendorf-Bravyi-Harrington (RBH) cluster-state code
K. Lee, M. Lam, R. Pedarsani, D. Papailiopoulos, and K. Ramchandran, “Speeding Up Distributed Machine Learning Using Codes”, IEEE Transactions on Information Theory 64, 1514 (2018) arXiv:1512.02673 DOI. Appears in: Distributed computation code, Maximum distance separable (MDS) code
S.-H. Lee, S. Omkar, Y. S. Teo, and H. Jeong, “Parity-encoding-based quantum computing with Bayesian error tracking”, npj Quantum Information 9, (2023) arXiv:2207.06805 DOI. Appears in: Quantum parity code (QPC), Raussendorf-Bravyi-Harrington (RBH) cluster-state code
S.-H. Lee, F. Thomsen, N. Fazio, B. J. Brown, and S. D. Bartlett, “Low-overhead magic state distillation with color codes”, (2024) arXiv:2409.07707. Appears in: Honeycomb (6.6.6) color code
S.-H. Lee, A. Li, and S. D. Bartlett, “Color code decoder with improved scaling for correcting circuit-level noise”, Quantum 9, 1609 (2025) arXiv:2404.07482 DOI. Appears in: 2D color code, Honeycomb (6.6.6) color code
S.-W. Lee and H. Jeong, “Near-deterministic quantum teleportation and resource-efficient quantum computation using linear optics and hybrid qubits”, Physical Review A 87, (2013) arXiv:1112.0825 DOI. Appears in: Hybrid cat code
S.-W. Lee, K. Park, T. C. Ralph, and H. Jeong, “Nearly Deterministic Bell Measurement for Multiphoton Qubits and its Application to Quantum Information Processing”, Physical Review Letters 114, (2015) arXiv:1502.07437 DOI. Appears in: Cluster-state code, Quantum repetition code
J. Leech, “Some Sphere Packings in Higher Space”, Canadian Journal of Mathematics 16, 657 (1964) DOI. Appears in: Julin-Golay code
J. Leech, “Notes on Sphere Packings”, Canadian Journal of Mathematics 19, 251 (1967) DOI. Appears in: Construction-$A$ code, $\Lambda_{24}$ Leech lattice, $\Lambda_{24}$ Leech lattice-shell code
J. Leech and N. J. A. Sloane, “Sphere Packings and Error-Correcting Codes”, Canadian Journal of Mathematics 23, 718 (1971) DOI. Appears in: Best $(10,40,4)$ code, Construction-$A$ code, Julin-Golay code, Sphere packing
P. Lefevre, P. Carre, and P. Gaborit, “Watermarking and Rank Metric Codes”, 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 2087 (2018) DOI. Appears in: Gabidulin code
P. Lefèvre, P. Carré, and P. Gaborit, “Application of rank metric codes in digital image watermarking”, Signal Processing: Image Communication 74, 119 (2019) DOI. Appears in: Rank-metric code
Z. Leghtas, G. Kirchmair, B. Vlastakis, R. J. Schoelkopf, M. H. Devoret, and M. Mirrahimi, “Hardware-Efficient Autonomous Quantum Memory Protection”, Physical Review Letters 111, (2013) arXiv:1207.0679 DOI. Appears in: Cat code
Z. Leghtas et al., “Confining the state of light to a quantum manifold by engineered two-photon loss”, Science 347, 853 (2015) arXiv:1412.4633 DOI. Appears in: Two-component cat code
M. S. Leifer and D. Poulin, “Quantum Graphical Models and Belief Propagation”, Annals of Physics 323, 1899 (2008) arXiv:0708.1337 DOI. Appears in: Quantum LDPC (QLDPC) code
J. M. Leinaas and J. Myrheim, “On the theory of identical particles”, Il Nuovo Cimento B Series 11 37, 1 (1977) DOI. Appears in: Topological code
Y. D. Lensky, K. Kechedzhi, I. Aleiner, and E.-A. Kim, “Graph gauge theory of mobile non-Abelian anyons in a qubit stabilizer code”, Annals of Physics 452, 169286 (2023) arXiv:2210.09282 DOI. Appears in: Abelian topological code
A. K. Lenstra, H. W. Lenstra Jr., and L. Lovász, “Factoring polynomials with rational coefficients”, Mathematische Annalen 261, 515 (1982) DOI. Appears in: Lattice-based code
M. Lentmaier, D. V. Truhachev, and K. Sh. Zigangirov, Problems of Information Transmission 37, 288 (2001) DOI. Appears in: LDPC convolutional code (LDPC-CC), Spatially coupled LDPC (SC-LDPC) code
M. Lentmaier, A. Sridharan, K. Sh. Zigangirov, and D. J. Costello, “Terminated LDPC convolutional codes with thresholds close to capacity”, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005. (2005) arXiv:cs/0508030 DOI. Appears in: Spatially coupled LDPC (SC-LDPC) code
J. Leon, J. Masley, and V. Pless, “Duadic Codes”, IEEE Transactions on Information Theory 30, 709 (1984) DOI. Appears in: Binary duadic code
R. Lescanne, M. Villiers, T. Peronnin, A. Sarlette, M. Delbecq, B. Huard, T. Kontos, M. Mirrahimi, and Z. Leghtas, “Exponential suppression of bit-flips in a qubit encoded in an oscillator”, Nature Physics 16, 509 (2020) arXiv:1907.11729 DOI. Appears in: Two-component cat code
M. Leslie, “Hypermap-Homology Quantum Codes (Ph.D. thesis)”, (2013) arXiv:1310.5376. Appears in: Qubit CSS code
D. W. Leung, M. A. Nielsen, I. L. Chuang, and Y. Yamamoto, “Approximate quantum error correction can lead to better codes”, Physical Review A 56, 2567 (1997) arXiv:quant-ph/9704002 DOI. Appears in: Amplitude-damping (AD) code, Approximate quantum error-correcting code (AQECC), Constant-excitation (CE) code, $[[4,2,2]]$ Four-qubit code
D. W. Leung, M. A. Nielsen, I. L. Chuang, and Y. Yamamoto, “Approximate quantum error correction can lead to better codes”, Physical Review A 56, 2567 (1997) DOI. Appears in: Approximate quantum error-correcting code (AQECC)
D. W. Leung, “Towards Robust Quantum Computation”, (2000) arXiv:cs/0012017. Appears in: Quantum repetition code
D. Leung, L. Vandersypen, X. Zhou, M. Sherwood, C. Yannoni, M. Kubinec, and I. Chuang, “Experimental realization of a two-bit phase damping quantum code”, Physical Review A 60, 1924 (1999) arXiv:quant-ph/9811068 DOI. Appears in: Quantum repetition code
D. Leung and G. Smith, “Communicating over adversarial quantum channels using quantum list codes”, (2007) arXiv:quant-ph/0605086. Appears in: Singleton-bound approaching AQECC
D. Leung and W. Matthews, “On the Power of PPT-Preserving and Non-Signalling Codes”, IEEE Transactions on Information Theory 61, 4486 (2015) arXiv:1406.7142 DOI. Appears in: Quantum error-correcting code (QECC)
P. Lévay and F. Holweck, “A fermionic code related to the exceptional group E ${}_{\text{8}}$”, Journal of Physics A: Mathematical and Theoretical 51, 325301 (2018) arXiv:1801.06998 DOI. Appears in: $E_8$ Gosset lattice, $[[2^{m-1},2^{m-1}-m-1,4]]_{f}$ Hamming Majorana code, $[[4,2,2]]$ Four-qubit code
V. I. Levenshtein, “Designs as maximum codes in polynomial metric spaces”, Acta Applicandae Mathematicae 29, 1 (1992) DOI. Appears in: Constant-weight code, Sharp configuration, $q$-ary sharp configuration, Spherical sharp configuration, Universally optimal $q$-ary code
V. I. Levenshtein, “Krawtchouk polynomials and universal bounds for codes and designs in Hamming spaces”, IEEE Transactions on Information Theory 41, 1303 (1995) DOI. Appears in: Universally optimal $q$-ary code
Levenshtein, V. I. (1960). A class of systematic codes. In Doklady Akademii Nauk (Vol. 131, No. 5, pp. 1011-1014). Russian Academy of Sciences.. Appears in: Lexicographic code
Levenshtein, V. I. (1982). Bounds on the maximal cardinality of a code with bounded modulus of the inner product. In Soviet Math. Dokl (Vol. 25, No. 2, pp. 526-531).. Appears in: 24-cell code, Kerdock code
V. I. Levenshtein. Bounds for packings of metric spaces and some of their applications. Problemy Kibernet, 40 (1983), 43-110.. Appears in: $\Lambda_{24}$ Leech lattice-shell code, Universally optimal $q$-ary code
Levenshtein, V. I. "Bounds on the maximal cardinality of a code with bounded modulus of the inner product." Soviet Math. Dokl. Vol. 25. No. 2. 1982.. Appears in: Kerdock spherical code
V.I. Levenshtein, Application of Hadamard matrices to a problem in coding theory, Problems of Cybernetics, vol. 5, GIFML, Moscow, 1961, 125–136.. Appears in: Levenshtein code
V. I. Levenshtein, Binary codes capable of correcting deletions, insertions and reversals (translated to English), Soviet Physics Dokl., 10(8), 707-710 (1966).. Appears in: Varshamov-Tenengolts (VT) code
V. I. Levenshtein, Binary codes capable of correcting spurious insertions and deletions of one (translated to English), Prob. Inf. Transmission, 1(1), 8-17 (1965).. Appears in: Varshamov-Tenengolts (VT) code
V. I. Levenshtein, “On bounds for packings in n-dimensional Euclidean space”, Dokl. Akad. Nauk SSSR, 245:6 (1979), 1299–1303. Appears in: Sharp configuration, $\Lambda_{24}$ Leech lattice-shell code, Spherical sharp configuration
V. I. Levenshtein, "On choosing polynomials to obtain bounds in packing problems." Proc. Seventh All-Union Conf. on Coding Theory and Information Transmission, Part II, Moscow, Vilnius. 1978.. Appears in: Sharp configuration, Spherical sharp configuration
V. I. Levenshtein, “Universal bounds for codes and designs,” in Handbook of Coding Theory 1, eds. V. S. Pless and W. C. Huffman. Amsterdam: Elsevier, 1998, pp.499-648.. Appears in: Combinatorial design, Sharp configuration, $q$-ary sharp configuration, Orthogonal array (OA), Subspace design, $t$-design, Universally optimal $q$-ary code
Levenshtein, Vladimir I. "Binary codes capable of correcting deletions, insertions, and reversals." Soviet physics doklady. Vol. 10. No. 8. 1966.. Appears in: Editing code
A. Leverrier, J.-P. Tillich, and G. Zemor, “Quantum Expander Codes”, 2015 IEEE 56th Annual Symposium on Foundations of Computer Science 810 (2015) arXiv:1504.00822 DOI. Appears in: Quantum expander code
A. Leverrier, S. Apers, and C. Vuillot, “Quantum XYZ Product Codes”, Quantum 6, 766 (2022) arXiv:2011.09746 DOI. Appears in: 3D surface code, Chamon model code, Repetition code, XYZ product code, XZZX surface code
A. Leverrier, V. Londe, and G. Zémor, “Towards local testability for quantum coding”, Quantum 6, 661 (2022) arXiv:1911.03069 DOI. Appears in: Binary linear LTC, Hemicubic code, $q$-ary linear LTC
A. Leverrier and G. Zémor, “Quantum Tanner codes”, (2022) arXiv:2202.13641. Appears in: Left-right Cayley complex code, Quantum Tanner code
A. Leverrier and G. Zémor, “Decoding quantum Tanner codes”, (2022) arXiv:2208.05537. Appears in: Expander LP code, Quantum Tanner code, Tensor-product code
A. Leverrier and G. Zémor, “Efficient decoding up to a constant fraction of the code length for asymptotically good quantum codes”, (2022) arXiv:2206.07571. Appears in: Expander LP code, Quantum Tanner code
P. Leviant, Q. Xu, L. Jiang, and S. Rosenblum, “Quantum capacity and codes for the bosonic loss-dephasing channel”, Quantum 6, 821 (2022) arXiv:2205.00341 DOI. Appears in: Numerically optimized bosonic code
M. A. Levin and X.-G. Wen, “String-net condensation: A physical mechanism for topological phases”, Physical Review B 71, (2005) arXiv:cond-mat/0404617 DOI. Appears in: Double-semion stabilizer code, Fibonacci string-net code, String-net code, Toric code, Walker-Wang model code
M. Levin and X.-G. Wen, “Fermions, strings, and gauge fields in lattice spin models”, Physical Review B 67, (2003) arXiv:cond-mat/0302460 DOI. Appears in: 3D fermionic surface code
M. Levin and X.-G. Wen, “Detecting Topological Order in a Ground State Wave Function”, Physical Review Letters 96, (2006) arXiv:cond-mat/0510613 DOI. Appears in: Topological code
M. Levin and Z.-C. Gu, “Braiding statistics approach to symmetry-protected topological phases”, Physical Review B 86, (2012) arXiv:1202.3120 DOI. Appears in: 2D color code, 3D color code, 3D subsystem color code, 3D surface code, Color code, Cubic theory code, Double-semion stabilizer code, Homological code, Abelian quantum-double stabilizer code, Dihedral $G=D_m$ quantum-double code, Concatenated qubit code, Subsystem modular-qudit stabilizer code, Modular-qudit surface code, Symmetry-protected topological (SPT) code, Kitaev surface code, Twisted quantum double (TQD) code, Abelian TQD stabilizer code, Two-foliated fracton code, Two-gauge theory code
H. Levine et al., “Demonstrating a Long-Coherence Dual-Rail Erasure Qubit Using Tunable Transmons”, Physical Review X 14, (2024) arXiv:2307.08737 DOI. Appears in: Dual-rail quantum code
S. Levy, K. B. Ferreira, N. DeBardeleben, T. Siddiqua, V. Sridharan, and E. Baseman, “Lessons Learned from Memory Errors Observed Over the Lifetime of Cielo”, SC18: International Conference for High Performance Computing, Networking, Storage and Analysis (2018) DOI. Appears in: Error-correcting code (ECC)
Y. Levy and J. Costello, Jr., “An algebraic approach to constructing convolutional codes from quasi-cyclic codes,” DIMACS Ser. Discr. Math. and Theor. Comp. Sci., vol. 14, pp. 189–198, 1993.. Appears in: Convolutional code, Quasi-cyclic code
B. Li, H. Shen, and D. Tse, “An Adaptive Successive Cancellation List Decoder for Polar Codes with Cyclic Redundancy Check”, IEEE Communications Letters 16, 2044 (2012) DOI. Appears in: Cyclic redundancy check (CRC) code, Polar code
B. Li, Z. Wang, G. Zheng, and L. Jiang, “Optimality Condition for the Transpose Channel”, (2024) arXiv:2410.23622. Appears in: Approximate quantum error-correcting code (AQECC)
K. Li, Y. Zuo, and B. Zhu, “Suppressing the Errors Due to Mode Mismatch for $M$-Ary PSK Quantum Receivers Using Photon-Number-Resolving Detector”, IEEE Photonics Technology Letters 25, 2182 (2013) arXiv:1304.7316 DOI. Appears in: PSK c-q code
K. Li and D. Yang, “Reliability Function of Classical-Quantum Channels”, (2024) arXiv:2407.12403. Appears in: Classical-quantum (c-q) code
L. Li, D. J. Young, V. V. Albert, K. Noh, C.-L. Zou, and L. Jiang, “Phase-engineered bosonic quantum codes”, Physical Review A 103, (2021) arXiv:1901.05358 DOI. Appears in: Two-component cat code
M. Li, M. Gutiérrez, S. E. David, A. Hernandez, and K. R. Brown, “Fault tolerance with bare ancillary qubits for a [[7,1,3]] code”, Physical Review A 96, (2017) arXiv:1702.01155 DOI. Appears in: $[[7,1,3]]$ bare code
M. Li, D. Miller, M. Newman, Y. Wu, and K. R. Brown, “2D Compass Codes”, Physical Review X 9, (2019) arXiv:1809.01193 DOI. Appears in: Asymmetric quantum code, Bacon-Shor code, Compass code, Quantum parity code (QPC)
M. Li and T. J. Yoder, “A Numerical Study of Bravyi-Bacon-Shor and Subsystem Hypergraph Product Codes”, (2020) arXiv:2002.06257. Appears in: Bravyi-Bacon-Shor (BBS) code, Hypergraph product (HGP) code, Subsystem hypergraph product (SHP) code
R. Li and Z. Xu, “Construction of[[n,n−4,3]]qquantum codes for odd prime powerq”, Physical Review A 82, (2010) arXiv:0906.2509 DOI. Appears in: Constacyclic code, Quantum maximum-distance-separable (MDS) code, Hermitian Galois-qudit code
R. Li, F. Zou, Y. Liu, and Z. Xu, “Hermitian dual containing BCH codes and Construction of new quantum codes”, Quantum Information and Computation 13, 21 (2013) DOI. Appears in: Galois-qudit BCH code
R. Li, X. Li, and L. Guo, “On entanglement-assisted quantum codes achieving the entanglement-assisted Griesmer bound”, Quantum Information Processing 14, 4427 (2015) DOI. Appears in: EA qubit stabilizer code
R. Li, Y. Ren, C. Guan, and Y. Liu, “Geometry of symplectic group and optimal EAQECC codes”, (2025) arXiv:2501.15465. Appears in: EA qubit stabilizer code, Additive $q$-ary code
S. Li, M. Yu, C.-S. Yang, A. S. Avestimehr, S. Kannan, and P. Viswanath, “PolyShard: Coded Sharding Achieves Linearly Scaling Efficiency and Security Simultaneously”, (2020) arXiv:1809.10361. Appears in: Reed-Solomon (RS) code
X. Li, T.-C. Lin, and M.-H. Hsieh, “Transform Arbitrary Good Quantum LDPC Codes into Good Geometrically Local Codes in Any Dimension”, (2024) arXiv:2408.01769. Appears in: 2D lattice stabilizer code, Good QLDPC code, Quantum LDPC (QLDPC) code, Lattice stabilizer code
Y. Li, I. Dumer, M. Grassl, and L. P. Pryadko, “Structured error recovery for code-word-stabilized quantum codes”, Physical Review A 81, (2010) arXiv:0912.3245 DOI. Appears in: Codeword stabilized (CWS) code, Union stabilizer (USt) code
Y. Li, I. Dumer, and L. P. Pryadko, “Clustered Error Correction of Codeword-Stabilized Quantum Codes”, Physical Review Letters 104, (2010) arXiv:0907.2038 DOI. Appears in: Codeword stabilized (CWS) code, Union stabilizer (USt) code, Modular-qudit CWS code, Modular-qudit USt code
Y. Li, I. Dumer, M. Grassl, and L. P. Pryadko, “Clustered bounded-distance decoding of codeword-stabilized quantum codes”, 2010 IEEE International Symposium on Information Theory (2010) DOI. Appears in: Codeword stabilized (CWS) code, Union stabilizer (USt) code
Y. Li, X. Chen, and M. P. A. Fisher, “Quantum Zeno effect and the many-body entanglement transition”, Physical Review B 98, (2018) DOI. Appears in: Monitored random-circuit code
Y. Li, X. Chen, and M. P. A. Fisher, “Measurement-driven entanglement transition in hybrid quantum circuits”, Physical Review B 100, (2019) arXiv:1901.08092 DOI. Appears in: Monitored random-circuit code, Random stabilizer code
Y. Li and M. P. A. Fisher, “Statistical mechanics of quantum error correcting codes”, Physical Review B 103, (2021) arXiv:2007.03822 DOI. Appears in: Monitored random-circuit code
Y. Li, “Low-density parity-check representation of fault-tolerant quantum circuits”, (2024) arXiv:2403.10268. Appears in: Low-density parity-check (LDPC) code, Spacetime circuit code
Y. Li, C. W. von Keyserlingk, G. Zhu, and T. Jochym-O’Connor, “Phase diagram of the three-dimensional subsystem toric code”, Physical Review Research 6, (2024) arXiv:2305.06389 DOI. Appears in: 3D subsystem color code, 3D subsystem surface code, 3D surface code, Abelian quantum-double stabilizer code, Self-correcting quantum code, Symmetry-protected self-correcting quantum code
Z. Li, L.-J. Xing, and X.-M. Wang, “A family of asymptotically good quantum codes based on code concatenation”, (2008) arXiv:0901.0042. Appears in: Galois-qudit RS code, Concatenated quantum code
Z. Li, L.-J. Xing, and X.-M. Wang, “Quantum generalized Reed-Solomon codes: Unified framework for quantum maximum-distance-separable codes”, Physical Review A 77, (2008) arXiv:0812.4514 DOI. Appears in: Galois-qudit GRS code
Z. Li and L. Xing, “No More Perfect Codes: Classification of Perfect Quantum Codes”, (2009) arXiv:0907.0049. Appears in: Perfect quantum code, Quantum twisted code
Z. Li, T. Roy, D. R. Perez, K.-H. Lee, E. Kapit, and D. I. Schuster, “Autonomous error correction of a single logical qubit using two transmons”, (2023) arXiv:2302.06707. Appears in: Very small logical qubit (VSLQ) code
Z. Li, I. Kim, and P. Hayden, “Concatenation Schemes for Topological Fault-tolerant Quantum Error Correction”, Quantum 7, 1089 (2023) arXiv:2209.09390 DOI. Appears in: $[[4,1,1,2]]$ Four-qubit subsystem code, Concatenated qubit code, Raussendorf-Bravyi-Harrington (RBH) cluster-state code, $[[7,1,3]]$ Steane code
Z. Li and L. Boyle, “The Penrose Tiling is a Quantum Error-Correcting Code”, (2024) arXiv:2311.13040. Appears in: Penrose tiling code
Z. Liang, Z. Yi, F. Yang, J. Chen, Z. Wang, and X. Wang, “High-dimensional quantum XYZ product codes for biased noise”, (2024) arXiv:2408.03123. Appears in: Asymmetric quantum code, XYZ product code
Z. Liang, B. Yang, J. T. Iosue, and Y.-A. Chen, “Operator algebra and algorithmic construction of boundaries and defects in (2+1)D topological Pauli stabilizer codes”, (2024) arXiv:2410.11942. Appears in: 2D lattice stabilizer code, $[[144,12,12]]$ gross code, Bivariate bicycle (BB) code, Kitaev surface code
Z. Liang, Y. Xu, J. T. Iosue, and Y.-A. Chen, “Extracting Topological Orders of Generalized Pauli Stabilizer Codes in Two Dimensions”, PRX Quantum 5, (2024) arXiv:2312.11170 DOI. Appears in: 2D lattice stabilizer code, Kitaev surface code
Z. Liang, F. Yang, Z. Yi, and X. Wang, “Quantum XYZ cyclic codes for biased noise”, (2025) arXiv:2501.16827. Appears in: Asymmetric quantum code, Cyclic quantum code
H. Liao, G. S. Hartnett, A. Kakkar, A. Tan, M. Hush, P. S. Mundada, M. J. Biercuk, and Y. Baum, “Achieving computational gains with quantum error correction primitives: Generation of long-range entanglement enhanced by error detection”, (2024) arXiv:2411.14638. Appears in: Quantum repetition code
P. Liao, B. C. Sanders, and D. L. Feder, “Topological graph states and quantum error-correction codes”, Physical Review A 105, (2022) arXiv:2112.02502 DOI. Appears in: Cluster-state code, Topological code
D. A. Lidar, I. L. Chuang, and K. B. Whaley, “Decoherence-Free Subspaces for Quantum Computation”, Physical Review Letters 81, 2594 (1998) arXiv:quant-ph/9807004 DOI. Appears in: Constant-excitation (CE) code, Dual-rail quantum code, Five-qubit perfect code
D. A. Lidar, D. Bacon, and K. B. Whaley, “Concatenating Decoherence-Free Subspaces with Quantum Error Correcting Codes”, Physical Review Letters 82, 4556 (1999) arXiv:quant-ph/9809081 DOI. Appears in: Constant-excitation (CE) code, Five-qubit perfect code
D. A. Lidar, D. Bacon, J. Kempe, and K. Birgitta Whaley, “Protecting quantum information encoded in decoherence-free states against exchange errors”, Physical Review A 61, (2000) arXiv:quant-ph/9907096 DOI. Appears in: Constant-excitation (CE) code, Five-qubit perfect code
D. A. Lidar, D. Bacon, J. Kempe, and K. B. Whaley, “Decoherence-free subspaces for multiple-qubit errors. I. Characterization”, Physical Review A 63, (2001) arXiv:quant-ph/9908064 DOI. Appears in: Constant-excitation (CE) code, Dual-rail quantum code, Five-qubit perfect code
D. A. Lidar, D. Bacon, J. Kempe, and K. B. Whaley, “Decoherence-free subspaces for multiple-qubit errors. II. Universal, fault-tolerant quantum computation”, Physical Review A 63, (2001) arXiv:quant-ph/0007013 DOI. Appears in: Constant-excitation (CE) code, Dual-rail quantum code, Five-qubit perfect code
D. A. Lidar and T. A. Brun, editors , Quantum Error Correction (Cambridge University Press, 2013) DOI. Appears in: Quantum error-correcting code (QECC)
E. H. Lieb and R. Seiringer, The Stability of Matter in Quantum Mechanics (Cambridge University Press, 2009) DOI. Appears in: Hamiltonian-based code
S. Lieu, R. Belyansky, J. T. Young, R. Lundgren, V. V. Albert, and A. V. Gorshkov, “Symmetry Breaking and Error Correction in Open Quantum Systems”, Physical Review Letters 125, (2020) arXiv:2008.02816 DOI. Appears in: Quantum repetition code, Two-component cat code
S. Lieu, Y.-J. Liu, and A. V. Gorshkov, “Candidate for a passively protected quantum memory in two dimensions”, (2023) arXiv:2205.09767. Appears in: Cat-repetition code, Self-correcting quantum code
S. Lieu, E. L. Rosenfeld, K. Noh, and C. T. Hann, “Viewing fluxonium through the lens of the cat qubit”, (2025) arXiv:2501.16425. Appears in: Two-component cat code
Lihao Xu and J. Bruck, “X-code: MDS array codes with optimal encoding”, IEEE Transactions on Information Theory 45, 272 (1999) DOI. Appears in: X-code
J.-M. Lihm, K. Noh, and U. R. Fischer, “Implementation-independent sufficient condition of the Knill-Laflamme type for the autonomous protection of logical qudits by strong engineered dissipation”, Physical Review A 98, (2018) arXiv:1711.02999 DOI. Appears in: Finite-dimensional quantum error-correcting code
H.-K. Lin and L. P. Pryadko, “Quantum two-block group algebra codes”, (2023) arXiv:2306.16400. Appears in: Two-block group-algebra (2BGA) codes, Generalized bicycle (GB) code, Single-shot code, Two-block CSS code
M. Lin, C. Chamberland, and K. Noh, “Closest Lattice Point Decoding for Multimode Gottesman-Kitaev-Preskill Codes”, PRX Quantum 4, (2023) arXiv:2303.04702 DOI. Appears in: GKP-surface code, Gottesman-Kitaev-Preskill (GKP) code, Numerically optimized bosonic code, Rotated surface code
M. Lin and K. Noh, “Exploring the quantum capacity of a Gaussian random displacement channel using Gottesman-Kitaev-Preskill codes and maximum likelihood decoding”, (2024) arXiv:2411.04277. Appears in: Concatenated GKP code, GKP-surface code, Five-qubit perfect code, Honeycomb (6.6.6) color code
T.-C. Lin and M.-H. Hsieh, “$c^3$-Locally Testable Codes from Lossless Expanders”, (2022) arXiv:2201.11369. Appears in: Lossless expander balanced-product code, Locally testable code (LTC)
T.-C. Lin and M.-H. Hsieh, “Good quantum LDPC codes with linear time decoder from lossless expanders”, (2022) arXiv:2203.03581. Appears in: Good QLDPC code, Lossless expander balanced-product code
T.-C. Lin, A. Wills, and M.-H. Hsieh, “Geometrically Local Quantum and Classical Codes from Subdivision”, (2024) arXiv:2309.16104. Appears in: Good QLDPC code, Quantum LDPC (QLDPC) code, Qubit CSS code, Abelian topological code, Lattice stabilizer code
T.-C. Lin, “Transversal non-Clifford gates for quantum LDPC codes on sheaves”, (2024) arXiv:2410.14631. Appears in: Qubit CSS code
Y. Lin and M. Jimbo, “Extremal properties of t-SEEDs and recursive constructions”, Designs, Codes and Cryptography 73, 805 (2013) DOI. Appears in: Combinatorial design, Jump code
S. Lin and D. J. Costello, Error Control Coding, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, 2004.. Appears in: Binary BCH code, Cyclic redundancy check (CRC) code, Low-density parity-check (LDPC) code, Bose–Chaudhuri–Hocquenghem (BCH) code
Lindström, Bernt. "On group and nongroup perfect codes in q symbols." Mathematica Scandinavica 25.2 (1969): 149-158.. Appears in: Perfect code
K. Lindström, “All nearly perfect codes are known”, Information and Control 35, 40 (1977) DOI. Appears in: Nearly perfect code, Perfect code, Perfect binary code
K. Lindstrom and M. J. Aaltonen, "The nonexistence of nearly perfect nonbinary codes for 1 =< e =< 10", Ann. Univ. Turku, Ser. A I, No. 172, 1976.. Appears in: Nearly perfect code
S. Ling and P. Sole. 2008. Nonadditive quantum codes from Z4-codes. https://hal.archives-ouvertes.fr/hal-00338309/fr/.. Appears in: Goethals code, Gray code, Preparata code, $((2^m,2^{2^m−5m+1},8))$ Goethals-Preparata code
N. Linial and E. Loyfer, “An Elementary Proof of the First LP Bound on the Rate of Binary Codes”, (2023) arXiv:2303.16619. Appears in: Binary code
N. M. Linke, M. Gutierrez, K. A. Landsman, C. Figgatt, S. Debnath, K. R. Brown, and C. Monroe, “Fault-tolerant quantum error detection”, Science Advances 3, (2017) arXiv:1611.06946 DOI. Appears in: $[[4,2,2]]$ Four-qubit code
Linshu Li, private communication, 2018. Appears in: Binomial code, $[[4,2,2]]$ Four-qubit code
J. H. van Lint Jr. and G. J. M. van Wee, “Generalized bounds on binary/ternary mixed packing and covering codes”, Journal of Combinatorial Theory, Series A 57, 130 (1991) DOI. Appears in: Binary-ternary mixed code, Covering code
J. H. van Lint, Introduction to Coding Theory (Springer Berlin Heidelberg, 1992) DOI. Appears in: Weighted-covering code
J. H. van Lint, Introduction to Coding Theory (Springer Berlin Heidelberg, 1999) DOI. Appears in: Block code
J. H. Lint, “Generalized quadratic-residue codes”, Algebraic Coding Theory and Applications 285 (1979) DOI. Appears in: Quadratic-residue (QR) code
J. van Lint, “A new description of the Nadler code (Corresp.)”, IEEE Transactions on Information Theory 18, 825 (1972) DOI. Appears in: Nadler code, Nordstrom-Robinson (NR) code
J. van Lint and F. MacWilliams, “Generalized quadratic residue codes”, IEEE Transactions on Information Theory 24, 730 (1978) DOI. Appears in: Quadratic-residue (QR) code
J. van Lint and R. Wilson, “On the minimum distance of cyclic codes”, IEEE Transactions on Information Theory 32, 23 (1986) DOI. Appears in: Cyclic linear binary code, Cyclic linear $q$-ary code
P.-H. Liou and C.-Y. Lai, “Parallel syndrome extraction with shared flag qubits for Calderbank-Shor-Steane codes of distance three”, Physical Review A 107, (2023) arXiv:2208.00581 DOI. Appears in: Qubit CSS code
A. E. Lipstein and R. A. Reid-Edwards, “Lattice gerbe theory”, Journal of High Energy Physics 2014, (2014) arXiv:1404.2634 DOI. Appears in: Two-gauge theory code
P. Lisoněk and V. Singh, “Quantum codes from nearly self-orthogonal quaternary linear codes”, Designs, Codes and Cryptography 73, 417 (2014) DOI. Appears in: Hermitian Galois-qudit code
Lisonek, Petr, and Reza Dastbasteh. "Constructions of quantum codes." In 3rd International Workshop on Boolean Functions and their Applications, loen, norway. https://org. uib. no/selmer/workshops/BFA2018/Slides/Lisonek. pdf. 2018.. Appears in: Hermitian Galois-qudit code
P. Lisonek, A. Roy, and S. Trandafir, private communication, 2019. Appears in: Subsystem CSS code
D. Litinski, M. S. Kesselring, J. Eisert, and F. von Oppen, “Combining Topological Hardware and Topological Software: Color-Code Quantum Computing with Topological Superconductor Networks”, Physical Review X 7, (2017) arXiv:1704.01589 DOI. Appears in: Majorana color code
D. Litinski and F. von Oppen, “Braiding by Majorana tracking and long-range CNOT gates with color codes”, Physical Review B 96, (2017) arXiv:1708.05012 DOI. Appears in: Majorana color code
D. Litinski and F. von Oppen, “Quantum computing with Majorana fermion codes”, Physical Review B 97, (2018) arXiv:1801.08143 DOI. Appears in: 2D color code, Majorana color code, $[[2^{m-1},2^{m-1}-m-1,4]]_{f}$ Hamming Majorana code, Majorana surface code, Majorana box qubit
D. Litinski and F. von Oppen, “Lattice Surgery with a Twist: Simplifying Clifford Gates of Surface Codes”, Quantum 2, 62 (2018) arXiv:1709.02318 DOI. Appears in: Kitaev surface code, Twist-defect color code
D. Litinski, “A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery”, Quantum 3, 128 (2019) arXiv:1808.02892 DOI. Appears in: Kitaev surface code
D. Litinski, “Magic State Distillation: Not as Costly as You Think”, Quantum 3, 205 (2019) arXiv:1905.06903 DOI. Appears in: Kitaev surface code
D. Litinski and N. Nickerson, “Active volume: An architecture for efficient fault-tolerant quantum computers with limited non-local connections”, (2022) arXiv:2211.15465. Appears in: Kitaev surface code
B. Litjens, “Semidefinite bounds for mixed binary/ternary codes”, Discrete Mathematics 341, 1740 (2018) arXiv:1606.06930 DOI. Appears in: Binary-ternary mixed code
S. Litsyn and A. Vardy, “The uniqueness of the Best code”, IEEE Transactions on Information Theory 40, 1693 (1994) DOI. Appears in: Best $(10,40,4)$ code
J. B. Little, “Algebraic geometry codes from higher dimensional varieties”, (2008) arXiv:0802.2349. Appears in: Polynomial evaluation code, Evaluation code, Extended GRS code, Generalized RM (GRM) code, Grassmannian code, Griesmer code, Projective RM (PRM) code
J. Little and H. Schenck, “Toric surface codes and Minkowski sums”, (2006) arXiv:math/0507598. Appears in: Hansen toric code
C. Liu, “Exact performance of the five-qubit code with coherent errors”, (2022) arXiv:2203.01706. Appears in: Five-qubit perfect code
H. Liu and S. Liu, “A class of constacyclic codes are generalized Reed–Solomon codes”, Designs, Codes and Cryptography 91, 4143 (2023) DOI. Appears in: Generalized RS (GRS) code, Quantum maximum-distance-separable (MDS) code
M. L. Liu, N. Tantivasadakarn, and V. V. Albert, “Subsystem CSS codes, a tighter stabilizer-to-CSS mapping, and Goursat&apos;s Lemma”, Quantum 8, 1403 (2024) arXiv:2311.18003 DOI. Appears in: Subsystem modular-qudit CSS code, Subsystem modular-qudit stabilizer code, Subsystem CSS code, Subsystem qubit stabilizer code
S. Liu, F. Manganiello, and F. R. Kschischang, “Construction and decoding of generalized skew-evaluation codes”, 2015 IEEE 14th Canadian Workshop on Information Theory (CWIT) (2015) DOI. Appears in: Linearized RS code
X. Liu, L. Yu, and H. Liu, “New quantum codes from Hermitian dual-containing codes”, International Journal of Quantum Information 17, 1950006 (2019) DOI. Appears in: Galois-qudit GRS code
X. Liu, H. Liu, and L. Yu, “On New Quantum Codes From Matrix Product Codes”, (2021) arXiv:1604.05823. Appears in: Matrix-product code, Hermitian Galois-qudit code
Y.-H. Liu and D. Poulin, “Neural Belief-Propagation Decoders for Quantum Error-Correcting Codes”, Physical Review Letters 122, (2019) arXiv:1811.07835 DOI. Appears in: Quantum LDPC (QLDPC) code
Y.-J. Liu, K. Shtengel, A. Smith, and F. Pollmann, “Methods for Simulating String-Net States and Anyons on a Digital Quantum Computer”, PRX Quantum 3, (2022) arXiv:2110.02020 DOI. Appears in: String-net code, Kitaev surface code
Y. Liu et al., “Hybrid Oscillator-Qubit Quantum Processors: Instruction Set Architectures, Abstract Machine Models, and Applications”, (2024) arXiv:2407.10381. Appears in: Hybrid cat code, Hybrid qudit-oscillator code
Y. Liu, S. Che, J. Zhou, Y. Shi, and G. Li, “Fermihedral: On the Optimal Compilation for Fermion-to-Qubit Encoding”, arXiv (2024) DOI. Appears in: Fermion-into-qubit code
Z.-W. Liu and S. Zhou, “Quantum error correction meets continuous symmetries: fundamental trade-offs and case studies”, (2023) arXiv:2111.06360. Appears in: Covariant block quantum code, Eigenstate thermalization hypothesis (ETH) code, Quantum Reed-Muller code
Z.-W. Liu and S. Zhou, “Approximate symmetries and quantum error correction”, npj Quantum Information 9, (2023) arXiv:2111.06355 DOI. Appears in: Covariant block quantum code
Z. Liu and D. A. Pados, “LDPC Codes From Generalized Polygons”, IEEE Transactions on Information Theory 51, 3890 (2005) DOI. Appears in: Algebraic LDPC code
G. Liva, F. Steiner. “pretty-good-codes.org: Online library of good channel codes”, URL: http://pretty-good-codes.org/. Appears in: Low-density parity-check (LDPC) code, Polar code
W. P. Livingston, M. S. Blok, E. Flurin, J. Dressel, A. N. Jordan, and I. Siddiqi, “Experimental demonstration of continuous quantum error correction”, Nature Communications 13, (2022) arXiv:2107.11398 DOI. Appears in: Quantum repetition code
Li, Yunfan. Codeword Stabilized Quantum Codes and Their Error Correction. Diss. UC Riverside, 2010.. Appears in: Codeword stabilized (CWS) code, Union stabilizer (USt) code, Modular-qudit CWS code, Modular-qudit USt code
S. Lloyd, “Universal Quantum Simulators”, Science 273, 1073 (1996) DOI. Appears in: Hamiltonian-based code
S. Lloyd, “Capacity of the noisy quantum channel”, Physical Review A 55, 1613 (1997) arXiv:quant-ph/9604015 DOI. Appears in: Quantum error-correcting code (QECC)
S. Lloyd and J.-J. E. Slotine, “Analog Quantum Error Correction”, Physical Review Letters 80, 4088 (1998) arXiv:quant-ph/9711021 DOI. Appears in: $[[9,1,3]]_{\mathbb{R}}$ Lloyd-Slotine code, Oscillator-into-oscillator code
S. Lloyd and S. L. Braunstein, “Quantum Computation over Continuous Variables”, Physical Review Letters 82, 1784 (1999) arXiv:quant-ph/9810082 DOI. Appears in: Bosonic code
S. Lloyd, P. Shor, and K. Thompson, “polylog-LDPC Capacity Achieving Codes for the Noisy Quantum Erasure Channel”, (2017) arXiv:1703.00382. Appears in: Quantum LDPC (QLDPC) code
H.-K. Lo and H. F. Chau, “Unconditional Security of Quantum Key Distribution over Arbitrarily Long Distances”, Science 283, 2050 (1999) arXiv:quant-ph/9803006 DOI. Appears in: Qubit code
M. C. Löbl, S. X. Chen, S. Paesani, and A. S. Sørensen, “Breadth-first graph traversal union-find decoder”, (2024) arXiv:2407.15988. Appears in: Quantum LDPC (QLDPC) code
D. F. Locher, L. Cardarelli, and M. Müller, “Quantum Error Correction with Quantum Autoencoders”, Quantum 7, 942 (2023) arXiv:2202.00555 DOI. Appears in: Approximate quantum error-correcting code (AQECC)
J. Łodyga, P. Mazurek, A. Grudka, and M. Horodecki, “Simple scheme for encoding and decoding a qubit in unknown state for various topological codes”, Scientific Reports 5, (2015) arXiv:1404.2495 DOI. Appears in: Qubit CSS code, Kitaev surface code
H.-A. Loeliger, “Signal sets matched to groups”, IEEE Transactions on Information Theory 37, 1675 (1991) DOI. Appears in: Linear code over $G$, Slepian group-orbit code
P. Loidreau, “A Welch–Berlekamp Like Algorithm for Decoding Gabidulin Codes”, Lecture Notes in Computer Science 36 (2006) DOI. Appears in: Rank-metric code
C. Lomont, “Error Correcting Codes on Algebraic Surfaces”, (2003) arXiv:math/0309123. Appears in: Ruled-surface code
P. van Loock and S. L. Braunstein, “Unconditional teleportation of continuous-variable entanglement”, Physical Review A 61, (1999) arXiv:quant-ph/9907073 DOI. Appears in: Coherent-state c-q code
P. van Loock and S. L. Braunstein, “Multipartite Entanglement for Continuous Variables: A Quantum Teleportation Network”, Physical Review Letters 84, 3482 (2000) arXiv:quant-ph/9906021 DOI. Appears in: Analog repetition code
P. van Loock, “Quantum Communication with Continuous Variables”, Fortschritte der Physik 50, 1177 (2002) DOI. Appears in: Analog repetition code
P. van Loock, “A note on quantum error correction with continuous variables”, (2008) arXiv:0811.3616. Appears in: Analog stabilizer code
S. Y. Looi, L. Yu, V. Gheorghiu, and R. B. Griffiths, “Quantum-error-correcting codes using qudit graph states”, Physical Review A 78, (2008) arXiv:0712.1979 DOI. Appears in: Codeword stabilized (CWS) code, Qubit code, Modular-qudit CWS code, Modular-qudit USt code
L. Lootens, J. Fuchs, J. Haegeman, C. Schweigert, and F. Verstraete, “Matrix product operator symmetries and intertwiners in string-nets with domain walls”, SciPost Physics 10, (2021) arXiv:2008.11187 DOI. Appears in: String-net code
L. Lootens, B. Vancraeynest-De Cuiper, N. Schuch, and F. Verstraete, “Mapping between Morita-equivalent string-net states with a constant depth quantum circuit”, Physical Review B 105, (2022) arXiv:2112.12757 DOI. Appears in: Cubic theory code, Dijkgraaf-Witten gauge theory code, Abelian quantum-double stabilizer code, Dihedral $G=D_m$ quantum-double code, Abelian TQD stabilizer code, Two-gauge theory code
H. H. López, C. Rentería-Márquez, and R. H. Villarreal, “Affine cartesian codes”, Designs, Codes and Cryptography 71, 5 (2012) arXiv:1202.0085 DOI. Appears in: Hansen toric code
H. Lou and J. Garcia-Frias, "On the Application of Error-Correcting Codes with Low-Density Generator Matrix over Different Quantum Channels," 4th International Symposium on Turbo Codes & Related Topics; 6th International ITG-Conference on Source and Channel Coding, Munich, Germany, 2006, pp. 1-6.. Appears in: Low-density generator-matrix (LDGM) code, Quantum LDPC (QLDPC) code
G. H. Low and I. L. Chuang, “Hamiltonian Simulation by Qubitization”, Quantum 3, 163 (2019) arXiv:1610.06546 DOI. Appears in: Spin GKP code
G. H. Low, V. Kliuchnikov, and L. Schaeffer, “Trading T gates for dirty qubits in state preparation and unitary synthesis”, Quantum 8, 1375 (2024) arXiv:1812.00954 DOI. Appears in: Qubit code
C.-Y. Lu, W.-B. Gao, J. Zhang, X.-Q. Zhou, T. Yang, and J.-W. Pan, “Experimental quantum coding against qubit loss error”, Proceedings of the National Academy of Sciences 105, 11050 (2008) arXiv:0804.2268 DOI. Appears in: $[[4,2,2]]$ Four-qubit code
L. Lu, W. Ma, R. Li, Y. Ma, and L. Guo, “New Quantum MDS codes constructed from Constacyclic codes”, (2018) arXiv:1803.07927. Appears in: Constacyclic code, Quantum maximum-distance-separable (MDS) code, Hermitian Galois-qudit code
X. Lu, J. Jeong, J.-W. Kim, J.-S. No, H. Park, A. No, and S. Kim, “Error Rate-Based Log-Likelihood Ratio Processing for Low-Density Parity-Check Codes in DNA Storage”, IEEE Access 8, 162892 (2020) DOI. Appears in: DNA storage code, Low-density parity-check (LDPC) code
Y. Lu, A. Maiti, J. W. O. Garmon, S. Ganjam, Y. Zhang, J. Claes, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, “High-fidelity parametric beamsplitting with a parity-protected converter”, Nature Communications 14, (2023) DOI. Appears in: Dual-rail quantum code
A. Lubotzky, R. Phillips, and P. Sarnak, “Ramanujan graphs”, Combinatorica 8, 261 (1988) DOI. Appears in: Expander code, Margulis LDPC code, High-dimensional expander (HDX) code
M. Luby, “LT codes”, The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings. DOI. Appears in: Luby transform (LT) code
M. G. Luby, M. Mitzenmacher, M. A. Shokrollahi, D. A. Spielman, and V. Stemann, “Practical loss-resilient codes”, Proceedings of the twenty-ninth annual ACM symposium on Theory of computing - STOC ’97 150 (1997) DOI. Appears in: Irregular LDPC code, Tornado code
M. G. Luby, M. Mitzenmacher, M. A. Shokrollahi, and D. A. Spielman, “Efficient erasure correcting codes”, IEEE Transactions on Information Theory 47, 569 (2001) DOI. Appears in: Hypergraph product (HGP) code, Tornado code
M. G. Luby, M. Mitzenmacher, M. A. Shokrollahi, and D. A. Spielman, “Improved low-density parity-check codes using irregular graphs”, IEEE Transactions on Information Theory 47, 585 (2001) DOI. Appears in: Irregular LDPC code
M. G. Luby, R. Padovani, T. J. Richardson, L. Minder, and P. Aggarwal, “Liquid Cloud Storage”, (2017) arXiv:1705.07983. Appears in: Distributed-storage code, Fountain code
A. Lucia, D. Pérez-García, and A. Pérez-Hernández, “Thermalization in Kitaev’s quantum double models via tensor network techniques”, Forum of Mathematics, Sigma 11, (2023) arXiv:2107.01628 DOI. Appears in: Self-correcting quantum code
A. P. Lund and T. C. Ralph, “Nondeterministic gates for photonic single-rail quantum logic”, Physical Review A 66, (2002) arXiv:quant-ph/0205044 DOI. Appears in: Single-mode bosonic code
A. P. Lund, T. C. Ralph, and H. L. Haselgrove, “Fault-Tolerant Linear Optical Quantum Computing with Small-Amplitude Coherent States”, Physical Review Letters 100, (2008) arXiv:0707.0327 DOI. Appears in: Concatenated cat code, $[[23, 1, 7]]$ Quantum Golay code, $[[7,1,3]]$ Steane code, Two-component cat code
C. Lund, L. Fortnow, H. Karloff, and N. Nisan, “Algebraic methods for interactive proof systems”, Journal of the ACM 39, 859 (1992) DOI. Appears in: Locally testable code (LTC)
G. Luo, M. F. Ezerman, M. Grassl, and S. Ling, “Constructing quantum error-correcting codes that require a variable amount of entanglement”, Quantum Information Processing 23, (2023) arXiv:2207.05647 DOI. Appears in: EA qubit stabilizer code
G. Luo, M. F. Ezerman, M. Grassl, and S. Ling, “Constructing quantum error-correcting codes that require a variable amount of entanglement”, Quantum Information Processing 23, (2023) DOI. Appears in: EA qubit stabilizer code
Y.-H. Luo et al., “Quantum teleportation of physical qubits into logical code spaces”, Proceedings of the National Academy of Sciences 118, (2021) arXiv:2009.06242 DOI. Appears in: $[[9,1,3]]$ Shor code
A. I. Lvovsky and M. G. Raymer, “Continuous-variable optical quantum-state tomography”, Reviews of Modern Physics 81, 299 (2009) arXiv:quant-ph/0511044 DOI. Appears in: Bosonic code
D. W. Lyons, D. J. Upchurch, S. N. Walck, and C. D. Yetter, “Local unitary symmetries of hypergraph states”, Journal of Physics A: Mathematical and Theoretical 48, 095301 (2015) arXiv:1410.3904 DOI. Appears in: Cluster-state code, Qubit stabilizer code, XP stabilizer code
R. E. Lyons and W. Vanderkulk, “The Use of Triple-Modular Redundancy to Improve Computer Reliability”, IBM Journal of Research and Development 6, 200 (1962) DOI. Appears in: Repetition code
H. Ma, E. Lake, X. Chen, and M. Hermele, “Fracton topological order via coupled layers”, Physical Review B 95, (2017) arXiv:1701.00747 DOI. Appears in: X-cube model code
Y. Ma, “The asymptotic probability distribution of the relative distance of additive quantum codes”, Journal of Mathematical Analysis and Applications 340, 550 (2008) DOI. Appears in: Block quantum code
Z. Ma, X. Lu, K. Feng, and D. Feng, “On Non-binary Quantum BCH Codes”, Lecture Notes in Computer Science 675 (2006) DOI. Appears in: Galois-qudit BCH code
H. Maassen and J. B. M. Uffink, “Generalized entropic uncertainty relations”, Physical Review Letters 60, 1103 (1988) DOI. Appears in: Qubit CSS code
J. E. MacDonald, “Design Methods for Maximum Minimum-Distance Error-Correcting Codes”, IBM Journal of Research and Development 4, 43 (1960) DOI. Appears in: $q$-ary simplex code, $[2^m-1,m,2^{m-1}]$ simplex code
M. Mackaay, “Finite groups, spherical 2-categories, and 4-manifold invariants”, (1999) arXiv:math/9903003. Appears in: Two-gauge theory code
D. J. C. MacKay and R. M. Neal, “Good codes based on very sparse matrices”, Cryptography and Coding 100 (1995) DOI. Appears in: MacKay-Neal LDPC (MN-LDPC) code
D. J. C. MacKay and R. M. Neal, “Near Shannon limit performance of low density parity check codes”, Electronics Letters 33, 457 (1997) DOI. Appears in: Gallager (GL) code, Low-density parity-check (LDPC) code
D. J. C. MacKay, “Good error-correcting codes based on very sparse matrices”, IEEE Transactions on Information Theory 45, 399 (1999) DOI. Appears in: Gallager (GL) code, Low-density parity-check (LDPC) code, MacKay-Neal LDPC (MN-LDPC) code
D. J. C. MacKay and M. C. Davey, “Evaluation of Gallager Codes for Short Block Length and High Rate Applications”, Codes, Systems, and Graphical Models 113 (2001) DOI. Appears in: Combinatorial design, Difference-set cyclic (DSC) code, Gallager (GL) code, Protograph LDPC code, Quasi-cyclic LDPC (QC-LDPC) code
D. J. C. MacKay, G. Mitchison, and P. L. McFadden, “Sparse-Graph Codes for Quantum Error Correction”, IEEE Transactions on Information Theory 50, 2315 (2004) arXiv:quant-ph/0304161 DOI. Appears in: Bicycle code, Generalized bicycle (GB) code, Quantum LDPC (QLDPC) code
D. J. C. MacKay, “Fountain codes”, IEE Proceedings - Communications 152, 1062 (2005) DOI. Appears in: Fountain code
MacKay, David JC. "Encyclopedia of sparse graph codes." (2005).. Appears in: Low-density parity-check (LDPC) code
F. J. MacWilliams, N. J. A. Sloane, and J.-M. Goethals, “The MacWilliams Identities for Nonlinear Codes”, Bell System Technical Journal 51, 803 (1972) DOI. Appears in: $q$-ary code
J. Macwilliams, “A Theorem on the Distribution of Weights in a Systematic Code†”, Bell System Technical Journal 42, 79 (1963) DOI. Appears in: $q$-ary code
J. Macwilliams, “Permutation Decoding of Systematic Codes”, Bell System Technical Journal 43, 485 (1964) DOI. Appears in: Cyclic linear binary code, Cyclic linear $q$-ary code
F. J. MacWilliams and N. J. A. Sloane. The theory of error correcting codes. Elsevier, 1977.. Appears in: Alternant code, Anticode, Binary BCH code, Cyclic linear binary code, Linear binary code, Binary quadratic-residue (QR) code, $[2^m,m+1,2^{m-1}]$ First-order RM code, Binary code, Block code, Combinatorial design, Conference code, Constant-weight code, Delsarte-Goethals (DG) code, Dual linear code, $[24, 12, 8]$ Extended Golay code, $[2^r,2^r-r-1,4]$ Extended Hamming code, Gabidulin code, Chien-Choy generalized BCH (GBCH) code, Generalized concatenated code (GCC), Generalized Srivastava code, Goethals code, $[23, 12, 7]$ Golay code, Goppa code, Griesmer code, $[7,4,3]$ Hamming code, $[8,4,4]$ extended Hamming code, $[2^r-1,2^r-r-1,3]$ Hamming code, Hexacode, Julin-Golay code, Justesen code, Karlin double circulant code, Kerdock code, Levenshtein code, Lexicographic code, Maximum distance separable (MDS) code, Nadler code, Nearly perfect code, Nordstrom-Robinson (NR) code, Orthogonal array (OA), Lattice-based code, Preparata code, Bose–Chaudhuri–Hocquenghem (BCH) code, Cyclic linear $q$-ary code, $q$-ary code, $q$-ary Hamming code, Linear $q$-ary code, Quadratic-residue (QR) code, Quasi-cyclic code, Quasi-perfect code, Real-number block code, Reed-Muller (RM) code, Self-dual linear code, $[48,24,12]$ self-dual code, $[2^m-1,m,2^{m-1}]$ simplex code, Small-distance block code, Srivastava code, Tensor-product code, Ternary Golay code, Uniformly packed code, $(u|u+v)$-construction code, Vasilyev code
J. C. Magdalena de la Fuente, N. Tarantino, and J. Eisert, “Non-Pauli topological stabilizer codes from twisted quantum doubles”, Quantum 5, 398 (2021) arXiv:2001.11516 DOI. Appears in: Double-semion stabilizer code, Abelian TQD stabilizer code
A. Mahmoodi, Designs, Codes and Cryptography 14, 81 (1998) DOI. Appears in: Combinatorial design, Editing code, Perfect code
S. Majidy, “A Unification of the Coding Theory and OAQEC Perspectives on Hybrid Codes”, International Journal of Theoretical Physics 62, (2023) arXiv:1806.03702 DOI. Appears in: Hybrid qubit code, Hybrid stabilizer code, $[[4,2,2]]$ Four-qubit code
C. L. Mallows and N. J. A. Sloane, “Weight enumerators of self-orthogonal codes”, Discrete Mathematics 9, 391 (1974) DOI. Appears in: Dual linear code, $[23, 12, 7]$ Golay code, $[7,4,3]$ Hamming code, $[7,3,4]$ simplex code
S. A. Malyugin, “On the order of the automorphism group of perfect binary codes”, Diskretn. Anal. Issled. Oper., Ser. 1, 7:4 (2000), 91–100. Appears in: Perfect binary code
M. Mamindlapally and A. Winter, “Singleton Bounds for Entanglement-Assisted Classical and Quantum Error Correcting Codes”, IEEE Transactions on Information Theory 69, 5857 (2023) arXiv:2202.02184 DOI. Appears in: Entanglement-assisted (EA) hybrid QECC
S. Mamone, G. Pileio, and M. H. Levitt, “Orientational Sampling Schemes Based on Four Dimensional Polytopes”, Symmetry 2, 1423 (2010) DOI. Appears in: 120-cell code, 24-cell code, 600-cell code
H. Manabu and H. Imai, “Non stabilizer Clifford codes with qupits”, (2004) arXiv:quant-ph/0402060. Appears in: Knill code
S. Mandal and N. Surendran, “Exactly solvable Kitaev model in three dimensions”, Physical Review B 79, (2009) arXiv:0801.0229 DOI. Appears in: 3D fermionic surface code
P. Mandayam and H. K. Ng, “Towards a unified framework for approximate quantum error correction”, Physical Review A 86, (2012) arXiv:1202.5139 DOI. Appears in: Approximate quantum error-correcting code (AQECC), Subsystem QECC
A. G. Manes and J. Claes, “Distance-preserving stabilizer measurements in hypergraph product codes”, Quantum 9, 1618 (2025) arXiv:2308.15520 DOI. Appears in: Hypergraph product (HGP) code
H. Mani, T. Gehring, P. Grabenweger, B. Ömer, C. Pacher, and U. L. Andersen, “Multiedge-type low-density parity-check codes for continuous-variable quantum key distribution”, Physical Review A 103, (2021) DOI. Appears in: Multi-edge LDPC code
Yu. I. Manin, “Some remarks on Koszul algebras and quantum groups”, Annales de l’institut Fourier 37, 191 (1987) DOI. Appears in: Modular-qudit code
L. Manivel, “Configurations of lines and models of Lie algebras”, (2005) arXiv:math/0507118. Appears in: $E_6$ root lattice, Hessian polyhedron code
X. Mao, Q. Xu, and L. Jiang, “Optimized four-qubit quantum error correcting code for amplitude damping channel”, (2024) arXiv:2411.12952. Appears in: Numerically optimized four-qubit AD code
M. Marcolli, “Holographic Codes on Bruhat--Tits buildings and Drinfeld Symmetric Spaces”, (2018) arXiv:1801.09623. Appears in: Perfect-tensor code, Galois-qudit GRS code, Galois-qudit RS code, Holographic tensor-network code
G. A. Margulis, “Explicit constructions of graphs without short cycles and low density codes”, Combinatorica 2, 71 (1982) DOI. Appears in: Algebraic LDPC code, Low-density parity-check (LDPC) code, Margulis LDPC code
A. Mari and J. Eisert, “Positive Wigner Functions Render Classical Simulation of Quantum Computation Efficient”, Physical Review Letters 109, (2012) arXiv:1208.3660 DOI. Appears in: Bosonic code, Stabilizer code
A. Marinoni, P. Savazzi, and R. D. Wesel, “Protograph-based q-ary LDPC codes for higher-order modulation”, 2010 6th International Symposium on Turbo Codes & Iterative Information Processing (2010) DOI. Appears in: $q$-ary protograph LDPC code
Markus Grassl, private communication, 2024. Appears in: Galois-qudit stabilizer code, Modular-qudit stabilizer code
J. F. Marques et al., “Logical-qubit operations in an error-detecting surface code”, Nature Physics 18, 80 (2021) arXiv:2102.13071 DOI. Appears in: Rotated surface code, $[[4,2,2]]$ Four-qubit code
A. Marquet et al., “Autoparametric Resonance Extending the Bit-Flip Time of a Cat Qubit up to 0.3 s”, Physical Review X 14, (2024) arXiv:2307.06761 DOI. Appears in: Two-component cat code
T. Marshall, “Coding of Real-Number Sequences for Error Correction: A Digital Signal Processing Problem”, IEEE Journal on Selected Areas in Communications 2, 381 (1984) DOI. Appears in: Analog RS code, Real-number block code
W. J. Martin, Designs, Codes and Cryptography 16, 271 (1999) DOI. Appears in: Combinatorial design, Mixed code
W. J. Martin and D. R. Stinson, “Association Schemes for Ordered Orthogonal Arrays and (T, M, S)-Nets”, Canadian Journal of Mathematics 51, 326 (1999) DOI. Appears in: $t$-design
U. Martínez-Peñas, “Skew and linearized Reed-Solomon codes and maximum sum rank distance codes over any division ring”, (2018) arXiv:1710.03109. Appears in: Binary code, Gabidulin code, Linearized RS code, Maximum-sum-rank distance (MSRD) code, Rank-metric code, Reed-Solomon (RS) code, Sum-rank-metric code
U. Martinez-Penas and F. R. Kschischang, “Reliable and Secure Multishot Network Coding Using Linearized Reed-Solomon Codes”, IEEE Transactions on Information Theory 65, 4785 (2019) arXiv:1805.03789 DOI. Appears in: Linearized RS code
U. Martínez-Peñas and F. R. Kschischang, “Universal and Dynamic Locally Repairable Codes with Maximal Recoverability via Sum-Rank Codes”, (2019) arXiv:1809.11158. Appears in: Distributed-storage code, Linearized RS code, Locally recoverable code (LRC), Sum-rank-metric code
I. Marvian and D. A. Lidar, “Quantum Error Suppression with Commuting Hamiltonians: Two Local is Too Local”, Physical Review Letters 113, (2014) arXiv:1410.5487 DOI. Appears in: Bravyi-Bacon-Shor (BBS) code, Commuting-projector Hamiltonian code, Subsystem qubit stabilizer code
M. Marvian and D. A. Lidar, “Error Suppression for Hamiltonian-Based Quantum Computation Using Subsystem Codes”, Physical Review Letters 118, (2017) arXiv:1606.03795 DOI. Appears in: Bravyi-Bacon-Shor (BBS) code, Commuting-projector Hamiltonian code, Subsystem qubit stabilizer code
M. Marvian and S. Lloyd, “Robust universal Hamiltonian quantum computing using two-body interactions”, (2019) arXiv:1911.01354. Appears in: $[[6r,2r,2]]$ Ganti-Onunkwo-Young code, Subsystem CSS code, Trapezoid subsystem code
A. Maschietti, Designs, Codes and Cryptography 14, 89 (1998) DOI. Appears in: Difference-set cyclic (DSC) code, Hyperoval code
G. Masera, G. Piccinini, M. R. Roch, and M. Zamboni, “VLSI architectures for turbo codes”, IEEE Transactions on Very Large Scale Integration (VLSI) Systems 7, 369 (1999) DOI. Appears in: Turbo code
N. Maskara, A. Kubica, and T. Jochym-O’Connor, “Advantages of versatile neural-network decoding for topological codes”, Physical Review A 99, (2019) arXiv:1802.08680 DOI. Appears in: Honeycomb (6.6.6) color code
J. L. Massey, “Deep-space communications and coding: A marriage made in heaven”, Lecture Notes in Control and Information Sciences 1 DOI. Appears in: Reed-Muller (RM) code
J. L. Massey, “Linear codes with complementary duals”, Discrete Mathematics 106–107, 337 (1992) DOI. Appears in: Linear code with complementary dual (LCD)
J. Massey, “Shift-register synthesis and BCH decoding”, IEEE Transactions on Information Theory 15, 122 (1969) DOI. Appears in: Binary BCH code, Generalized RS (GRS) code, Bose–Chaudhuri–Hocquenghem (BCH) code, Reed-Solomon (RS) code
Massey, J. L. "Convolutional codes over rings." Fourth Joint Swedish-Soviet International Workshop on Information Theory. 1989.. Appears in: Phase-shift keying (PSK) code
Massey, J. L. "Ring convolutional codes for phase modulation." presented at the IEEE Int. Symp. on Information Theory, San Diego, CA, Jan. 14-19. 1990.. Appears in: Phase-shift keying (PSK) code
J. L. Massey, Threshold Decoding. Cambridge, MA: M.I.T. Press, 1963.. Appears in: Wozencraft ensemble code
E. S. Matekole, E. Ye, R. Iyer, and S. Y.-C. Chen, “Decoding surface codes with deep reinforcement learning and probabilistic policy reuse”, (2022) arXiv:2212.11890. Appears in: Kitaev surface code
V. G. Matsos, C. H. Valahu, T. Navickas, A. D. Rao, M. J. Millican, X. C. Kolesnikow, M. J. Biercuk, and T. R. Tan, “Robust and Deterministic Preparation of Bosonic Logical States in a Trapped Ion”, Physical Review Letters 133, (2024) arXiv:2310.15546 DOI. Appears in: Binomial code, Square-lattice GKP code
V. G. Matsos, C. H. Valahu, M. J. Millican, T. Navickas, X. C. Kolesnikow, M. J. Biercuk, and T. R. Tan, “Universal Quantum Gate Set for Gottesman-Kitaev-Preskill Logical Qubits”, (2024) arXiv:2409.05455. Appears in: Square-lattice GKP code
R. Matsumoto and T. Uyematsu, “Constructing quantum error-correcting codes for p^m-state systems from classical error-correcting codes”, (2000) arXiv:quant-ph/9911011. Appears in: Galois-qudit CSS code
R. Matsumoto, “Improvement of Ashikhmin-Litsyn-Tsfasman bound for quantum codes”, IEEE Transactions on Information Theory 48, 2122 (2002) arXiv:quant-ph/0107129 DOI. Appears in: Quantum Goppa code, Quantum AG code
R. Matsumoto, “Conversion of a general quantum stabilizer code to an entanglement distillation protocol”, Journal of Physics A: Mathematical and General 36, 8113 (2003) arXiv:quant-ph/0209091 DOI. Appears in: Qubit stabilizer code
R. Matsumoto, “Two Gilbert–Varshamov-type existential bounds for asymmetric quantum error-correcting codes”, Quantum Information Processing 16, (2017) arXiv:1705.04087 DOI. Appears in: Asymmetric quantum code
T. Matsuura, H. Yamasaki, and M. Koashi, “Equivalence of approximate Gottesman-Kitaev-Preskill codes”, Physical Review A 102, (2020) arXiv:1910.08301 DOI. Appears in: Square-lattice GKP code
T. Matsuura, N. C. Menicucci, and H. Yamasaki, “Continuous-Variable Fault-Tolerant Quantum Computation under General Noise”, (2024) arXiv:2410.12365. Appears in: GKP CV-cluster-state code
W. Matthews and S. Wehner, “Finite Blocklength Converse Bounds for Quantum Channels”, IEEE Transactions on Information Theory 60, 7317 (2014) arXiv:1210.4722 DOI. Appears in: Quantum error-correcting code (QECC)
D. Maurice, J.-P. Tillich, and I. Andriyanova, “A family of quantum codes with performances close to the hashing bound under iterative decoding”, 2013 IEEE International Symposium on Information Theory 907 (2013) DOI. Appears in: Qubit CSS code
Maurice, Denise. Codes correcteurs quantiques pouvant se décoder itérativement. Diss. Université Pierre et Marie Curie-Paris VI, 2014.. Appears in: Chamon model code, Repetition code, XYZ product code, XZZX surface code
C. Mauron, T. Farrelly, and T. M. Stace, “Optimization of Tensor Network Codes with Reinforcement Learning”, (2023) arXiv:2305.11470. Appears in: Asymmetric quantum code, Tensor-network code, Neural network quantum code
A. May, G. Penington, and J. Sorce, “Holographic scattering requires a connected entanglement wedge”, Journal of High Energy Physics 2020, (2020) arXiv:1912.05649 DOI. Appears in: Holographic tensor-network code
K. Mayer et al., “Benchmarking logical three-qubit quantum Fourier transform encoded in the Steane code on a trapped-ion quantum computer”, (2024) arXiv:2404.08616. Appears in: $[[7,1,3]]$ Steane code
A. Mazumdar, A. Barg, and G. Zémor, “Constructions of Rank Modulation Codes”, (2011) arXiv:1110.2557. Appears in: Linear $q$-ary code, Rank-modulation code
A. Mazumdar, “Storage Capacity of Repairable Networks”, IEEE Transactions on Information Theory 61, 5810 (2015) arXiv:1408.4862 DOI. Appears in: Locally recoverable code (LRC)
P. Mazurek, A. Grudka, M. Horodecki, P. Horodecki, J. Łodyga, Ł. Pankowski, and A. Przysiężna, “Long-distance quantum communication over noisy networks without long-time quantum memory”, Physical Review A 90, (2014) arXiv:1202.1016 DOI. Appears in: Kitaev surface code
S. McArdle, A. Mayorov, X. Shan, S. Benjamin, and X. Yuan, “Digital quantum simulation of molecular vibrations”, Chemical Science 10, 5725 (2019) arXiv:1811.04069 DOI. Appears in: One-hot quantum code
T. McCourt, I. R. Fiete, and I. L. Chuang, “Noisy dynamical systems evolve error correcting codes and modularity”, (2023) arXiv:2303.14448. Appears in: Finite-dimensional error-correcting code (ECC)
R. J. McEliece, “On periodic sequences from GF(q)”, Journal of Combinatorial Theory, Series A 10, 80 (1971) DOI. Appears in: $[[2^r-1,1,3]]$ simplex code, Divisible code, Quantum divisible code, Reed-Muller (RM) code
R. J. McEliece, “Weight congruences for p-ary cyclic codes”, Discrete Mathematics 3, 177 (1972) DOI. Appears in: $[[2^r-1,1,3]]$ simplex code, Divisible code, Quantum divisible code, Reed-Muller (RM) code
R. J. McEliece and E. R. Rodemich, “The constantinrao construction for binary asymmetric error-correcting codes”, Information and Control 44, 187 (1980) DOI. Appears in: Constantin-Rao (CR) code
R. J. McEliece, D. J. C. MacKay, and Jung-Fu Cheng, “Turbo decoding as an instance of Pearl’s “belief propagation” algorithm”, IEEE Journal on Selected Areas in Communications 16, 140 (1998) DOI. Appears in: Turbo code
R. McEliece, E. Rodemich, H. Rumsey, and L. Welch, “New upper bounds on the rate of a code via the Delsarte-MacWilliams inequalities”, IEEE Transactions on Information Theory 23, 157 (1977) DOI. Appears in: Binary code
R. McEliece, The Theory of Information and Coding (Cambridge University Press, 2002) DOI. Appears in: Binary BCH code, Goppa code, Bose–Chaudhuri–Hocquenghem (BCH) code, Tanner code
R. J. McEliece, A public-key cryptosystem based on algebraic coding theory, Technical report, Jet Propulsion Lab. DSN Progress Report (1978).. Appears in: Generalized RS (GRS) code, Goppa code
T. McElvanney and M. Backens, “Complete Flow-Preserving Rewrite Rules for MBQC Patterns with Pauli Measurements”, Electronic Proceedings in Theoretical Computer Science 394, 66 (2023) arXiv:2205.02009 DOI. Appears in: Qubit stabilizer code
J. D. McEwen and Y. Wiaux, “A Novel Sampling Theorem on the Sphere”, IEEE Transactions on Signal Processing 59, 5876 (2011) arXiv:1110.6298 DOI. Appears in: Spherical design
M. McEwen, D. Bacon, and C. Gidney, “Relaxing Hardware Requirements for Surface Code Circuits using Time-dynamics”, Quantum 7, 1172 (2023) arXiv:2302.02192 DOI. Appears in: Kitaev surface code
J. McGreevy, “Generalized Symmetries in Condensed Matter”, Annual Review of Condensed Matter Physics 14, 57 (2023) arXiv:2204.03045 DOI. Appears in: Symmetry-protected topological (SPT) code
G. McGuire, “Quasi-Symmetric Designs and Codes Meeting the Grey–Rankin Bound”, Journal of Combinatorial Theory, Series A 78, 280 (1997) DOI. Appears in: Combinatorial design
C. McLauchlan, G. P. Gehér, and A. E. Moylett, “Accommodating Fabrication Defects on Floquet Codes with Minimal Hardware Requirements”, Quantum 8, 1562 (2024) arXiv:2405.15854 DOI. Appears in: Hastings-Haah Floquet code
C. McLauchlan and B. Béri, “A new twist on the Majorana surface code: Bosonic and fermionic defects for fault-tolerant quantum computation”, Quantum 8, 1400 (2024) arXiv:2211.11777 DOI. Appears in: Majorana color code, Majorana surface code
A. McLoughlin, “The complexity of computing the covering radius of a code”, IEEE Transactions on Information Theory 30, 800 (1984) DOI. Appears in: Covering code
I. McLoughlin and T. Hurley, “A Group Ring Construction of the Extended Binary Golay Code”, IEEE Transactions on Information Theory 54, 4381 (2008) DOI. Appears in: $[24, 12, 8]$ Extended Golay code, Group-algebra code
I. McLoughlin, “A group ring construction of the [48,24,12] type II linear block code”, Designs, Codes and Cryptography 63, 29 (2011) DOI. Appears in: Group-algebra code, $[48,24,12]$ self-dual code
J. Meggitt, “Error correcting codes and their implementation for data transmission systems”, IEEE Transactions on Information Theory 7, 234 (1961) DOI. Appears in: Cyclic linear binary code, Cyclic linear $q$-ary code, Zetterberg code
A. M. Meier, B. Eastin, and E. Knill, “Magic-state distillation with the four-qubit code”, (2012) arXiv:1204.4221. Appears in: Concatenated qubit code, $[[4,2,2]]$ Four-qubit code, $[[6,2,2]]$ $C_6$ code
K. Meinerz, C.-Y. Park, and S. Trebst, “Scalable Neural Decoder for Topological Surface Codes”, Physical Review Letters 128, (2022) arXiv:2101.07285 DOI. Appears in: Kitaev surface code
O. Meir, “Combinatorial construction of locally testable codes”, Proceedings of the fortieth annual ACM symposium on Theory of computing 285 (2008) DOI. Appears in: Meir code
N. Meister, C. A. Pattison, and J. Preskill, “Efficient soft-output decoders for the surface code”, (2024) arXiv:2405.07433. Appears in: Hierarchical code
C. M. Melas, “A Cyclic Code for Double Error Correction [Letter to the Editor]”, IBM Journal of Research and Development 4, 364 (1960) DOI. Appears in: Melas code
F. A. Mele, L. Lami, and V. Giovannetti, “Maximum tolerable excess noise in continuous-variable quantum key distribution and improved lower bound on two-way capacities”, Nature Photonics (2025) arXiv:2303.12867 DOI. Appears in: Bosonic code
T. W. Melnyk, O. Knop, and W. R. Smith, “Extremal arrangements of points and unit charges on a sphere: equilibrium configurations revisited”, Canadian Journal of Chemistry 55, 1745 (1977) DOI. Appears in: Annealing-based spherical code
N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, “Universal Quantum Computation with Continuous-Variable Cluster States”, Physical Review Letters 97, (2006) arXiv:quant-ph/0605198 DOI. Appears in: Analog-cluster-state code, GKP CV-cluster-state code
N. C. Menicucci, S. T. Flammia, and O. Pfister, “One-Way Quantum Computing in the Optical Frequency Comb”, Physical Review Letters 101, (2008) arXiv:0804.4468 DOI. Appears in: Analog-cluster-state code
N. C. Menicucci, S. T. Flammia, and P. van Loock, “Graphical calculus for Gaussian pure states”, Physical Review A 83, (2011) arXiv:1007.0725 DOI. Appears in: Analog stabilizer code, Analog-cluster-state code, Bosonic code
N. C. Menicucci, “Temporal-mode continuous-variable cluster states using linear optics”, Physical Review A 83, (2011) arXiv:1007.3434 DOI. Appears in: Analog-cluster-state code
N. C. Menicucci, “Fault-Tolerant Measurement-Based Quantum Computing with Continuous-Variable Cluster States”, Physical Review Letters 112, (2014) arXiv:1310.7596 DOI. Appears in: GKP CV-cluster-state code, Square-lattice GKP code, Gottesman-Kitaev-Preskill (GKP) code
L. J. Mensen, B. Q. Baragiola, and N. C. Menicucci, “Phase-space methods for representing, manipulating, and correcting Gottesman-Kitaev-Preskill qubits”, Physical Review A 104, (2021) arXiv:2012.12488 DOI. Appears in: Square-lattice GKP code
N. D. Mermin, “Quantum mysteries revisited”, American Journal of Physics 58, 731 (1990) DOI. Appears in: Quantum repetition code
F. Merz and J. T. Chalker, “Two-dimensional random-bond Ising model, free fermions, and the network model”, Physical Review B 65, (2002) arXiv:cond-mat/0106023 DOI. Appears in: Toric code
A. Mesaros and Y. Ran, “Classification of symmetry enriched topological phases with exactly solvable models”, Physical Review B 87, (2013) arXiv:1212.0835 DOI. Appears in: Dijkgraaf-Witten gauge theory code
S. Mesnager, Bent Functions (Springer International Publishing, 2016) DOI. Appears in: Two-weight code
A. Messinger, M. Fellner, and W. Lechner, “Constant Depth Code Deformations in the Parity Architecture”, 2023 IEEE International Conference on Quantum Computing and Engineering (QCE) (2023) arXiv:2303.08602 DOI. Appears in: Lechner-Hauke-Zoller (LHZ) code
A. Messinger, V. Torggler, B. Klaver, M. Fellner, and W. Lechner, “Fault-tolerant quantum computing with the parity code and noise-biased qubits”, (2024) arXiv:2404.11332. Appears in: Concatenated cat code, Lechner-Hauke-Zoller (LHZ) code
J. Meza, Q. Wu, S. Kumar, and O. Mutlu, “Revisiting Memory Errors in Large-Scale Production Data Centers: Analysis and Modeling of New Trends from the Field”, 2015 45th Annual IEEE/IFIP International Conference on Dependable Systems and Networks (2015) DOI. Appears in: Error-correcting code (ECC)
M. Mézard and A. Montanari, “Information, Physics, and Computation”, (2009) DOI. Appears in: Convolutional code, Hamiltonian-based code, Low-density parity-check (LDPC) code
X. Mi et al., “Noise-resilient edge modes on a chain of superconducting qubits”, Science 378, 785 (2022) arXiv:2204.11372 DOI. Appears in: Kitaev chain code
K. C. Miao et al., “Overcoming leakage in quantum error correction”, Nature Physics 19, 1780 (2023) arXiv:2211.04728 DOI. Appears in: Quantum repetition code, XZZX surface code
S. Miao, A. Schnerring, H. Li, and L. Schmalen, “Neural Belief Propagation Decoding of Quantum LDPC Codes Using Overcomplete Check Matrices”, (2023) arXiv:2212.10245. Appears in: Quantum LDPC (QLDPC) code
S. Miao, J. Mandelbaum, H. Jäkel, and L. Schmalen, “A Joint Code and Belief Propagation Decoder Design for Quantum LDPC Codes”, (2024) arXiv:2401.06874. Appears in: Abelian LP code, Finite-geometry LDPC (FG-LDPC) code, Quasi-cyclic LDPC (QC-LDPC) code
D. Micciancio, “The Shortest Vector in a Lattice is Hard to Approximate to within Some Constant”, SIAM Journal on Computing 30, 2008 (2001) DOI. Appears in: Lattice-based code
M. H. Michael, M. Silveri, R. T. Brierley, V. V. Albert, J. Salmilehto, L. Jiang, and S. M. Girvin, “New Class of Quantum Error-Correcting Codes for a Bosonic Mode”, Physical Review X 6, (2016) arXiv:1602.00008 DOI. Appears in: Binomial code, Cat code, Numerically optimized bosonic code, Two-mode binomial code
Michael Helmling, Stefan Scholl, Florian Gensheimer, Tobias Dietz, Kira Kraft, Stefan Ruzika, and Norbert Wehn. Database of Channel Codes and ML Simulation Results. URL, 2022.. Appears in: Binary BCH code, $[2^r-1,2^r-r-1,3]$ Hamming code, Low-density parity-check (LDPC) code, Polar code, Bose–Chaudhuri–Hocquenghem (BCH) code, Reed-Solomon (RS) code
Michael Helmling, Stefan Scholl, Florian Gensheimer, Tobias Dietz, Kira Kraft, Stefan Ruzika, and Norbert Wehn. Database of Channel Codes and ML Simulation Results. www.uni-kl.de/channel-codes, 2022.. Appears in: Turbo code
Michael Lahanas. "Ancient Greek Communication Methods". https://web.archive.org/web/20141102224501/https://www.mlahanas.de/Greeks/Communication.htm. Archived from the original on 2014-11-02.. Appears in: Pulse-position modulation (PPM) code
Michael A. Perlin. qLDPC. https://github.com/Infleqtion/qLDPC, 2023.. Appears in: Quantum LDPC (QLDPC) code
R. Michael Tanner. Convolutional codes from quasi-cyclic codes: A link between the theories of block and convolutional codes. University of California, Santa Cruz, Computer Research Laboratory, 1987.. Appears in: Convolutional code, Quasi-cyclic code
R. Michael Tanner, “Error-correcting coding system,” U.S. Patent 4295218, 1981.. Appears in: Convolutional code, Quasi-cyclic code
S. Michalakis and J. P. Zwolak, “Stability of Frustration-Free Hamiltonians”, Communications in Mathematical Physics 322, 277 (2013) arXiv:1109.1588 DOI. Appears in: Commuting-projector Hamiltonian code, Frustration-free Hamiltonian code, Hamiltonian-based code, Quantum LDPC (QLDPC) code, Topological code
K. P. Michnicki, “3D Topological Quantum Memory with a Power-Law Energy Barrier”, Physical Review Letters 113, (2014) arXiv:1406.4227 DOI. Appears in: 3D surface code, Self-correcting quantum code
J. F. S. Miguel, D. J. Williamson, and B. J. Brown, “A cellular automaton decoder for a noise-bias tailored color code”, Quantum 7, 940 (2023) arXiv:2203.16534 DOI. Appears in: Asymmetric quantum code, Fracton stabilizer code, XYZ color code
A. Milekhin, “Quantum error correction and large $N$”, SciPost Physics 11, (2021) arXiv:2008.12869 DOI. Appears in: Matrix-model code
O. Milenkovic and S. Laendner, “Analysis of the cycle-structure of LDPC codes based on Latin squares”, 2004 IEEE International Conference on Communications (IEEE Cat. No.04CH37577) 777 (2004) DOI. Appears in: Algebraic LDPC code
M. Milicevic, C. Feng, L. M. Zhang, and P. G. Gulak, “Quasi-cyclic multi-edge LDPC codes for long-distance quantum cryptography”, npj Quantum Information 4, (2018) arXiv:1702.07740 DOI. Appears in: Multi-edge LDPC code
A. Miller, Z. Zimborás, S. Knecht, S. Maniscalco, and G. García-Pérez, “Bonsai Algorithm: Grow Your Own Fermion-to-Qubit Mappings”, PRX Quantum 4, (2023) arXiv:2212.09731 DOI. Appears in: Fermion-into-qubit code
D. Miller, D. Loss, I. Tavernelli, H. Kampermann, D. Bruß, and N. Wyderka, “Shor–Laflamme distributions of graph states and noise robustness of entanglement”, Journal of Physics A: Mathematical and Theoretical 56, 335303 (2023) arXiv:2207.07665 DOI. Appears in: Cluster-state code
D. Miller et al., “Experimental measurement and a physical interpretation of quantum shadow enumerators”, (2024) arXiv:2408.16914. Appears in: Good QLDPC code, Qubit code, $[[7,1,3]]$ Steane code
M. Miller and D. Miller, “GraphStateVis: Interactive Visual Analysis of Qubit Graph States and their Stabilizer Groups”, 2021 IEEE International Conference on Quantum Computing and Engineering (QCE) 6, 378 (2021) arXiv:2105.12752 DOI. Appears in: Cluster-state code
S. Milz and K. Modi, “Quantum Stochastic Processes and Quantum non-Markovian Phenomena”, PRX Quantum 2, (2021) arXiv:2012.01894 DOI. Appears in: Qubit code
Min-Hsiu Hsieh and M. M. Wilde, “Trading classical communication, quantum communication, and entanglement in quantum Shannon theory”, IEEE Transactions on Information Theory 56, 4705 (2010) arXiv:0901.3038 DOI. Appears in: Entanglement-assisted (EA) hybrid QECC
Z. K. Minev, K. Najafi, S. Majumder, J. Wang, A. Stern, E.-A. Kim, C.-M. Jian, and G. Zhu, “Realizing string-net condensation: Fibonacci anyon braiding for universal gates and sampling chromatic polynomials”, (2024) arXiv:2406.12820. Appears in: Fibonacci string-net code, String-net code
F. Minganti, A. Biella, N. Bartolo, and C. Ciuti, “Spectral theory of Liouvillians for dissipative phase transitions”, Physical Review A 98, (2018) arXiv:1804.11293 DOI. Appears in: Quantum repetition code, Two-component cat code
M. Mirrahimi, Z. Leghtas, V. V. Albert, S. Touzard, R. J. Schoelkopf, L. Jiang, and M. H. Devoret, “Dynamically protected cat-qubits: a new paradigm for universal quantum computation”, New Journal of Physics 16, 045014 (2014) arXiv:1312.2017 DOI. Appears in: Cat code, Two-component cat code
P. A. Mishchenko and K. Xagawa, “Secure multiparty quantum computation protocol for quantum circuits: The exploitation of triply even quantum error-correcting codes”, Physical Review A 110, (2024) arXiv:2206.04871 DOI. Appears in: Quantum divisible code
R. Misoczki, J.-P. Tillich, N. Sendrier, and P. S. L. M. Barreto, “MDPC-McEliece: New McEliece variants from Moderate Density Parity-Check codes”, 2013 IEEE International Symposium on Information Theory 2069 (2013) DOI. Appears in: Low-rank parity-check (LRPC) code
N. Mitani, On the transmission of numbers in a sequential computer, delivered at the National Convention of the Inst. of Elect. Engineers of Japan, November 1951.. Appears in: Reed-Muller (RM) code
D. G. M. Mitchell, R. Smarandache, and D. J. Costello, “Quasi-cyclic LDPC codes based on pre-lifted protographs”, 2011 IEEE Information Theory Workshop (2011) DOI. Appears in: Multi-edge LDPC code, Protograph LDPC code
H. H. Mitchell, “Determination of All Primitive Collineation Groups in More than Four Variables which Contain Homologies”, American Journal of Mathematics 36, 1 (1914) DOI. Appears in: Coxeter-Todd $K_{12}$ lattice
T. Mittelholzer, “Efficient encoding and minimum distance bounds of Reed-Solomon-type array codes”, Proceedings IEEE International Symposium on Information Theory, DOI. Appears in: Array-based LDPC (AB-LDPC) code
T. Mittelholzer and J. Lahtonen, “Group codes generated by finite reflection groups”, IEEE Transactions on Information Theory 42, 519 (1996) DOI. Appears in: Slepian group-orbit code
Y. Miwa, J. Yoshikawa, P. van Loock, and A. Furusawa, “Demonstration of a universal one-way quantum quadratic phase gate”, Physical Review A 80, (2009) arXiv:0906.3141 DOI. Appears in: Analog-cluster-state code
A. Miyake, “Quantum computational capability of a 2D valence bond solid phase”, Annals of Physics 326, 1656 (2011) arXiv:1009.3491 DOI. Appears in: Cluster-state code, Symmetry-protected topological (SPT) code, Lattice stabilizer code
H. K. Miyamoto, H. N. Sa Earp, and S. I. R. Costa, “Constructive spherical codes in 2${}^{\text{k}}$ dimensions”, 2019 IEEE International Symposium on Information Theory (ISIT) 1612 (2019) DOI. Appears in: Torus-layer spherical code (TLSC)
A. Mizel, D. A. Lidar, and M. Mitchell, “Simple Proof of Equivalence between Adiabatic Quantum Computation and the Circuit Model”, Physical Review Letters 99, (2007) arXiv:quant-ph/0609067 DOI. Appears in: Circuit-to-Hamiltonian approximate code, Brown-Fawzi random Clifford-circuit code
C. Mochon, “Anyon computers with smaller groups”, Physical Review A 69, (2004) arXiv:quant-ph/0306063 DOI. Appears in: Quantum-double code, Dihedral $G=D_m$ quantum-double code
R. Moessner and J. E. Moore, Topological Phases of Matter (Cambridge University Press, 2021) DOI. Appears in: Topological code
M. Mohamed, S. Rizkalla, H. Zoerlein and M. Bossert, "Deterministic Compressed Sensing with Power Decoding for Complex Reed-Solomon Codes," SCC 2015; 10th International ITG Conference on Systems, Communications and Coding, Hamburg, Germany, 2015, pp. 1-6.. Appears in: Analog RS code
M. Mohammadpour and S. Waldron, “Complex spherical designs from group orbits”, (2024) arXiv:2308.02499. Appears in: Slepian group-orbit code, Spherical design
M. Mollard, “Une nouvelle famille de 3-codes parfaits sur GF(q)”, Discrete Mathematics 49, 209 (1984) DOI. Appears in: Perfect code
M. Mollard, “A Generalized Parity Function and Its Use in the Construction of Perfect Codes”, SIAM Journal on Algebraic Discrete Methods 7, 113 (1986) DOI. Appears in: Perfect code
K. Mølmer, “Optical coherence: A convenient fiction”, Physical Review A 55, 3195 (1997) DOI. Appears in: Bosonic code
A. Molnar, A. R. de Alarcón, J. Garre-Rubio, N. Schuch, J. I. Cirac, and D. Pérez-García, “Matrix product operator algebras I: representations of weak Hopf algebras and projected entangled pair states”, (2022) arXiv:2204.05940. Appears in: Multi-fusion string-net code, Hopf-algebra quantum-double code
A. J. Moncy and P. Kiran Sarvepalli, “Performance of Nonbinary Cubic Codes”, 2018 International Symposium on Information Theory and Its Applications (ISITA) (2018) DOI. Appears in: Qudit cubic code
M. Mondelli, S. H. Hassani, and R. L. Urbanke, “From Polar to Reed-Muller Codes: A Technique to Improve the Finite-Length Performance”, IEEE Transactions on Communications 62, 3084 (2014) DOI. Appears in: Polar code, Reed-Muller (RM) code
M. Mondelli, S. H. Hassani, and R. L. Urbanke, “Unified Scaling of Polar Codes: Error Exponent, Scaling Exponent, Moderate Deviations, and Error Floors”, IEEE Transactions on Information Theory 62, 6698 (2016) DOI. Appears in: Polar code
P. S. Montague, “A new construction of lattices from codes over GF(3)”, Discrete Mathematics 135, 193 (1994) DOI. Appears in: Niemeier lattice, Self-dual linear code
A. Montanari and R. Urbanke, “Course 2 Modern coding theory: The statistical mechanics and computer science point of view”, Complex Systems 67 (2007) DOI. Appears in: Low-density parity-check (LDPC) code
H. L. Montgomery, “Minimal theta functions”, Glasgow Mathematical Journal 30, 75 (1988) DOI. Appears in: $A_2$ triangular lattice, Universally optimal sphere packing
Mooers, Calvin N. "Application of random codes to the gathering of statistical information." PhD diss., Massachusetts Institute of Technology, 1948.. Appears in: Superimposed code
G. Moore and N. Seiberg, “Classical and quantum conformal field theory”, Communications in Mathematical Physics 123, 177 (1989) DOI. Appears in: Topological code
J. E. Moore and D.-H. Lee, “Geometric effects onT-breaking inp+ipandd+idsuperconducting arrays”, Physical Review B 69, (2004) arXiv:cond-mat/0309717 DOI. Appears in: Plaquette Ising code
A. J. Moorthy and L. G. Gunderman, “Local-dimension-invariant Calderbank-Shor-Steane Codes with an Improved Distance Promise”, (2021) arXiv:2110.11510. Appears in: Qubit stabilizer code, $[[2^r-1, 2^r-2r-1, 3]]_p$ quantum Hamming code, Modular-qudit stabilizer code
T. Morimae and K. Fujii, “Blind topological measurement-based quantum computation”, Nature Communications 3, (2012) arXiv:1110.5460 DOI. Appears in: Raussendorf-Bravyi-Harrington (RBH) cluster-state code
L. Moro, M. G. A. Paris, M. Restelli, and E. Prati, “Quantum compiling by deep reinforcement learning”, Communications Physics 4, (2021) arXiv:2105.15048 DOI. Appears in: Qubit code
S. A. Moses et al., “A Race-Track Trapped-Ion Quantum Processor”, Physical Review X 13, (2023) arXiv:2305.03828 DOI. Appears in: $[[12,2,4]]$ carbon code, Quantum repetition code
J. Mosheiff, N. Resch, N. Ron-Zewi, S. Silas, and M. Wootters, “Low-Density Parity-Check Codes Achieve List-Decoding Capacity”, SIAM Journal on Computing FOCS20 (2021) arXiv:1909.06430 DOI. Appears in: Low-density parity-check (LDPC) code
M. Moshinsky and C. Quesne, “Linear Canonical Transformations and Their Unitary Representations”, Journal of Mathematical Physics 12, 1772 (1971) DOI. Appears in: Bosonic code
M. Mosonyi and T. Ogawa, “Strong Converse Exponent for Classical-Quantum Channel Coding”, Communications in Mathematical Physics 355, 373 (2017) arXiv:1409.3562 DOI. Appears in: Classical-quantum (c-q) code
O. Å. Mostad, E. Rosnes, and H.-Y. Lin, “Generalizing Quantum Tanner Codes”, (2024) arXiv:2405.07980. Appears in: Generalized quantum Tanner code, Quantum Tanner code
M. Möttönen, J. J. Vartiainen, V. Bergholm, and M. M. Salomaa, “Quantum Circuits for General Multiqubit Gates”, Physical Review Letters 93, (2004) arXiv:quant-ph/0404089 DOI. Appears in: Qubit code
P.-A. Mouny, M. Benhouria, V. Yon, P. Dufour, L. Huang, Y. Beilliard, S. Rochette, D. Drouin, and P. Ronagh, “Towards a Cryogenic CMOS-Memristor Neural Decoder for Quantum Error Correction”, 2024 IEEE International Conference on Quantum Computing and Engineering (QCE) 1258 (2024) arXiv:2501.14525 DOI. Appears in: Kitaev surface code
J. E. Moussa, “Transversal Clifford gates on folded surface codes”, Physical Review A 94, (2016) arXiv:1603.02286 DOI. Appears in: Qubit CSS code, Kitaev surface code
O. Moussa, J. Baugh, C. A. Ryan, and R. Laflamme, “Demonstration of Sufficient Control for Two Rounds of Quantum Error Correction in a Solid State Ensemble Quantum Information Processor”, Physical Review Letters 107, (2011) arXiv:1108.4842 DOI. Appears in: Quantum repetition code
R. Movassagh and Y. Ouyang, “Constructing quantum codes from any classical code and their embedding in ground space of local Hamiltonians”, Quantum 8, 1541 (2024) arXiv:2012.01453 DOI. Appears in: Codeword stabilized (CWS) code, Frustration-free Hamiltonian code, Hamiltonian-based code, Justesen code, Movassagh-Ouyang Hamiltonian code, Spin code
M. Mudassar, R. W. Chien, and D. Gottesman, “Encoding Majorana codes”, (2024) arXiv:2402.07829. Appears in: Majorana stabilizer code
Mujtaba Hamid and Andy Miller, Gold Code Generators in Virtex Devices, (2000). Appears in: Gold code
D. E. Muller, “Application of Boolean algebra to switching circuit design and to error detection”, Transactions of the I.R.E. Professional Group on Electronic Computers EC-3, 6 (1954) DOI. Appears in: Reed-Muller (RM) code
“Multiple-particle interference and quantum error correction”, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 452, 2551 (1996) arXiv:quant-ph/9601029 DOI. Appears in: Galois-qudit CSS code, Qubit CSS code, Modular-qudit CSS code
“Multiple-particle interference and quantum error correction”, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 452, 2551 (1996) DOI. Appears in: $[[7,1,3]]$ Steane code
G. A. Munné, A. Nemec, and F. Huber, “SDP bounds on quantum codes”, (2024) arXiv:2408.10323. Appears in: Qubit code
S. Muralidharan, J. Kim, N. Lütkenhaus, M. D. Lukin, and L. Jiang, “Ultrafast and Fault-Tolerant Quantum Communication across Long Distances”, Physical Review Letters 112, (2014) arXiv:1310.5291 DOI. Appears in: Generalized Shor code, Quantum parity code (QPC)
Muralidhar, S., Lloyd, W., Roy, S., Hill, C., Lin, E., Liu, W., Pan, S., Shankar, S., Sivakumar, V., Tang, L. and Kumar, S., 2014. f4: Facebook's warm BLOB storage system. In 11th USENIX Symposium on Operating Systems Design and Implementation (OSDI 14) (pp. 383-398).. Appears in: Locally recoverable code (LRC)
P. G. P. Murillo, “Systole of congruence coverings of arithmetic hyperbolic manifolds”, (2017) arXiv:1610.03870. Appears in: Guth-Lubotzky code
O. R. Musin, “The kissing number in four dimensions”, (2006) arXiv:math/0309430. Appears in: 24-cell code, Witting polytope code
T. Mütze, “Combinatorial Gray codes-an updated survey”, (2024) arXiv:2202.01280. Appears in: Gray code
L. D. H. My, S. Qin, and H. K. Ng, “Circuit-level fault tolerance of cat codes”, (2024) arXiv:2406.04157. Appears in: Bosonic rotation code
C. R. Myers and R. Laflamme, “Linear Optics Quantum Computation: an Overview”, (2005) arXiv:quant-ph/0512104. Appears in: Dual-rail quantum code
S. Myung, K. Yang, and J. Kim, “Quasi-Cyclic LDPC Codes for Fast Encoding”, IEEE Transactions on Information Theory 51, 2894 (2005) DOI. Appears in: Block LDPC (B-LDPC) code
P. Naaijkens, Quantum Spin Systems on Infinite Lattices (Springer International Publishing, 2017) arXiv:1311.2717 DOI. Appears in: Hamiltonian-based code
E. Nachmani, Y. Beery, and D. Burshtein, “Learning to Decode Linear Codes Using Deep Learning”, (2016) arXiv:1607.04793. Appears in: Linear binary code
B. Nachtergaele, R. Sims, and A. Young, “Quasi-locality bounds for quantum lattice systems. I. Lieb-Robinson bounds, quasi-local maps, and spectral flow automorphisms”, Journal of Mathematical Physics 60, (2019) arXiv:1810.02428 DOI. Appears in: Commuting-projector Hamiltonian code, Hamiltonian-based code, Quantum LDPC (QLDPC) code, Topological code
B. Nachtergaele, R. Sims, and A. Young, “Quasi-Locality Bounds for Quantum Lattice Systems. Part II. Perturbations of Frustration-Free Spin Models with Gapped Ground States”, Annales Henri Poincaré 23, 393 (2021) arXiv:2010.15337 DOI. Appears in: Commuting-projector Hamiltonian code, Hamiltonian-based code, Quantum LDPC (QLDPC) code, Topological code
B. Nachtergaele, “From Lieb-Robinson Bounds to Automorphic Equivalence”, (2022) arXiv:2205.10460. Appears in: Hamiltonian-based code
P. J. Nadkarni and S. S. Garani, “Quantum error correction architecture for qudit stabilizer codes”, Physical Review A 103, (2021) DOI. Appears in: EA Galois-qudit stabilizer code, Galois-qudit stabilizer code
P. J. Nadkarni and S. S. Garani, “Entanglement-assisted Reed–Solomon codes over qudits: theory and architecture”, Quantum Information Processing 20, (2021) DOI. Appears in: EA Galois-qudit stabilizer code, Galois-qudit GRS code
P. J. Nadkarni, S. Adonsou, G. Dauphinais, D. W. Kribs, and M. Vasmer, “Unified and Generalized Approach to Entanglement-Assisted Quantum Error Correction”, (2024) arXiv:2411.14389. Appears in: Entanglement-assisted operator-algebra QECC (EAOAQECC), $[2^r-1,2^r-r-1,3]$ Hamming code, Subsystem color code
P. J. Nadkarni, N. Rengaswamy, and B. Vasić, “Tutorial on Quantum Error Correction for 2024 Quantum Information Knowledge (QuIK) Workshop”, (2024) arXiv:2407.12737. Appears in: Quantum error-correcting code (QECC)
P. J. Nadkarni, P. Jayakumar, A. Behera, and S. S. Garani, “Entanglement-assisted Quantum Reed-Muller Tensor Product Codes”, Quantum 8, 1329 (2024) arXiv:2303.08294 DOI. Appears in: EA qubit stabilizer code, Quantum Reed-Muller code, Quantum tensor-product code
M. Nadler, “A 32-point n=12, d=5 code (Corresp.)”, IRE Transactions on Information Theory 8, 58 (1962) DOI. Appears in: Nadler code
H. Nagayoshi, W. Asavanant, R. Ide, K. Fukui, A. Sakaguchi, J. Yoshikawa, N. C. Menicucci, and A. Furusawa, “ZX Graphical Calculus for Continuous-Variable Quantum Processes”, (2024) arXiv:2405.07246. Appears in: Bosonic code
D. Naidu, “Categorical Morita equivalence for group-theoretical categories”, (2006) arXiv:math/0605530. Appears in: Quantum-double code
D. Naidu and D. Nikshych, “Lagrangian Subcategories and Braided Tensor Equivalences of Twisted Quantum Doubles of Finite Groups”, Communications in Mathematical Physics 279, 845 (2008) arXiv:0705.0665 DOI. Appears in: Dijkgraaf-Witten gauge theory code, Twisted quantum double (TQD) code
M. Nakahara, “Quantum Computing”, (2008) DOI. Appears in: $[[9,1,3]]$ Shor code, Five-qubit perfect code, $[[7,1,3]]$ Steane code
A. Nakayama and M. Hagiwara, “Single Quantum Deletion Error-Correcting Codes”, (2020) arXiv:2004.00814. Appears in: Block quantum code, Four-qubit single-deletion code, Permutation-invariant (PI) code, PI qubit code
T. Nakazato, R. Reyes, N. Imaike, K. Matsuda, K. Tsurumoto, Y. Sekiguchi, and H. Kosaka, “Quantum error correction of spin quantum memories in diamond under a zero magnetic field”, Communications Physics 5, (2022) DOI. Appears in: Quantum repetition code
Y. Nam, N. J. Ross, Y. Su, A. M. Childs, and D. Maslov, “Automated optimization of large quantum circuits with continuous parameters”, npj Quantum Information 4, (2018) arXiv:1710.07345 DOI. Appears in: Qubit code
J. Naor and M. Naor, “Small-bias probability spaces: efficient constructions and applications”, Proceedings of the twenty-second annual ACM symposium on Theory of computing - STOC ’90 213 (1990) DOI. Appears in: Justesen code
M. Naor and B. Pinkas, “Oblivious transfer and polynomial evaluation”, Proceedings of the thirty-first annual ACM symposium on Theory of Computing 245 (1999) DOI. Appears in: Reed-Solomon (RS) code
J. Napp and J. Preskill, “Optimal Bacon-Shor codes”, (2012) arXiv:1209.0794. Appears in: Asymmetric quantum code, Bacon-Shor code
K. R. Narayanan and G. L. Stuber, “List decoding of turbo codes”, IEEE Transactions on Communications 46, 754 (1998) DOI. Appears in: Turbo code
R. Nasser and J. M. Renes, “Polar Codes for Arbitrary Classical-Quantum Channels and Arbitrary cq-MACs”, IEEE Transactions on Information Theory 64, 7424 (2018) arXiv:1701.03397 DOI. Appears in: Polar c-q code
H. P. Nautrup and T.-C. Wei, “Symmetry-protected topologically ordered states for universal quantum computation”, Physical Review A 92, (2015) arXiv:1509.02947 DOI. Appears in: Cluster-state code, Symmetry-protected topological (SPT) code, Lattice stabilizer code
H. P. Nautrup, N. Delfosse, V. Dunjko, H. J. Briegel, and N. Friis, “Optimizing Quantum Error Correction Codes with Reinforcement Learning”, Quantum 3, 215 (2019) arXiv:1812.08451 DOI. Appears in: Neural network quantum code, Kitaev surface code
M. Navon and A. Samorodnitsky, “Linear Programming Bounds for Codes via a Covering Argument”, Discrete & Computational Geometry 41, 199 (2008) DOI. Appears in: Binary code
C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. Das Sarma, “Non-Abelian anyons and topological quantum computation”, Reviews of Modern Physics 80, 1083 (2008) arXiv:0707.1889 DOI. Appears in: Topological code
G. Nebe, E. M. Rains, and N. J. A. Sloane, “The invariants of the Clifford groups”, (2000) arXiv:math/0001038. Appears in: Barnes-Wall (BW) lattice, Clifford subgroup-orbit QSC, Real-Clifford subgroup-orbit code
G. Nebe and N. J. A. Sloane. "Catalogue of Lattices." https://www.math.rwth-aachen.de/ Gabriele.Nebe/LATTICES/index.html. Appears in: Lattice-based code
B. de Neeve, T. L. Nguyen, T. Behrle, and J. Home, “Error correction of a logical grid state qubit by dissipative pumping”, (2020) arXiv:2010.09681. Appears in: Square-lattice GKP code
J. Nelson, G. Bentsen, S. T. Flammia, and M. J. Gullans, “Fault-Tolerant Quantum Memory using Low-Depth Random Circuit Codes”, (2023) arXiv:2311.17985. Appears in: Brown-Fawzi random Clifford-circuit code
A. Nemec and A. Klappenecker, “Hybrid Codes”, 2018 IEEE International Symposium on Information Theory (ISIT) (2018) arXiv:1901.02913 DOI. Appears in: Hybrid qubit code
A. Nemec and A. Klappenecker, “Infinite Families of Quantum-Classical Hybrid Codes”, (2020) arXiv:1911.12260. Appears in: Entanglement-assisted (EA) hybrid QECC, $[[7, 1:1, 3]]$ hybrid stabilizer code, Hybrid qubit code, Hybrid stabilizer code, $[[2m,2m-2,2]]$ error-detecting code
A. Nemec and A. Klappenecker, “Nonbinary Error-Detecting Hybrid Codes”, (2020) arXiv:2002.11075. Appears in: Hybrid stabilizer code, $[[2m,2m-2,2]]$ error-detecting code
A. Nemec and A. Klappenecker, “Encoding classical information in gauge subsystems of quantum codes”, International Journal of Quantum Information 20, (2022) DOI. Appears in: Subsystem QECC, Subsystem hypergraph product (SHP) code
A. Nemec and A. Klappenecker, “Encoding classical information in gauge subsystems of quantum codes”, International Journal of Quantum Information 20, (2022) arXiv:2012.05896 DOI. Appears in: Bacon-Shor code, Hybrid stabilizer code, Subsystem hypergraph product (SHP) code, Subsystem qubit stabilizer code
A. Nemec and T. Tansuwannont, “A Hamming-Like Bound for Degenerate Stabilizer Codes”, (2023) arXiv:2306.00048. Appears in: Perfect quantum code
A. Nemec, “Quantum Data-Syndrome Codes: Subsystem and Impure Code Constructions”, (2023) arXiv:2302.01527. Appears in: Quantum data-syndrome (QDS) code, Subsystem qubit stabilizer code
M. V. den Nest, “Classical simulation of quantum computation, the Gottesman-Knill theorem, and slightly beyond”, (2009) arXiv:0811.0898. Appears in: Qubit stabilizer code, Qubit code
J. v. Neumann, “Die Eindeutigkeit der Schrödingerschen Operatoren”, Mathematische Annalen 104, 570 (1931) DOI. Appears in: Modular-qudit code
J. von Neumann, “Probabilistic Logics and the Synthesis of Reliable Organisms From Unreliable Components”, Automata Studies. (AM-34) 43 (1956) DOI. Appears in: Repetition code
D. Newman, “The hexagon theorem”, IEEE Transactions on Information Theory 28, 137 (1982) DOI. Appears in: $A_2$ triangular lattice
M. E. J. Newman and C. Moore, “Glassy dynamics and aging in an exactly solvable spin model”, Physical Review E 60, 5068 (1999) arXiv:cond-mat/9707273 DOI. Appears in: Newman-Moore code
M. Newman and Y. Shi, “Limitations on Transversal Computation through Quantum Homomorphic Encryption”, (2017) arXiv:1704.07798. Appears in: Qubit stabilizer code
M. Newman, L. A. de Castro, and K. R. Brown, “Generating Fault-Tolerant Cluster States from Crystal Structures”, Quantum 4, 295 (2020) arXiv:1909.11817 DOI. Appears in: Cluster-state code, Symmetry-protected topological (SPT) code, Lattice stabilizer code
S. Nezami and J. Haah, “Classification of small triorthogonal codes”, Physical Review A 106, (2022) arXiv:2107.09684 DOI. Appears in: Quantum Reed-Muller code, Triorthogonal code, $[[15,1,3]]$ quantum Reed-Muller code
H. K. Ng and P. Mandayam, “Simple approach to approximate quantum error correction based on the transpose channel”, Physical Review A 81, (2010) arXiv:0909.0931 DOI. Appears in: Approximate quantum error-correcting code (AQECC)
N. H. Nguyen, M. Li, A. M. Green, C. Huerta Alderete, Y. Zhu, D. Zhu, K. R. Brown, and N. M. Linke, “Demonstration of Shor Encoding on a Trapped-Ion Quantum Computer”, Physical Review Applied 16, (2021) arXiv:2104.01205 DOI. Appears in: Generalized Shor code, Quantum parity code (QPC), $[[9,1,3]]$ Shor code
Q. T. Nguyen, “Good binary quantum codes with transversal CCZ gate”, (2024) arXiv:2408.10140. Appears in: Quantum AG code, Triorthogonal code
T. T. Nguyen, K. Cai, K. A. Schouhamer Immink, and H. M. Kiah, “Capacity-Approaching Constrained Codes With Error Correction for DNA-Based Data Storage”, IEEE Transactions on Information Theory 67, 5602 (2021) DOI. Appears in: DNA storage code
X. Ni, O. Buerschaper, and M. Van den Nest, “A non-commuting stabilizer formalism”, Journal of Mathematical Physics 56, (2015) arXiv:1404.5327 DOI. Appears in: Abelian TQD stabilizer code, XS stabilizer code
Z. Ni et al., “Beating the break-even point with a discrete-variable-encoded logical qubit”, Nature 616, 56 (2023) arXiv:2211.09319 DOI. Appears in: Binomial code, Square-lattice GKP code
N. Nickerson and H. Bombín, “Measurement based fault tolerance beyond foliation”, (2018) arXiv:1810.09621. Appears in: Toric code
Niclas Wiberg, Codes and decoding on general graphs. 1996. PhD thesis, Linköping University, Linköping, Sweden. Appears in: Tanner code
H. Niederreiter, “Point sets and sequences with small discrepancy”, Monatshefte für Mathematik 104, 273 (1987) DOI. Appears in: Niederreiter-Rosenbloom-Tsfasman (NRT) code
H. Niederreiter, “A combinatorial problem for vector spaces over finite fields”, Discrete Mathematics 96, 221 (1991) DOI. Appears in: Niederreiter-Rosenbloom-Tsfasman (NRT) code
H. Niederreiter, “Orthogonal arrays and other combinatorial aspects in the theory of uniform point distributions in unit cubes”, Discrete Mathematics 106–107, 361 (1992) DOI. Appears in: Niederreiter-Rosenbloom-Tsfasman (NRT) code
H. Niederreiter and F. Özbudak, “Constructive Asymptotic Codes with an Improvement on the Tsfasman-Vlăduţ-Zink and Xing Bounds”, Coding, Cryptography and Combinatorics 259 (2004) DOI. Appears in: Nonlinear AG code
H. Niederreiter (1986). Knapsack-type cryptosystems and algebraic coding theory. Problems of Control and Information Theory. Problemy Upravlenija I Teorii Informacii. 15: 159–166.. Appears in: Generalized RS (GRS) code
A. Niehage, “Quantum Goppa Codes over Hyperelliptic Curves”, (2005) arXiv:quant-ph/0501074. Appears in: Quantum Goppa code, Galois-qudit color code, Galois-qudit code, Galois-qudit surface code, Group-based quantum code, Quantum AG code, Quantum-double code, Abelian quantum-double stabilizer code, Quantum Gabidulin code, Triorthogonal code, Modular-qudit code
A. Niehage, “Nonbinary Quantum Goppa Codes Exceeding the Quantum Gilbert-Varshamov Bound”, Quantum Information Processing 6, 143 (2006) DOI. Appears in: Quantum Goppa code, Galois-qudit CSS code, Quantum AG code
M. A. Nielsen, “Optical Quantum Computation Using Cluster States”, Physical Review Letters 93, (2004) arXiv:quant-ph/0402005 DOI. Appears in: Cluster-state code, Dual-rail quantum code
M. A. Nielsen and D. Poulin, “Algebraic and information-theoretic conditions for operator quantum error correction”, Physical Review A 75, (2007) arXiv:quant-ph/0506069 DOI. Appears in: Subsystem QECC
M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2012) DOI. Appears in: Approximate quantum error-correcting code (AQECC), Quantum error-correcting code (QECC), Finite-dimensional quantum error-correcting code, Qubit CSS code, Qubit stabilizer code, Modular-qudit stabilizer code
H.-V. Niemeier, “Definite quadratische formen der dimension 24 und diskriminante 1”, Journal of Number Theory 5, 142 (1973) DOI. Appears in: Niemeier lattice
D. Nigg, M. Müller, E. A. Martinez, P. Schindler, M. Hennrich, T. Monz, M. A. Martin-Delgado, and R. Blatt, “Quantum computations on a topologically encoded qubit”, Science 345, 302 (2014) arXiv:1403.5426 DOI. Appears in: $[[7,1,3]]$ Steane code
König, Hermann. "Isometric imbeddings of Euclidean spaces into finite dimensional lp-spaces." Banach Center Publications 34.1 (1995): 79-87. <https://eudml.org/doc/251336>.. Appears in: Kerdock spherical code
Nikolas P. Breuckmann, private communication, 2022. Appears in: Quantum Tanner code, Rotated surface code, Kitaev surface code
Nilsson, Magnus. "Linear block codes over rings for phase shift keying." Thesis no. 331, Linkoping University (1993).. Appears in: Polyphase code
Nilsson, Nils J. "Learning machines." (1965).. Appears in: Error-correcting output code (ECOC), One-hot code
C. Nirkhe, U. Vazirani, and H. Yuen, “Approximate Low-Weight Check Codes and Circuit Lower Bounds for Noisy Ground States”, (2018) arXiv:1802.07419 DOI. Appears in: Approximate quantum error-correcting code (AQECC), Quantum low-weight check (QLWC) code, Unary code
J. Niset, U. L. Andersen, and N. J. Cerf, “Experimentally Feasible Quantum Erasure-Correcting Code for Continuous Variables”, Physical Review Letters 101, (2008) arXiv:0710.4858 DOI. Appears in: Analog repetition code, Niset-Andersen-Cerf code
J. Niset, J. Fiurášek, and N. J. Cerf, “No-Go Theorem for Gaussian Quantum Error Correction”, Physical Review Letters 102, (2009) arXiv:0811.3128 DOI. Appears in: Analog stabilizer code, Oscillator-into-oscillator GKP code
H. Nishimori, “Geometry-Induced Phase Transition in the ±JIsing Model”, Journal of the Physical Society of Japan 55, 3305 (1986) DOI. Appears in: Square-octagon (4.8.8) color code, Clifford-deformed surface code (CDSC), Subsystem surface code, Toric code, Honeycomb (6.6.6) color code, Union-Jack color code
H. Nishimori, “Statistical Physics of Spin Glasses and Information Processing”, (2001) DOI. Appears in: Convolutional code, Hamiltonian-based code, Low-density parity-check (LDPC) code
H. Nishimori and P. Sollich, “Error Counting in a Quantum Error-correcting Code and the Ground-State Energy of a Spin Glass”, Journal of the Physical Society of Japan 73, 2701 (2004) arXiv:cond-mat/0405313 DOI. Appears in: Toric code
M. Y. Niu, I. L. Chuang, and J. H. Shapiro, “Hardware-efficient bosonic quantum error-correcting codes based on symmetry operators”, Physical Review A 97, (2018) arXiv:1709.05302 DOI. Appears in: $\chi^{(2)}$ code, Two-mode binomial code
G. M. Nixon and B. J. Brown, “Correcting Spanning Errors With a Fractal Code”, IEEE Transactions on Information Theory 67, 4504 (2021) arXiv:2002.11738 DOI. Appears in: Fibonacci code, Haah cubic code (CC), Quantum-inspired classical block code, X-cube model code
R. W. Nobrega and B. F. Uchoa-Filho, “Multishot Codes for Network Coding using Rank-Metric Codes”, (2010) arXiv:1001.2059. Appears in: Sum-rank-metric code
C. Noel et al., “Measurement-induced quantum phases realized in a trapped-ion quantum computer”, Nature Physics 18, 760 (2022) arXiv:2106.05881 DOI. Appears in: Monitored random-circuit code
M. des Noes, V. Savin, J. M. Brossier, and L. Ros, “Iterative decoding of Gold sequences”, 2015 IEEE International Conference on Communications (ICC) 4840 (2015) DOI. Appears in: Gold code, $[2^m-1,m,2^{m-1}]$ simplex code
D. Yu. Nogin, “Codes associated to Grassmannians”, Arithmetic, Geometry, and Coding Theory DOI. Appears in: Grassmannian code
K. Noh, V. V. Albert, and L. Jiang, “Quantum Capacity Bounds of Gaussian Thermal Loss Channels and Achievable Rates With Gottesman-Kitaev-Preskill Codes”, IEEE Transactions on Information Theory 65, 2563 (2019) arXiv:1801.07271 DOI. Appears in: Approximate quantum error-correcting code (AQECC), Conformal-field theory (CFT) code, Square-lattice GKP code, Hexagonal GKP code, Gottesman-Kitaev-Preskill (GKP) code, Numerically optimized bosonic code, Bosonic code
K. Noh, S. M. Girvin, and L. Jiang, “Encoding an Oscillator into Many Oscillators”, Physical Review Letters 125, (2020) arXiv:1903.12615 DOI. Appears in: Oscillator-into-oscillator GKP code, Bosonic code
K. Noh and C. Chamberland, “Fault-tolerant bosonic quantum error correction with the surface–Gottesman-Kitaev-Preskill code”, Physical Review A 101, (2020) arXiv:1908.03579 DOI. Appears in: GKP-surface code, Gottesman-Kitaev-Preskill (GKP) code, Rotated surface code
K. Noh, “Quantum Computation and Communication in Bosonic Systems”, (2021) arXiv:2103.09445. Appears in: Bosonic code
K. Noh, C. Chamberland, and F. G. S. L. Brandão, “Low-Overhead Fault-Tolerant Quantum Error Correction with the Surface-GKP Code”, PRX Quantum 3, (2022) arXiv:2103.06994 DOI. Appears in: GKP-surface code, Gottesman-Kitaev-Preskill (GKP) code, Rotated surface code
“Nonbinary Stabilizer Codes”, Mathematics of Quantum Computation and Quantum Technology 305 (2007) DOI. Appears in: Galois-qudit quantum RM code, Galois-qudit stabilizer code, Generalized RM (GRM) code, Projective RM (PRM) code, Quantum convolutional code
M. Noormandipour and T. Haug, “MaxSAT decoders for arbitrary CSS codes”, (2024) arXiv:2410.01673. Appears in: Qubit CSS code
A. W. Nordstrom and J. P. Robinson, “An optimum nonlinear code”, Information and Control 11, 613 (1967) DOI. Appears in: Nordstrom-Robinson (NR) code
E. Novais and E. R. Mucciolo, “Surface Code Threshold in the Presence of Correlated Errors”, Physical Review Letters 110, (2013) arXiv:1209.2157 DOI. Appears in: Toric code
O. Novak and N. Rengaswamy, “GNarsil: Splitting Stabilizers into Gauges”, (2024) arXiv:2404.18302. Appears in: Qubit CSS code, Subsystem lifted-product (SLP) code, Subsystem qubit stabilizer code
S. Novák, “Homological Quantum Error Correction with Torsion”, (2024) arXiv:2405.03559. Appears in: Modular-qudit CSS code
Günther, Annika. Automorphism groups of self-dual codes. Diss. Aachen, Techn. Hochsch., Diss., 2009, 2009.. Appears in: Group-algebra code
Z. Nussinov and G. Ortiz, “Autocorrelations and thermal fragility of anyonic loops in topologically quantum ordered systems”, Physical Review B 77, (2008) arXiv:0709.2717 DOI. Appears in: Self-correcting quantum code
Z. Nussinov and J. van den Brink, “Compass and Kitaev models -- Theory and Physical Motivations”, (2013) arXiv:1303.5922. Appears in: Bacon-Shor code, Compass code, Hamiltonian-based code
J. L. O’Brien, G. J. Pryde, A. G. White, and T. C. Ralph, “High-fidelityZ-measurement error encoding of optical qubits”, Physical Review A 71, (2005) arXiv:quant-ph/0408064 DOI. Appears in: Quantum repetition code
O. O’Brien, L. Lootens, and F. Verstraete, “Local Jordan-Wigner transformations on the torus”, (2024) arXiv:2404.07727. Appears in: 2D bosonization code
T. E. O’Brien, B. Tarasinski, and L. DiCarlo, “Density-matrix simulation of small surface codes under current and projected experimental noise”, npj Quantum Information 3, (2017) arXiv:1703.04136 DOI. Appears in: $[[9,1,3]]$ Surface-17 code
A. R. O’Rourke and S. Devitt, “Compare the Pair: Rotated vs. Unrotated Surface Codes at Equal Logical Error Rates”, (2024) arXiv:2409.14765. Appears in: Rotated surface code, Kitaev surface code
A. Ocneanu, “Operator Algebras, Topology and Subgroups of Quantum Symmetry – Construction of Subgroups of Quantum Groups –”, Advanced Studies in Pure Mathematics DOI. Appears in: Dijkgraaf-Witten gauge theory code, Two-gauge theory code
Ocneanu, Adrian. "Chirality for operator algebras." Subfactors (Kyuzeso, 1993) 39 (1994).. Appears in: Dijkgraaf-Witten gauge theory code, Two-gauge theory code
Odaka K., Sako Y., Iwamoto I., Doi T.; Vries L.B.; SONY: Error correctable data transmission method (Patent US4413340) filing date May 21, 1980.. Appears in: Cross-interleaved RS (CIRS) code
A. M. Odlyzko and N. J. A. Sloane, “New bounds on the number of unit spheres that can touch a unit sphere in n dimensions”, Journal of Combinatorial Theory, Series A 26, 210 (1979) DOI. Appears in: $\Lambda_{24}$ Leech lattice-shell code, Witting polytope code
T. R. Oenning and Jaekyun Moon, “A low-density generator matrix interpretation of parallel concatenated single bit parity codes”, IEEE Transactions on Magnetics 37, 737 (2001) DOI. Appears in: Low-density generator-matrix (LDGM) code, Single parity-check (SPC) code, $q$-ary LDGM code, $q$-ary parity-check code
N. Ofek et al., “Demonstrating Quantum Error Correction that Extends the Lifetime of Quantum Information”, (2016) arXiv:1602.04768. Appears in: Cat code
F. Oggier, "Spacetime Coding." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI. Appears in: Orthogonal Spacetime Block Code (OSTBC), Spacetime code (STC)
T. Ohno, G. Arakawa, I. Ichinose, and T. Matsui, “Phase structure of the random-plaquette gauge model: accuracy threshold for a toric quantum memory”, Nuclear Physics B 697, 462 (2004) arXiv:quant-ph/0401101 DOI. Appears in: Cluster-state code, Kitaev surface code
M. Ohzeki, “Accuracy thresholds of topological color codes on the hexagonal and square-octagonal lattices”, Physical Review E 80, (2009) arXiv:0903.2102 DOI. Appears in: Square-octagon (4.8.8) color code, Honeycomb (6.6.6) color code
M. Ohzeki, “Locations of multicritical points for spin glasses on regular lattices”, Physical Review E 79, (2009) arXiv:0811.0464 DOI. Appears in: Kitaev surface code, Toric code
T. Okamura, “Designing LDPC codes using cyclic shifts”, IEEE International Symposium on Information Theory, 2003. Proceedings. (2003) DOI. Appears in: Quasi-cyclic LDPC (QC-LDPC) code
J. Old and M. Rispler, “Generalized Belief Propagation Algorithms for Decoding of Surface Codes”, Quantum 7, 1037 (2023) arXiv:2212.03214 DOI. Appears in: Qubit stabilizer code, Kitaev surface code, Toric code
J. Old, M. Rispler, and M. Müller, “Lift-connected surface codes”, Quantum Science and Technology 9, 045012 (2024) arXiv:2401.02911 DOI. Appears in: Lift-connected surface (LCS) code
J. Olle, R. Zen, M. Puviani, and F. Marquardt, “Simultaneous Discovery of Quantum Error Correction Codes and Encoders with a Noise-Aware Reinforcement Learning Agent”, (2024) arXiv:2311.04750. Appears in: Neural network quantum code, Small-distance qubit stabilizer code, $[[11,1,5]]$ quantum dodecacode
H. Ollivier and J.-P. Tillich, “Description of a Quantum Convolutional Code”, Physical Review Letters 91, (2003) arXiv:quant-ph/0304189 DOI. Appears in: Quantum convolutional code, $(5,1,2)$-convolutional code
H. Ollivier and J.-P. Tillich, “Quantum convolutional codes: fundamentals”, (2004) arXiv:quant-ph/0401134. Appears in: Quantum convolutional code, Lattice stabilizer code
H. Ollivier and J.-P. Tillich, “Trellises for stabilizer codes: Definition and uses”, Physical Review A 74, (2006) arXiv:quant-ph/0512041 DOI. Appears in: Quantum turbo code, Qubit stabilizer code
F. W. J. Olver, A. B. Olde Daalhuis, D. W. Lozier, B. Schneider, R. F. Boisvert, C. W. Clark, B. R. Miller, B. V. Saunders, H. S. Cohl, and M. A. McClain, “Digital Library of Mathematical Functions”, (2019) DOI. Appears in: $t$-design
S. Omanakuttan and J. A. Gross, “Multispin Clifford codes for angular momentum errors in spin systems”, Physical Review A 108, (2023) arXiv:2304.08611 DOI. Appears in: Clifford spin code, PI qubit code, Single-spin code
S. Omanakuttan and T. J. Volkoff, “Spin-squeezed Gottesman-Kitaev-Preskill codes for quantum error correction in atomic ensembles”, Physical Review A 108, (2023) arXiv:2211.05181 DOI. Appears in: Spin GKP code
S. Omanakuttan, V. Buchemmavari, J. A. Gross, I. H. Deutsch, and M. Marvian, “Fault-Tolerant Quantum Computation Using Large Spin-Cat Codes”, PRX Quantum 5, (2024) arXiv:2401.04271 DOI. Appears in: Spin cat code
S. Omkar, S.-H. Lee, Y. S. Teo, S.-W. Lee, and H. Jeong, “All-Photonic Architecture for Scalable Quantum Computing with Greenberger-Horne-Zeilinger States”, PRX Quantum 3, (2022) arXiv:2109.12280 DOI. Appears in: Cluster-state code, Quantum repetition code
H. Oral, “Constructing self-dual codes using graphs”, Journal of Combinatorial Theory, Series B 52, 250 (1991) DOI. Appears in: 2D color code, Linear binary code
O. Oreshkov and T. A. Brun, “Continuous quantum error correction for non-Markovian decoherence”, Physical Review A 76, (2007) arXiv:0705.2342 DOI. Appears in: Finite-dimensional quantum error-correcting code
O. Oreshkov, D. A. Lidar, and T. A. Brun, “Operator quantum error correction for continuous dynamics”, Physical Review A 78, (2008) arXiv:0806.3145 DOI. Appears in: Subsystem QECC
O. Oreshkov, “Robustness of operator quantum error correction with respect to initialization errors”, Physical Review A 77, (2008) arXiv:0709.3533 DOI. Appears in: Subsystem QECC
O. Oreshkov, “Topics in quantum information and the theory of open quantum systems”, (2008) arXiv:0812.4682. Appears in: Qubit stabilizer code
O. Oreshkov, T. A. Brun, and D. A. Lidar, “Fault-Tolerant Holonomic Quantum Computation”, Physical Review Letters 102, (2009) arXiv:0806.0875 DOI. Appears in: Qubit stabilizer code
O. Oreshkov, T. A. Brun, and D. A. Lidar, “Scheme for fault-tolerant holonomic computation on stabilizer codes”, Physical Review A 80, (2009) arXiv:0904.2143 DOI. Appears in: Qubit stabilizer code
O. Oreshkov, F. Costa, and Č. Brukner, “Quantum correlations with no causal order”, Nature Communications 3, (2012) arXiv:1105.4464 DOI. Appears in: Quantum error-correcting code (QECC)
O. Oreshkov, “Continuous-time quantum error correction”, (2013) arXiv:1311.2485. Appears in: Finite-dimensional quantum error-correcting code
O. Oreshkov, T. A. Brun, and D. A. Lidar, “Fault tolerance for holonomic quantum computation”, (2013) arXiv:1312.0165. Appears in: Qubit stabilizer code
G. OROSZ and L. TAKÁCS, “SOME PROBABILITY PROBLEMS CONCERNING THE MARKING OF CODES INTO THE SUPERIMPOSITION FIELD”, Journal of Documentation 12, 231 (1956) DOI. Appears in: Superimposed code
T. J. Osborne, “Simulating adiabatic evolution of gapped spin systems”, Physical Review A 75, (2007) arXiv:quant-ph/0601019 DOI. Appears in: Hamiltonian-based code
T. J. Osborne and D. E. Stiegemann, “Dynamics for holographic codes”, Journal of High Energy Physics 2020, (2020) arXiv:1706.08823 DOI. Appears in: Pastawski-Yoshida-Harlow-Preskill (HaPPY) code
P. R. J. Ostergard, O. Pottonen, and K. T. Phelps, “The Perfect Binary One-Error-Correcting Codes of Length 15: Part II—Properties”, IEEE Transactions on Information Theory 56, 2571 (2010) arXiv:0903.2749 DOI. Appears in: Orthogonal array (OA), Perfect binary code
P. Ostergard and O. Pottonen, “The Perfect Binary One-Error-Correcting Codes of Length <formula formulatype="inline"><tex Notation="TeX">$15$</tex></formula>: Part I—Classification”, IEEE Transactions on Information Theory 55, 4657 (2009) arXiv:0806.2513 DOI. Appears in: Perfect code, Perfect binary code
D. Ostrev, “Canonical Form and Finite Blocklength Bounds for Stabilizer Codes”, (2024) arXiv:2408.15202. Appears in: Qubit stabilizer code, Qubit code
D. Ostrev, D. Orsucci, F. Lázaro, and B. Matuz, “Classical product code constructions for quantum Calderbank-Shor-Steane codes”, Quantum 8, 1420 (2024) arXiv:2209.13474 DOI. Appears in: Classical-product code, Quantum Tanner code, Qubit CSS code
D. Ostrev, “Quantum LDPC Codes From Intersecting Subsets”, IEEE Transactions on Information Theory 70, 5692 (2024) arXiv:2306.06056 DOI. Appears in: Classical-product code
C. Ottaviani, R. Laurenza, T. P. W. Cope, G. Spedalieri, S. L. Braunstein, and S. Pirandola, “Secret key capacity of the thermal-loss channel: improving the lower bound”, SPIE Proceedings 9996, 999609 (2016) arXiv:1609.02169 DOI. Appears in: Bosonic code
Ottoson, Ragnar. "Performance of phase- and amplitude-modulated signals on a Gaussian channel(Phase and amplitude modulated signals transmission over band limited channel disturbed by additive white Gaussian noise)." Ericsson Technics 25.3 (1969): 153-198.. Appears in: Polyphase code
Y. Ouyang, “Permutation-invariant quantum codes”, Physical Review A 90, (2014) arXiv:1302.3247 DOI. Appears in: Bacon-Shor code, GNU PI code, Permutation-invariant (PI) code, $((9,2,3))$ Ruskai code
Y. Ouyang, “Concatenated Quantum Codes Can Attain the Quantum Gilbert–Varshamov Bound”, IEEE Transactions on Information Theory 60, 3117 (2014) arXiv:1004.1127 DOI. Appears in: Galois-qudit GRS code, Concatenated quantum code, Random stabilizer code
Y. Ouyang and J. Fitzsimons, “Permutation-invariant codes encoding more than one qubit”, Physical Review A 93, (2016) DOI. Appears in: Permutation-invariant (PI) code
Y. Ouyang and J. Fitzsimons, “Permutation-invariant codes encoding more than one qubit”, Physical Review A 93, (2016) arXiv:1512.02469 DOI. Appears in: GNU PI code
Y. Ouyang, “Permutation-invariant qudit codes from polynomials”, Linear Algebra and its Applications 532, 43 (2017) DOI. Appears in: Permutation-invariant (PI) code
Y. Ouyang, “Permutation-invariant qudit codes from polynomials”, Linear Algebra and its Applications 532, 43 (2017) arXiv:1604.07925 DOI. Appears in: Qudit GNU PI code
Y. Ouyang and R. Chao, “Permutation-Invariant Constant-Excitation Quantum Codes for Amplitude Damping”, IEEE Transactions on Information Theory 66, 2921 (2020) arXiv:1809.09801 DOI. Appears in: Ouyang-Chao constant-excitation PI code, Permutation-invariant (PI) code, Wasilewski-Banaszek code
Y. Ouyang, “Avoiding coherent errors with rotated concatenated stabilizer codes”, npj Quantum Information 7, (2021) arXiv:2010.00538 DOI. Appears in: Amplitude-damping (AD) code, Constant-excitation (CE) code, Dual-rail quantum code, Concatenated bosonic code, Quantum parity code (QPC), Concatenated qubit code, Qubit stabilizer code, $[[4,2,2]]$ Four-qubit code
Y. Ouyang and E. T. Campbell, “Trade-Offs on Number and Phase Shift Resilience in Bosonic Quantum Codes”, IEEE Transactions on Information Theory 67, 6644 (2021) arXiv:2008.12576 DOI. Appears in: Fock-state bosonic code
Y. Ouyang, “Permutation-invariant quantum coding for quantum deletion channels”, 2021 IEEE International Symposium on Information Theory (ISIT) 1499 (2021) arXiv:2102.02494 DOI. Appears in: Block quantum code, Four-qubit single-deletion code, GNU PI code, Permutation-invariant (PI) code
Y. Ouyang, “Quantum storage in quantum ferromagnets”, Physical Review B 103, (2021) arXiv:1904.01458 DOI. Appears in: Frustration-free Hamiltonian code, GNU PI code
Y. Ouyang and C.-Y. Lai, “Linear Programming Bounds for Approximate Quantum Error Correction Over Arbitrary Quantum Channels”, IEEE Transactions on Information Theory 68, 5234 (2022) arXiv:2108.04434 DOI. Appears in: Approximate quantum error-correcting code (AQECC)
Y. Ouyang, “Robust projective measurements through measuring code-inspired observables”, npj Quantum Information 10, (2024) arXiv:2402.04093 DOI. Appears in: Binomial code, $((9,12,3))$ qubit code, Qubit stabilizer code
Y. Ouyang and G. K. Brennen, “Finite-round quantum error correction on symmetric quantum sensors”, (2024) arXiv:2212.06285. Appears in: GNU PI code, Error-corrected sensing code, PI qubit code
Y. Ouyang, “A new take on permutation-invariant quantum codes”, Quantum Views 8, 80 (2024) DOI. Appears in: Combinatorial PI code
Y. Ouyang, Y. Jing, and G. K. Brennen, “Measurement-free code-switching for low overhead quantum computation using permutation invariant codes”, (2024) arXiv:2411.13142. Appears in: PI qubit code, Qubit stabilizer code
M. Özen, N. Tuğba Özzaim, and H. İnce, “Skew quasi cyclic codes over 𝔽q + v𝔽q”, Journal of Algebra and Its Applications 18, 1950077 (2019) DOI. Appears in: Skew-cyclic CSS code
N. Pace and A. Sonnino, “On linear codes admitting large automorphism groups”, Designs, Codes and Cryptography 83, 115 (2016) DOI. Appears in: $[56,6,36]_3$ Hill-cap code, Quasi-twisted code
M. Pacenti, M. F. Flanagan, D. Chytas, and B. Vasić, “Progressive-Proximity Bit-Flipping for Decoding Surface Codes”, IEEE Transactions on Communications 1 (2024) arXiv:2402.15924 DOI. Appears in: Kitaev surface code
C. Pache, “Shells of selfdual lattices viewed as spherical designs”, (2005) arXiv:math/0502313. Appears in: Unimodular lattice, Spherical design
J. K. Pachos, Introduction to Topological Quantum Computation (Cambridge University Press, 2012) DOI. Appears in: Quantum-double code, Dihedral $G=D_m$ quantum-double code
P. Padmanabhan and I. Jana, “Groupoid Toric Codes”, (2022) arXiv:2212.01021. Appears in: Groupoid toric code
P. Padmanabhan, A. Chowdhury, F. Sugino, M. G. Majumdar, and K. K. Sabapathy, “Non-CSS color codes on 2D lattices : Models and Topological Properties”, (2022) arXiv:2112.13617. Appears in: 2D color code, Twist-defect color code
S. Paesani and B. J. Brown, “High-Threshold Quantum Computing by Fusing One-Dimensional Cluster States”, Physical Review Letters 131, (2023) arXiv:2212.06775 DOI. Appears in: Floquet color code
A. Paetznick and B. W. Reichardt, “Universal Fault-Tolerant Quantum Computation with Only Transversal Gates and Error Correction”, Physical Review Letters 111, (2013) arXiv:1304.3709 DOI. Appears in: Triorthogonal code, $[[15,1,3]]$ quantum Reed-Muller code, $[[15, 7, 3]]$ quantum Hamming code, $[[7,1,3]]$ Steane code
A. Paetznick and B. W. Reichardt, “Fault-tolerant ancilla preparation and noise threshold lower bounds for the 23-qubit Golay code”, (2013) arXiv:1106.2190. Appears in: $[[23, 1, 7]]$ Quantum Golay code
A. Paetznick, C. Knapp, N. Delfosse, B. Bauer, J. Haah, M. B. Hastings, and M. P. da Silva, “Performance of Planar Floquet Codes with Majorana-Based Qubits”, PRX Quantum 4, (2023) arXiv:2202.11829 DOI. Appears in: Hastings-Haah Floquet code, Honeycomb Floquet code, Majorana stabilizer code
A. Paetznick et al., “Demonstration of logical qubits and repeated error correction with better-than-physical error rates”, (2024) arXiv:2404.02280. Appears in: $[[12,2,4]]$ carbon code, $[[7,1,3]]$ Steane code
L. J. Paige, “A Note on the Mathieu Groups”, Canadian Journal of Mathematics 9, 15 (1957) DOI. Appears in: Combinatorial design, $[24, 12, 8]$ Extended Golay code, $[23, 12, 7]$ Golay code, Ternary Golay code
A. Paler and S. J. Devitt, “An introduction to Fault-tolerant Quantum Computing”, (2015) arXiv:1508.03695. Appears in: Quantum error-correcting code (QECC)
A. Paler and A. G. Fowler, “Pipelined correlated minimum weight perfect matching of the surface code”, Quantum 7, 1205 (2023) arXiv:2205.09828 DOI. Appears in: Kitaev surface code
F. Paluncic, H. C. Ferreira, and W. A. Clarke, “A comparison between single asymmetric and single insertion/deletion correcting codes using group-theory”, 2009 IEEE Information Theory Workshop (2009) DOI. Appears in: Constantin-Rao (CR) code
L. Pamies-Juarez, H. D. L. Hollmann, and F. Oggier, “Locally repairable codes with multiple repair alternatives”, 2013 IEEE International Symposium on Information Theory (2013) arXiv:1302.5518 DOI. Appears in: Parallel-recovery code
X. Pan, J. Schwinger, N.-N. Huang, P. Song, W. Chua, F. Hanamura, A. Joshi, F. Valadares, R. Filip, and Y. Y. Gao, “Protecting the quantum interference of cat states by phase-space compression”, (2022) arXiv:2212.01271. Appears in: Squeezed cat code, Two-component cat code
M. Pant, H. Krovi, D. Englund, and S. Guha, “Rate-distance tradeoff and resource costs for all-optical quantum repeaters”, Physical Review A 95, (2017) arXiv:1603.01353 DOI. Appears in: Tree cluster-state code
P. Panteleev and G. Kalachev, “Degenerate Quantum LDPC Codes With Good Finite Length Performance”, Quantum 5, 585 (2021) arXiv:1904.02703 DOI. Appears in: Abelian LP code, Balanced product (BP) code, Generalized bicycle (GB) code, Lifted-product (LP) code, Bivariate bicycle (BB) code, Quantum LDPC (QLDPC) code
P. Panteleev and G. Kalachev, “Asymptotically Good Quantum and Locally Testable Classical LDPC Codes”, (2022) arXiv:2111.03654. Appears in: Expander LP code, Haah cubic code (CC), Lifted-product (LP) code, $q$-ary linear LTC, Random code, Tensor-product code, Toric code
P. Panteleev and G. Kalachev, “Quantum LDPC Codes With Almost Linear Minimum Distance”, IEEE Transactions on Information Theory 68, 213 (2022) arXiv:2012.04068 DOI. Appears in: Abelian LP code, Expander LP code, Generalized bicycle (GB) code, Haah cubic code (CC), Lifted-product (LP) code
P. Panteleev and G. Kalachev, “Maximally Extendable Sheaf Codes”, (2024) arXiv:2403.03651. Appears in: Balanced product (BP) code, Dinur-Hsieh-Lin-Vidick (DHLV) code, Generalized homological-product CSS code, Lifted-product (LP) code, Locally testable code (LTC), Tanner code
D. S. Papailiopoulos and A. G. Dimakis, “Locally Repairable Codes”, (2014) arXiv:1206.3804. Appears in: Optimal LRC
T. Parella-Dilmé, K. Kottmann, L. Zambrano, L. Mortimer, J. S. Kottmann, and A. Acín, “Reducing Entanglement with Physically Inspired Fermion-To-Qubit Mappings”, PRX Quantum 5, (2024) arXiv:2311.07409 DOI. Appears in: Fermion-into-qubit code
F. Parisen Toldin, A. Pelissetto, and E. Vicari, “Strong-Disorder Paramagnetic-Ferromagnetic Fixed Point in the Square-Lattice ±J Ising Model”, Journal of Statistical Physics 135, 1039 (2009) arXiv:0811.2101 DOI. Appears in: Toric code
M. Park, N. Maskara, M. Kalinowski, and M. D. Lukin, “Enhancing quantum memory lifetime with measurement-free local error correction and reinforcement learning”, Physical Review A 111, (2025) arXiv:2408.09524 DOI. Appears in: Loop toric code, Repetition code
P. Parrado-Rodríguez, M. Rispler, and M. Müller, “Rescaling decoder for two-dimensional topological quantum color codes on 4.8.8 lattices”, Physical Review A 106, (2022) arXiv:2112.09584 DOI. Appears in: Honeycomb (6.6.6) color code
F. Parvaresh and A. Vardy, “Correcting Errors Beyond the Guruswami-Sudan Radius in Polynomial Time”, 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS’05) 285 DOI. Appears in: Folded RS (FRS) code, Parvaresh-Vardy (PV) code
F. Parvaresh and B. Hassibi, “Explicit measurements with almost optimal thresholds for compressed sensing”, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing 3853 (2008) DOI. Appears in: Analog RS code
A. Passerini, M. Pontil, and P. Frasconi, “New Results on Error Correcting Output Codes of Kernel Machines”, IEEE Transactions on Neural Networks 15, 45 (2004) DOI. Appears in: Error-correcting output code (ECOC)
F. Pastawski, A. Kay, N. Schuch, and I. Cirac, “Limitations of Passive Protection of Quantum Information”, (2009) arXiv:0911.3843. Appears in: 2D lattice stabilizer code, Self-correcting quantum code
F. Pastawski, A. Kay, N. Schuch, and I. Cirac, “How Long Can a Quantum Memory Withstand Depolarizing Noise?”, Physical Review Letters 103, (2009) arXiv:0904.4861 DOI. Appears in: Self-correcting quantum code
F. Pastawski, L. Clemente, and J. I. Cirac, “Quantum memories based on engineered dissipation”, Physical Review A 83, (2011) arXiv:1010.2901 DOI. Appears in: Loop toric code
F. Pastawski, B. Yoshida, D. Harlow, and J. Preskill, “Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence”, Journal of High Energy Physics 2015, (2015) arXiv:1503.06237 DOI. Appears in: Pastawski-Yoshida-Harlow-Preskill (HaPPY) code, Hexacode, Holographic code, Holographic tensor-network code, Qubit stabilizer code, Five-qubit perfect code
F. Pastawski and B. Yoshida, “Fault-tolerant logical gates in quantum error-correcting codes”, Physical Review A 91, (2015) arXiv:1408.1720 DOI. Appears in: Modular-qudit code, Self-correcting quantum code, Lattice stabilizer code, Lattice subsystem code
F. Pastawski and J. Preskill, “Error correction for encoded quantum annealing”, Physical Review A 93, (2016) arXiv:1511.00004 DOI. Appears in: Lechner-Hauke-Zoller (LHZ) code
F. Pastawski and J. Preskill, “Code Properties from Holographic Geometries”, Physical Review X 7, (2017) arXiv:1612.00017 DOI. Appears in: Approximate operator-algebra QECC, Holographic code, Holographic tensor-network code
F. Pastawski, J. Eisert, and H. Wilming, “Towards Holography via Quantum Source-Channel Codes”, Physical Review Letters 119, (2017) arXiv:1611.07528 DOI. Appears in: Conformal-field theory (CFT) code
D. Pataki, Á. Márton, J. K. Asbóth, and A. Pályi, “Coherent errors in stabilizer codes caused by quasistatic phase damping”, Physical Review A 110, (2024) arXiv:2401.04530 DOI. Appears in: Kitaev surface code
A. Patel, “Maximal&lt;tex&gt;q&lt;/tex&gt;-nary linear codes with large minimum distance (Corresp.)”, IEEE Transactions on Information Theory 21, 106 (1975) DOI. Appears in: $q$-ary simplex code, $[2^m-1,m,2^{m-1}]$ simplex code, Two-weight code
M. V. Patil, S. Pawar, and Z. Saquib, “Coding Techniques for 5G Networks: A Review”, 2020 3rd International Conference on Communication System, Computing and IT Applications (CSCITA) 208 (2020) DOI. Appears in: Quasi-cyclic LDPC (QC-LDPC) code
B. Pato, T. Tansuwannont, and K. R. Brown, “Concatenated Steane code with single-flag syndrome checks”, Physical Review A 110, (2024) arXiv:2403.09978 DOI. Appears in: Concatenated Steane code
B. Pato, T. Tansuwannont, S. Huang, and K. R. Brown, “Optimization Tools for Distance-Preserving Flag Fault-Tolerant Error Correction”, PRX Quantum 5, (2024) arXiv:2306.12862 DOI. Appears in: Qubit CSS code
B. Pato, J. W. Staples Jr., and K. R. Brown, “Logical coherence in 2D compass codes”, (2024) arXiv:2405.09287. Appears in: Compass code
A. Patra and A. Barg, “Targeted Clifford logical gates for hypergraph product codes”, (2024) arXiv:2411.17050. Appears in: Hypergraph product (HGP) code
M. K. Patra and S. L. Braunstein, “An algebraic framework for information theory: Classical Information”, (2009) arXiv:0910.1536. Appears in: Classical-quantum (c-q) code, Error-correcting code (ECC)
N. Patterson, “The algebraic decoding of Goppa codes”, IEEE Transactions on Information Theory 21, 203 (1975) DOI. Appears in: Goppa code
C. A. Pattison, M. E. Beverland, M. P. da Silva, and N. Delfosse, “Improved quantum error correction using soft information”, (2021) arXiv:2107.13589. Appears in: Kitaev surface code
C. A. Pattison, A. Krishna, and J. Preskill, “Hierarchical memories: Simulating quantum LDPC codes with local gates”, (2023) arXiv:2303.04798. Appears in: Hierarchical code
C. A. Pattison, G. Baranes, J. P. B. Ataides, M. D. Lukin, and H. Zhou, “Fast quantum interconnects via constant-rate entanglement distillation”, (2024) arXiv:2408.15936. Appears in: $[[2m,2m-2,2]]$ error-detecting code, $[[2^r, 2^r-r-2, 3]]$ Gottesman code
Paul E. Black, “Dictionary of Algorithms and Data Structures (DADS)”, (2023) DOI. Appears in: Superimposed code
J. P. Paz and W. H. Zurek, “Continuous Error Correction”, (1997) arXiv:quant-ph/9707049. Appears in: Qubit stabilizer code
J. P. Paz and W. H. Zurek, “Continuous error correction”, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 454, 355 (1998) DOI. Appears in: Finite-dimensional quantum error-correcting code
J. P. Paz, A. J. Roncaglia, and M. Saraceno, “Qubits in phase space: Wigner-function approach to quantum-error correction and the mean-king problem”, Physical Review A 72, (2005) arXiv:quant-ph/0410117 DOI. Appears in: Galois-qudit code, Modular-qudit stabilizer code
G. A. Paz-Silva, G. K. Brennen, and J. Twamley, “Fault Tolerance with Noisy and Slow Measurements and Preparation”, Physical Review Letters 105, (2010) arXiv:1002.1536 DOI. Appears in: Qubit CSS code
J. Pearl, “Reverend Bayes on Inference Engines: A Distributed Hierarchical Approach”, Probabilistic and Causal Inference 129 (2022) DOI. Appears in: Luby transform (LT) code
Pearl, J. (2022). Reverend Bayes on inference engines: A distributed hierarchical approach. In Probabilistic and Causal Inference: The Works of Judea Pearl (pp. 129-138).. Appears in: Low-density parity-check (LDPC) code
L. Pecorari, S. Jandura, G. K. Brennen, and G. Pupillo, “High-rate quantum LDPC codes for long-range-connected neutral atom registers”, Nature Communications 16, (2025) arXiv:2404.13010 DOI. Appears in: La-cross code
T. Peham, L. Schmid, L. Berent, M. Müller, and R. Wille, “Automated Synthesis of Fault-Tolerant State Preparation Circuits for Quantum Error Correction Codes”, (2024) arXiv:2408.11894. Appears in: Qubit CSS code
R. Peierls, “On Ising’s model of ferromagnetism”, Mathematical Proceedings of the Cambridge Philosophical Society 32, 477 (1936) DOI. Appears in: Self-correcting quantum code
R. Pellikaan, “The shift bound for cyclic, Reed-Muller and geometric Goppa codes”, Arithmetic, Geometry, and Coding Theory DOI. Appears in: Evaluation AG code
R. Pellikaan, “On a decoding algorithm for codes on maximal curves”, IEEE Transactions on Information Theory 35, 1228 (1989) DOI. Appears in: Evaluation AG code
R. Pellikaan, “On decoding by error location and dependent sets of error positions”, Discrete Mathematics 106–107, 369 (1992) DOI. Appears in: Linear $q$-ary code
R. Pellikan, B.-Z. Shen, and G. J. M. van Wee, “Which linear codes are algebraic-geometric?”, IEEE Transactions on Information Theory 37, 583 (1991) DOI. Appears in: Evaluation AG code, Linear $q$-ary code
R.-H. Peng and R.-R. Chen, “Design of Nonbinary Quasi-Cyclic LDPC Cycle Codes”, 2007 IEEE Information Theory Workshop (2007) DOI. Appears in: $q$-ary LDPC code
A. M. Perelomov, “Coherent states and theta functions”, Functional Analysis and Its Applications 6, 292 (1973) DOI. Appears in: Square-lattice GKP code
A. M. Perelomov, “On the completeness of a system of coherent states”, (2002) arXiv:math-ph/0210005. Appears in: Bosonic code
A. Perelomov, Generalized Coherent States and Their Applications (Springer Berlin Heidelberg, 1986) DOI. Appears in: Square-lattice GKP code
A. Peres, “Reversible logic and quantum computers”, Physical Review A 32, 3266 (1985) DOI. Appears in: Quantum repetition code
A. Peres, “Unitary dynamics for quantum codewords”, (1996) arXiv:quant-ph/9609015. Appears in: Subsystem QECC
S. M. Perez-Garcia and A. Montanaro, “Quantum-enhanced belief propagation for LDPC decoding”, (2024) arXiv:2412.08596. Appears in: Low-density parity-check (LDPC) code
I. Z. Pesenson and D. Geller, “Cubature formulas and discrete fourier transform on compact manifolds”, (2011) arXiv:1111.5900. Appears in: $t$-design
Petar Maymounkov, Online codes, Technical report, New York University, 2002.. Appears in: Raptor (RAPid TORnado) code
Peter Elias. Coding for noisy channels. IRE Convention Records, 3(4):37–46, 1955.. Appears in: Convolutional code
C. Peters, “Information-Set Decoding for Linear Codes over F q”, Lecture Notes in Computer Science 81 (2010) DOI. Appears in: Linear $q$-ary code
Peter W. Shor, The quantum channel capacity and coherent information, 2002 (obtained from the MSRI Workshop on Quantum Computation website).. Appears in: Haar-random qubit code, Quantum error-correcting code (QECC)
W. Peterson, “Encoding and error-correction procedures for the Bose-Chaudhuri codes”, IEEE Transactions on Information Theory 6, 459 (1960) DOI. Appears in: Binary BCH code, Bose–Chaudhuri–Hocquenghem (BCH) code, Reed-Solomon (RS) code
W. Peterson and D. Brown, “Cyclic Codes for Error Detection”, Proceedings of the IRE 49, 228 (1961) DOI. Appears in: Cyclic redundancy check (CRC) code
W. W. Peterson and E. J. Weldon, Error-correcting codes. MIT press 1972.. Appears in: Binary BCH code, Cyclic redundancy check (CRC) code, Cyclic code, Bose–Chaudhuri–Hocquenghem (BCH) code
D. Petz, “Sufficient subalgebras and the relative entropy of states of a von Neumann algebra”, Communications in Mathematical Physics 105, 123 (1986) DOI. Appears in: Approximate quantum error-correcting code (AQECC)
D. PETZ, “SUFFICIENCY OF CHANNELS OVER VON NEUMANN ALGEBRAS”, The Quarterly Journal of Mathematics 39, 97 (1988) DOI. Appears in: Approximate quantum error-correcting code (AQECC)
H. Pfeiffer, “Higher gauge theory and a non-Abelian generalization of 2-form electrodynamics”, Annals of Physics 308, 447 (2003) arXiv:hep-th/0304074 DOI. Appears in: Two-gauge theory code
H. D. Pfister, I. Sason, and R. Urbanke, “Capacity-Achieving Ensembles for the Binary Erasure Channel With Bounded Complexity”, IEEE Transactions on Information Theory 51, 2352 (2005) DOI. Appears in: Irregular repeat-accumulate (IRA) code
H. D. Pfister, C. Piveteau, J. M. Renes, and N. Rengaswamy, “Belief Propagation for Classical and Quantum Systems: Overview and Recent Results”, IEEE BITS the Information Theory Magazine 2, 20 (2022) DOI. Appears in: Qubit c-q code, Kitaev surface code
K. T. Phelps, “A Combinatorial Construction of Perfect Codes”, SIAM Journal on Algebraic Discrete Methods 4, 398 (1983) DOI. Appears in: Perfect code, Perfect binary code
K. T. Phelps, “Every finite group is the automorphism group of some perfect code”, Journal of Combinatorial Theory, Series A 43, 45 (1986) DOI. Appears in: Perfect binary code
K. T. Phelps, “Combinatorial designs and perfect codes”, Electronic Notes in Discrete Mathematics 10, 220 (2001) DOI. Appears in: Combinatorial design, Perfect code
T. G. Philbin, “Generalized coherent states”, American Journal of Physics 82, 742 (2014) arXiv:1311.1920 DOI. Appears in: Two-component cat code
G. Philippe and Z. Gilles, “On the hardness of the decoding and the minimum distance problems for rank codes”, (2014) arXiv:1404.3482. Appears in: Rank-metric code
N. Pippenger, “On networks of noisy gates”, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985) (1985) DOI. Appears in: Repetition code
N. Pippenger, “Reliable computation by formulas in the presence of noise”, IEEE Transactions on Information Theory 34, 194 (1988) DOI. Appears in: Repetition code
S. Pirandola, S. Mancini, S. L. Braunstein, and D. Vitali, “Minimal qudit code for a qubit in the phase-damping channel”, Physical Review A 77, (2008) arXiv:0705.1099 DOI. Appears in: Perfect quantum code, Modular-qudit GKP code, Modular-qudit shift-resistant code
S. Pirandola, R. García-Patrón, S. L. Braunstein, and S. Lloyd, “Direct and Reverse Secret-Key Capacities of a Quantum Channel”, Physical Review Letters 102, (2009) arXiv:0809.3273 DOI. Appears in: Bosonic code
S. Pirandola, R. Laurenza, C. Ottaviani, and L. Banchi, “Fundamental limits of repeaterless quantum communications”, Nature Communications 8, (2017) arXiv:1510.08863 DOI. Appears in: Bosonic code, Qubit code
S. Pirandola, S. L. Braunstein, R. Laurenza, C. Ottaviani, T. P. W. Cope, G. Spedalieri, and L. Banchi, “Theory of channel simulation and bounds for private communication”, Quantum Science and Technology 3, 035009 (2018) arXiv:1711.09909 DOI. Appears in: Bosonic code
P. Piret, “Bounds for codes over the unit circle”, IEEE Transactions on Information Theory 32, 760 (1986) DOI. Appears in: Polyphase code
Piret, Philippe. Convolutional codes: an algebraic approach. MIT press, 1988.. Appears in: Convolutional code, Reed-Solomon (RS) code
L. Piroli, G. Styliaris, and J. I. Cirac, “Approximating Many-Body Quantum States with Quantum Circuits and Measurements”, Physical Review Letters 133, (2024) arXiv:2403.07604 DOI. Appears in: PI qubit code
T. B. Pittman, B. C. Jacobs, and J. D. Franson, “Demonstration of quantum error correction using linear optics”, Physical Review A 71, (2005) arXiv:quant-ph/0502042 DOI. Appears in: Quantum repetition code
C. Piveteau and J. M. Renes, “Quantum message-passing algorithm for optimal and efficient decoding”, Quantum 6, 784 (2022) arXiv:2109.08170 DOI. Appears in: Qubit c-q code
C. Piveteau, C. T. Chubb, and J. M. Renes, “Tensor-Network Decoding Beyond 2D”, PRX Quantum 5, (2024) arXiv:2310.10722 DOI. Appears in: 3D surface code
B. Placke, T. Rakovszky, N. P. Breuckmann, and V. Khemani, “Topological Quantum Spin Glass Order and its realization in qLDPC codes”, (2024) arXiv:2412.13248. Appears in: Dinur-Lin-Vidick (DLV) code, Expander LP code, Quantum expander code, Topological code
B. Placke and S. A. Parameswaran, “Slow measurement-only dynamics of entanglement in Pauli subsystem codes”, (2024) arXiv:2405.14927. Appears in: 3D Bacon-Shor code, CSS-Plaquette code
J. S. Plank and M. Blaum, “Sector-Disk (SD) Erasure Codes for Mixed Failure Modes in RAID Systems”, ACM Transactions on Storage 10, 1 (2014) DOI. Appears in: Maximally recoverable (MR) code
M. B. Plenio, V. Vedral, and P. L. Knight, “Quantum error correction in the presence of spontaneous emission”, Physical Review A 55, 67 (1997) arXiv:quant-ph/9603022 DOI. Appears in: Constant-excitation (CE) code, $((8,1,3))$ Plenio-Vedral-Knight CE code
M. B. Plenio, V. Vedral, and P. L. Knight, “Conditional generation of error syndromes in fault-tolerant error correction”, Physical Review A 55, 4593 (1997) arXiv:quant-ph/9608028 DOI. Appears in: Five-qubit perfect code
V. Pless, “The Weight of the Symmetry Code for p=29 and the 5‐Designs Contained Therein”, Annals of the New York Academy of Sciences 175, 310 (1970) DOI. Appears in: Combinatorial design, Pless symmetry code
V. Pless, “Symmetry codes over GF(3) and new five-designs”, Journal of Combinatorial Theory, Series A 12, 119 (1972) DOI. Appears in: Combinatorial design, Pless symmetry code
V. Pless, “Decoding the Golay codes”, IEEE Transactions on Information Theory 32, 561 (1986) DOI. Appears in: $[24, 12, 8]$ Extended Golay code, Hexacode, Ternary Golay code, Tetracode
V. Pless, “Q-codes”, Journal of Combinatorial Theory, Series A 43, 258 (1986) DOI. Appears in: $q$-ary duadic code
V. Pless, “Duadic Codes and Generalizations”, Eurocode ’92 3 (1993) DOI. Appears in: Binary duadic code, Binary quadratic-residue (QR) code, $q$-ary duadic code, Quadratic-residue (QR) code
V. Pless, On a new family of symmetry codes and related new five-designs, BAMS 75 (1969), 1339-1342. Appears in: Pless symmetry code
M. Plotkin, “Binary codes with specified minimum distance”, IEEE Transactions on Information Theory 6, 445 (1960) DOI. Appears in: $(u|u+v)$-construction code
S. Plugge, A. Rasmussen, R. Egger, and K. Flensberg, “Majorana box qubits”, New Journal of Physics 19, 012001 (2017) arXiv:1609.01697 DOI. Appears in: Majorana box qubit
H. C. Po, L. Fidkowski, A. Vishwanath, and A. C. Potter, “Radical chiral Floquet phases in a periodically driven Kitaev model and beyond”, Physical Review B 96, (2017) arXiv:1701.01440 DOI. Appears in: Kitaev honeycomb code
I. Pogorelov, F. Butt, L. Postler, C. D. Marciniak, P. Schindler, M. Müller, and T. Monz, “Experimental fault-tolerant code switching”, (2024) arXiv:2403.13732. Appears in: $[[10,1,2]]$ CSS code, $[[7,1,3]]$ Steane code
A. Polishchuk and D. A. Spielman, “Nearly-linear size holographic proofs”, Proceedings of the twenty-sixth annual ACM symposium on Theory of computing - STOC ’94 194 (1994) DOI. Appears in: Reed-Solomon (RS) code, Tensor-product code
H. Pollatsek and M. B. Ruskai, “Permutationally Invariant Codes for Quantum Error Correction”, (2004) arXiv:quant-ph/0304153. Appears in: $((7,2,3))$ Pollatsek-Ruskai code, Permutation-invariant (PI) code
F. Pollmann, E. Berg, A. M. Turner, and M. Oshikawa, “Symmetry protection of topological phases in one-dimensional quantum spin systems”, Physical Review B 85, (2012) arXiv:0909.4059 DOI. Appears in: Symmetry-protected topological (SPT) code
Y. Polyanskiy, H. V. Poor, and S. Verdu, “Channel Coding Rate in the Finite Blocklength Regime”, IEEE Transactions on Information Theory 56, 2307 (2010) DOI. Appears in: Error-correcting code (ECC)
Y. Polyanskiy and S. Verdu, “Channel dispersion and moderate deviations limits for memoryless channels”, 2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton) 1334 (2010) DOI. Appears in: Error-correcting code (ECC)
C. Poole, T. M. Graham, M. A. Perlin, M. Otten, and M. Saffman, “Architecture for fast implementation of qLDPC codes with optimized Rydberg gates”, (2024) arXiv:2404.18809. Appears in: Bivariate bicycle (BB) code
S. C. Porter, B.-Z. Shen, and R. Pellikaan, “Decoding geometric Goppa codes using an extra place”, IEEE Transactions on Information Theory 38, 1663 (1992) DOI. Appears in: Evaluation AG code
T. PORTER, “INTERPRETATIONS OF YETTER’S NOTION OF G-COLORING: SIMPLICIAL FIBRE BUNDLES AND NON-ABELIAN COHOMOLOGY”, Journal of Knot Theory and Its Ramifications 05, 687 (1996) DOI. Appears in: Two-gauge theory code
T. Porter, “Topological Quantum Field Theories from Homotopy n -Types”, Journal of the London Mathematical Society 58, 723 (1998) DOI. Appears in: Two-gauge theory code
Portnoi, S. L. "Characterizations of modulation and encoding systems as concatenated codes." Probl. Inform. Transm. 21.3 (1985): 14-27.. Appears in: Polyphase code
E. Portnoy, “Local Quantum Codes from Subdivided Manifolds”, (2023) arXiv:2303.06755. Appears in: Good QLDPC code, Lattice stabilizer code
S. T. Position. (2009) Common raid disk data format specification. [Online]. Available: https://www.snia.org/tech activities/standards/curr standards/ddf. Appears in: Array code, Reed-Solomon (RS) code
E.C. Posner, Combinatorial Structures in Planetary Reconnaissance in Error Correcting Codes, ed. H.B. Mann, Wiley, NY 1968.. Appears in: $[2^m,m+1,2^{m-1}]$ First-order RM code, Reed-Muller (RM) code
L. Postler et al., “Demonstration of fault-tolerant universal quantum gate operations”, Nature 605, 675 (2022) arXiv:2111.12654 DOI. Appears in: $[[7,1,3]]$ Steane code
L. Postler, F. Butt, I. Pogorelov, C. D. Marciniak, S. Heußen, R. Blatt, P. Schindler, M. Rispler, M. Müller, and T. Monz, “Demonstration of Fault-Tolerant Steane Quantum Error Correction”, PRX Quantum 5, (2024) arXiv:2312.09745 DOI. Appears in: Quantum repetition code, $[[7,1,3]]$ Steane code
K. Potdar, T. S., and C. D., “A Comparative Study of Categorical Variable Encoding Techniques for Neural Network Classifiers”, International Journal of Computer Applications 175, 7 (2017) DOI. Appears in: Error-correcting output code (ECOC), One-hot code
Potdar, Kedar, Taher S. Pardawala, and Chinmay D. Pai. "A comparative study of categorical variable encoding techniques for neural network classifiers." International journal of computer applications 175.4 (2017): 7-9.. Appears in: One-hot code
A. C. Potter and R. Vasseur, “Symmetry constraints on many-body localization”, Physical Review B 94, (2016) arXiv:1605.03601 DOI. Appears in: Abelian topological code, Lattice subsystem code
A. C. Potter and T. Morimoto, “Dynamically enriched topological orders in driven two-dimensional systems”, Physical Review B 95, (2017) arXiv:1610.03485 DOI. Appears in: Kitaev surface code
A. C. Potter and R. Vasseur, “Entanglement Dynamics in Hybrid Quantum Circuits”, Quantum Science and Technology 211 (2022) arXiv:2111.08018 DOI. Appears in: Random-circuit code
D. Poulin, “Stabilizer Formalism for Operator Quantum Error Correction”, Physical Review Letters 95, (2005) arXiv:quant-ph/0508131 DOI. Appears in: Generalized Shor code, Subsystem modular-qudit stabilizer code, Subsystem hypergraph product (SHP) code, Subsystem qubit stabilizer code
D. Poulin, “Optimal and efficient decoding of concatenated quantum block codes”, Physical Review A 74, (2006) arXiv:quant-ph/0606126 DOI. Appears in: Concatenated qubit code, Yoked surface code
D. Poulin and Y. Chung, “On the iterative decoding of sparse quantum codes”, (2008) arXiv:0801.1241. Appears in: Quantum LDPC (QLDPC) code
D. Poulin, J.-P. Tillich, and H. Ollivier, “Quantum serial turbo-codes”, (2009) arXiv:0712.2888. Appears in: Quantum turbo code
C. Poulliat, M. Fossorier, and D. Declercq, “Design of regular (2,d/sub c/)-LDPC codes over GF(q) using their binary images”, IEEE Transactions on Communications 56, 1626 (2008) DOI. Appears in: $q$-ary LDPC code
H. Poulsen Nautrup, N. Friis, and H. J. Briegel, “Fault-tolerant interface between quantum memories and quantum processors”, Nature Communications 8, (2017) arXiv:1609.08062 DOI. Appears in: Bacon-Shor code
J. F. Poyatos, J. I. Cirac, and P. Zoller, “Quantum Reservoir Engineering with Laser Cooled Trapped Ions”, Physical Review Letters 77, 4728 (1996) DOI. Appears in: Finite-dimensional quantum error-correcting code, Two-component cat code
P. Prabhu and B. W. Reichardt, “Distance-four quantum codes with combined postselection and error correction”, Physical Review A 110, (2024) arXiv:2112.03785 DOI. Appears in: Hypercube code, $[[16,6,4]]$ Tesseract color code
N. Prakash, G. M. Kamath, V. Lalitha, and P. V. Kumar, “Optimal Linear Codes with a Local-Error-Correction Property”, (2012) arXiv:1202.2414. Appears in: Code with locality
N. Prakash, V. Lalitha, and P. V. Kumar, “Codes with Locality for Two Erasures”, (2014) arXiv:1401.2422. Appears in: Sequential-recovery code
S. Prakash, “Magic state distillation with the ternary Golay code”, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, (2020) arXiv:2003.02717 DOI. Appears in: Graph quantum code, $[[23, 1, 7]]$ Quantum Golay code, $[[11,1,5]]_3$ qutrit Golay code
S. Prakash and T. Saha, “Low Overhead Qutrit Magic State Distillation”, (2024) arXiv:2403.06228. Appears in: Prime-qudit triorthogonal code, $[[9m-k,k,2]]_3$ triorthogonal code
E. Prange, “The use of information sets in decoding cyclic codes”, IEEE Transactions on Information Theory 8, 5 (1962) DOI. Appears in: Cyclic linear binary code, Cyclic linear $q$-ary code
E. Prange, An algorithm for factoring xn - I over a finite field. TN-59-/75, (October 1959). Appears in: Cyclic code
E. Prange, Cyclic Error-Correcting Codes in Two Symbols, TN-57-/03, (September 1957). Appears in: Cyclic code
E. Prange, Some cyclic error-correcting codes with simple decoding algorithms, TN-58-156, (April 1958). Appears in: Cyclic code
E. Prange, The use of coset equivalence in the analysis and decoding of group codes, TN-59-/64, (1959). Appears in: Cyclic code
E. Prange, The use of coset equivalene in the analysis and decoding of group codes. AIR FORCE CAMBRIDGE RESEARCH LABS HANSCOM AFB MA, 1959.. Appears in: Incidence-matrix projective code
E. Prange, "Some cyclic error-correcting codes with simple decoding algorithms." AFCRC-TN-58-156 (1985).. Appears in: Incidence-matrix projective code
“Preface to the Second Edition”, Quantum Information Theory xi (2016) arXiv:1106.1445 DOI. Appears in: Haar-random qubit code, Quantum error-correcting code (QECC)
F. P. Preparata, “A class of optimum nonlinear double-error-correcting codes”, Information and Control 13, 378 (1968) DOI. Appears in: Binary BCH code, Preparata code
J. Preskill, “Fault-tolerant quantum computation”, (1997) arXiv:quant-ph/9712048. Appears in: Quantum error-correcting code (QECC)
J. Preskill, “Reliable quantum computers”, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 454, 385 (1998) arXiv:quant-ph/9705031 DOI. Appears in: Concatenated qubit code, Qubit code
J. Preskill. Lecture notes on Quantum Computation. (1997–2020) URL. Appears in: $[[2m,2m-2,2]]$ error-detecting code, Quantum error-correcting code (QECC), Finite-dimensional quantum error-correcting code, Qubit CSS code, Qubit stabilizer code, Random stabilizer code, $[[2^{2r-1}-1,1,2^r-1]]$ quantum punctured Reed-Muller code
N. Presman, Simon Litsyn, "Polar codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI. Appears in: Polar code
W. H. Press, J. A. Hawkins, S. K. Jones Jr, J. M. Schaub, and I. J. Finkelstein, “HEDGES error-correcting code for DNA storage corrects indels and allows sequence constraints”, Proceedings of the National Academy of Sciences 117, 18489 (2020) DOI. Appears in: DNA storage code
M. Pretko, X. Chen, and Y. You, “Fracton phases of matter”, International Journal of Modern Physics A 35, 2030003 (2020) arXiv:2001.01722 DOI. Appears in: Fracton stabilizer code, Qudit cubic code
Proakis, John G., and Masoud Salehi. Digital communications. Vol. 4. New York: McGraw-hill, 2001.. Appears in: Modulation scheme
“Probabilistic Reasoning in Intelligent Systems”, (1988) DOI. Appears in: Low-density parity-check (LDPC) code
M. de W. Propitius, “Topological interactions in broken gauge theories”, (1995) arXiv:hep-th/9511195. Appears in: Cubic theory code, Abelian quantum-double stabilizer code, Dihedral $G=D_m$ quantum-double code, Abelian TQD stabilizer code
L. P. Pryadko, V. A. Shabashov, and V. K. Kozin, “QDistRnd: A GAP package for computing the distance of quantum error-correcting codes”, Journal of Open Source Software 7, 4120 (2022) arXiv:2308.15140 DOI. Appears in: Galois-qudit stabilizer code, Qubit stabilizer code
L. Pryadko and M. Woolls. Quantum_LDPC_Codes. https://github.com/QEC-pages/Quantum_LDPC_Codes, 2023.. Appears in: Quantum LDPC (QLDPC) code
K. L. Pudenz, T. Albash, and D. A. Lidar, “Error-corrected quantum annealing with hundreds of qubits”, Nature Communications 5, (2014) arXiv:1307.8190 DOI. Appears in: Quantum repetition code
K. L. Pudenz, T. Albash, and D. A. Lidar, “Quantum annealing correction for random Ising problems”, Physical Review A 91, (2015) arXiv:1408.4382 DOI. Appears in: Quantum repetition code
O. Pujol, S. Escalera, and P. Radeva, “An incremental node embedding technique for error correcting output codes”, Pattern Recognition 41, 713 (2008) DOI. Appears in: Error-correcting output code (ECOC)
S. Puri, S. Boutin, and A. Blais, “Engineering the quantum states of light in a Kerr-nonlinear resonator by two-photon driving”, npj Quantum Information 3, (2017) arXiv:1605.09408 DOI. Appears in: Hamiltonian-based code, Two-component cat code
S. Puri, A. Grimm, P. Campagne-Ibarcq, A. Eickbusch, K. Noh, G. Roberts, L. Jiang, M. Mirrahimi, M. H. Devoret, and S. M. Girvin, “Stabilized Cat in a Driven Nonlinear Cavity: A Fault-Tolerant Error Syndrome Detector”, Physical Review X 9, (2019) arXiv:1807.09334 DOI. Appears in: Qubit stabilizer code, Two-component cat code
S. Puri et al., “Bias-preserving gates with stabilized cat qubits”, Science Advances 6, (2020) arXiv:1905.00450 DOI. Appears in: Asymmetric quantum code, Concatenated cat code, Cat-repetition code, Quantum repetition code, Two-component cat code
R. Purnamasari, H. Wijanto, and I. Hidayat, “Design and implementation of LDPC(Low Density Parity Check) coding technique on FPGA (Field Programmable Gate Array) for DVB-S2 (Digital Video Broadcasting-Satellite)”, 2014 IEEE International Conference on Aerospace Electronics and Remote Sensing Technology 83 (2014) DOI. Appears in: Irregular repeat-accumulate (IRA) code
H. Putterman, J. Iverson, Q. Xu, L. Jiang, O. Painter, F. G. S. L. Brandão, and K. Noh, “Stabilizing a Bosonic Qubit Using Colored Dissipation”, Physical Review Letters 128, (2022) arXiv:2107.09198 DOI. Appears in: Two-component cat code
H. Putterman et al., “Hardware-efficient quantum error correction using concatenated bosonic qubits”, (2024) arXiv:2409.13025. Appears in: Cat-repetition code
H. Putterman et al., “Preserving phase coherence and linearity in cat qubits with exponential bit-flip suppression”, (2024) arXiv:2409.17556. Appears in: Two-component cat code
M. Puviani, S. Borah, R. Zen, J. Olle, and F. Marquardt, “Non-Markovian Feedback for Optimized Quantum Error Correction”, Physical Review Letters 134, (2025) arXiv:2312.07391 DOI. Appears in: Square-lattice GKP code
X.-L. Qi and Z. Yang, “Space-time random tensor networks and holographic duality”, (2018) arXiv:1801.05289. Appears in: Holographic tensor-network code, Random stabilizer code
J. Qian and L. Zhang, “Entanglement-assisted quantum codes from arbitrary binary linear codes”, Designs, Codes and Cryptography 77, 193 (2014) DOI. Appears in: Linear binary code, EA qubit stabilizer code, Maximal-entanglement EA Galois-qudit stabilizer code
W. Qin, A. Miranowicz, H. Jing, and F. Nori, “Generating Long-Lived Macroscopically Distinct Superposition States in Atomic Ensembles”, Physical Review Letters 127, (2021) arXiv:2101.03662 DOI. Appears in: Spin cat code
Y. Qiu and Z. Wang, “Ground subspaces of topological phases of matter as error correcting codes”, Annals of Physics 422, 168318 (2020) arXiv:2004.11982 DOI. Appears in: String-net code
D.-X. Quan, L.-L. Zhu, C.-X. Pei, and B. C. Sanders, “Fault-tolerant conversion between adjacent Reed–Muller quantum codes based on gauge fixing”, Journal of Physics A: Mathematical and Theoretical 51, 115305 (2018) arXiv:1703.03860 DOI. Appears in: $[[15,1,3]]$ quantum Reed-Muller code, $[[7,1,3]]$ Steane code
“Quantum computers and dissipation”, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 452, 567 (1996) arXiv:quant-ph/9702001 DOI. Appears in: Dual-rail quantum code
“Quantum Error Correction”, Artificial Intelligence and Quantum Computing for Advanced Wireless Networks 451 (2022) DOI. Appears in: Quantum error-correcting code (QECC)
Quantum Information and Computation 14, (2014) arXiv:1308.1463 DOI. Appears in: Fermion code
Quantum Information and Computation 18, (2018) arXiv:1705.08957 DOI. Appears in: $[[4,2,2]]$ Four-qubit code
Quantum Information and Computation 18, (2018) arXiv:1709.02789 DOI. Appears in: Cycle code, Qubit BCH code, Qubit CSS code, $[[3k + 8, k, 2]]$ triorthogonal code, $[[4,2,2]]$ Four-qubit code, $[[6,2,2]]$ $C_6$ code
Quantum Information and Computation 19, (2019) arXiv:1712.08578 DOI. Appears in: Golden code
QuantumSavory. https://github.com/QuantumSavory, 2025.. Appears in: Qubit stabilizer code
S. L. A. de Queiroz, “Multicritical point of Ising spin glasses on triangular and honeycomb lattices”, Physical Review B 73, (2006) arXiv:cond-mat/0510816 DOI. Appears in: Subsystem surface code
S. L. A. de Queiroz, “Location and properties of the multicritical point in the Gaussian and±JIsing spin glasses”, Physical Review B 79, (2009) arXiv:0902.4153 DOI. Appears in: Toric code
N. Quetschlich, L. Burgholzer, and R. Wille, “Compiler Optimization for Quantum Computing Using Reinforcement Learning”, 2023 60th ACM/IEEE Design Automation Conference (DAC) (2023) arXiv:2212.04508 DOI. Appears in: Qubit code
A. O. Quintavalle, M. Vasmer, J. Roffe, and E. T. Campbell, “Single-Shot Error Correction of Three-Dimensional Homological Product Codes”, PRX Quantum 2, (2021) arXiv:2009.11790 DOI. Appears in: 3D surface code, Homological product code, Quantum LDPC (QLDPC) code, Single-shot code
A. O. Quintavalle and E. T. Campbell, “ReShape: a decoder for hypergraph product codes”, (2022) arXiv:2105.02370. Appears in: Hypergraph product (HGP) code
A. O. Quintavalle, P. Webster, and M. Vasmer, “Partitioning qubits in hypergraph product codes to implement logical gates”, Quantum 7, 1153 (2023) arXiv:2204.10812 DOI. Appears in: Hypergraph product (HGP) code
B. Qvist. Some remarks concerning curves of the second degree in a finite plane. Suomalainen tiedeakatemia, 1952.. Appears in: Ovoid code
J. M. Radcliffe, “Some properties of coherent spin states”, Journal of Physics A: General Physics 4, 313 (1971) DOI. Appears in: Two-mode binomial code
M. Raginsky, “Almost any quantum spin system with short-range interactions can support toric codes”, Physics Letters A 294, 153 (2002) arXiv:quant-ph/0111035 DOI. Appears in: Commuting-projector Hamiltonian code, Hamiltonian-based code, Topological code
M. Raginsky, “Scaling and Renormalization in Fault-Tolerant Quantum Computers”, Quantum Information Processing 2, 249 (2003) arXiv:quant-ph/0307166 DOI. Appears in: Qubit code
B. Rahn, A. C. Doherty, and H. Mabuchi, “Exact and Approximate Performance of Concatenated Quantum Codes”, (2001) arXiv:quant-ph/0111003. Appears in: Concatenated Steane code, Concatenated qubit code, Five-qubit perfect code
B. Rahn, A. C. Doherty, and H. Mabuchi, “Exact performance of concatenated quantum codes”, Physical Review A 66, (2002) arXiv:quant-ph/0206061 DOI. Appears in: Concatenated Steane code, Concatenated qubit code, Five-qubit perfect code
O. Raii, F. Mintert, and D. Burgarth, “Scalable quantum control and non-Abelian anyon creation in the Kitaev honeycomb model”, Physical Review A 106, (2022) arXiv:2205.10114 DOI. Appears in: Kitaev honeycomb code
E. M. Rains, “Quantum Weight Enumerators”, (1996) arXiv:quant-ph/9612015. Appears in: Qubit code
E. M. Rains, “Quantum shadow enumerators”, (1997) arXiv:quant-ph/9611001. Appears in: Block quantum code, Good QLDPC code, Qubit code
E. M. Rains, “Nonbinary quantum codes”, (1997) arXiv:quant-ph/9703048. Appears in: Perfect-tensor code, Quantum quadratic-residue (QR) code, Quantum maximum-distance-separable (MDS) code, Qubit stabilizer code, $[[5,1,3]]_{\mathbb{Z}_q}$ modular-qudit code, Modular-qudit CSS code, Hermitian qubit code, Hermitian Galois-qudit code
E. M. Rains, “Quantum codes of minimum distance two”, (1997) arXiv:quant-ph/9704043. Appears in: $[[2m,2m-2,2]]$ error-detecting code, $((5,6,2))$ qubit code, Qubit code, $((5+2r,3\times 2^{2r+1},2))$ Rains code, Small-distance block quantum code, $[[4,2,2]]$ Four-qubit code, Five-qubit perfect code, Hermitian qubit code
E. M. Rains, R. H. Hardin, P. W. Shor, and N. J. A. Sloane, “A Nonadditive Quantum Code”, Physical Review Letters 79, 953 (1997) arXiv:quant-ph/9703002 DOI. Appears in: Galois-qudit USt code, Union stabilizer (USt) code, $((5,6,2))$ qubit code, $((5+2r,3\times 2^{2r+1},2))$ Rains code
E. M. Rains and N. J. A. Sloane, “The Shadow Theory of Modular and Unimodular Lattices”, Journal of Number Theory 73, 359 (1998) DOI. Appears in: Unimodular lattice
E. M. Rains, “Shadow bounds for self-dual codes”, IEEE Transactions on Information Theory 44, 134 (1998) DOI. Appears in: Self-dual linear code
E. M. Rains and N. J. A. Sloane, “Self-Dual Codes”, (2002) arXiv:math/0208001. Appears in: Octacode
E. Rains, private communication, April 1997.. Appears in: $[[13,1,5]]$ cyclic code, Hermitian qubit code
E. M. Rains and N. J. A. Sloane, “Self-dual codes,” in Handbook of Coding Theory, eds. V. S. Pless and W. C. Huffman. Amsterdam: Elsevier, 1998, pp. 177–294.. Appears in: $[24, 12, 8]$ Extended Golay code, Self-dual linear code, $[48,24,12]$ self-dual code, Self-dual additive code
Z. Raissi, C. Gogolin, A. Riera, and A. Acín, “Optimal quantum error correcting codes from absolutely maximally entangled states”, Journal of Physics A: Mathematical and Theoretical 51, 075301 (2018) arXiv:1701.03359 DOI. Appears in: Perfect-tensor code, Galois-qudit RS code, Maximum distance separable (MDS) code, Quantum maximum-distance-separable (MDS) code, Modular-qudit cluster-state code
Z. Raissi, “Modifying Method of Constructing Quantum Codes From Highly Entangled States”, IEEE Access 8, 222439 (2020) arXiv:2005.01426 DOI. Appears in: Perfect-tensor code, Three-qutrit code, Hermitian qubit code
A. B. Raj and A. K. Majumder, “Historical perspective of free space optical communications: from the early dates to today’s developments”, IET Communications 13, 2405 (2019) DOI. Appears in: Pulse-position modulation (PPM) code
G. Rajpoot, K. Kumari, and S. R. Jain, “Quantum error correction beyond the toric code: dynamical systems meet encoding”, The European Physical Journal Special Topics 233, 1341 (2023) arXiv:2307.04418 DOI. Appears in: Kitaev surface code
A. Rajput, A. Roggero, and N. Wiebe, “Quantum Error Correction with Gauge Symmetries”, (2022) arXiv:2112.05186. Appears in: Gauss' law code, Concatenated qubit code
T. Rakovszky and V. Khemani, “The Physics of (good) LDPC Codes I. Gauging and dualities”, (2023) arXiv:2310.16032. Appears in: Qubit CSS code, Abelian topological code, Lattice stabilizer code
T. Rakovszky and V. Khemani, “The Physics of (good) LDPC Codes II. Product constructions”, (2024) arXiv:2402.16831. Appears in: Balanced product (BP) code, Fracton stabilizer code, Good QLDPC code, Hypergraph product (HGP) code, Newman-Moore code, Quantum repetition code, Repetition code, Sierpinsky fractal spin-liquid (SFSL) code, Abelian topological code, X-cube model code
P. Rall, “Signed quantum weight enumerators characterize qubit magic state distillation”, (2017) arXiv:1702.06990. Appears in: Qubit code, Hermitian qubit code
T. C. Ralph, A. Gilchrist, G. J. Milburn, W. J. Munro, and S. Glancy, “Quantum computation with optical coherent states”, Physical Review A 68, (2003) arXiv:quant-ph/0306004 DOI. Appears in: Coherent-state repetition code, Quantum repetition code, Two-component cat code
T. C. Ralph, A. J. F. Hayes, and A. Gilchrist, “Loss-Tolerant Optical Qubits”, Physical Review Letters 95, (2005) arXiv:quant-ph/0501184 DOI. Appears in: Amplitude-damping (AD) code, Dual-rail quantum code, Generalized Shor code, Quantum parity code (QPC), Concatenated qubit code, $[[4,2,2]]$ Four-qubit code
V. Ramkumar, N. Raviv, and I. Tamo, “$\varepsilon$-MSR Codes for Any Set of Helper Nodes”, (2024) arXiv:2408.16584. Appears in: MDS array code, Minimum-storage regenerating (MSR) code
V. Ramkumar, M. Vajha, S. B. Balaji, M. Nikhil Krishnan, B. Sasidharan, P. Vijay Kumar, "Codes for Distributed Storage." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI. Appears in: Code with locality, Distributed-storage code, Locally recoverable code (LRC), Pyramid code, Linear $q$-ary code
H. Randriambololona, “(2,1)-separating systems beyond the probabilistic bound”, (2012) arXiv:1010.5764. Appears in: Evaluation AG code, Frameproof (FP) code
H. Randriambololona, “The syzygy distinguisher”, (2024) arXiv:2407.15740. Appears in: Goppa code
R. A. Rankin, “On the Closest Packing of Spheres in n Dimensions”, The Annals of Mathematics 48, 1062 (1947) DOI. Appears in: Spherical code
R. A. Rankin, “The Closest Packing of Spherical Caps in n Dimensions”, Proceedings of the Glasgow Mathematical Association 2, 139 (1955) DOI. Appears in: Spherical code
C. R. Rao, “Factorial Experiments Derivable from Combinatorial Arrangements of Arrays”, Supplement to the Journal of the Royal Statistical Society 9, 128 (1947) DOI. Appears in: Orthogonal array (OA)
C. R. Rao, “On a Class of Arrangements”, Proceedings of the Edinburgh Mathematical Society 8, 119 (1949) DOI. Appears in: Orthogonal array (OA)
C. R. RAO, “Some Combinatorial Problems of Arrays and Applications to Design of Experiments††Paper read at the International Symposium on Combinatorial Mathematics and its Applications, Fort Collins, Colorado, September 1971.”, A Survey of Combinatorial Theory 349 (1973) DOI. Appears in: Mixed code, Orthogonal array (OA)
C. R. Rao, Hypercubes of strength d leading to confounded designs in factorial experiments. Bull. Calcutta Math. Soc., 38, 67-78.. Appears in: Orthogonal array (OA)
K. V. Rashmi, N. B. Shah, and P. V. Kumar, “Optimal Exact-Regenerating Codes for Distributed Storage at the MSR and MBR Points via a Product-Matrix Construction”, IEEE Transactions on Information Theory 57, 5227 (2011) arXiv:1005.4178 DOI. Appears in: Product-matrix (PM) code
Rasmus R. Nielsen. List decoding of linear block codes. PhD thesis, Technical University of Denmark, 2001. Appears in: Multiplicity code
L. Rastanawi and G. Rote, “Towards a Geometric Understanding of the 4-Dimensional Point Groups”, (2022) arXiv:2205.04965. Appears in: 24-cell code, 600-cell code, Disphenoidal 288-cell code, Icosahedron code
S. A. Rather, A. Burchardt, W. Bruzda, G. Rajchel-Mieldzioć, A. Lakshminarayan, and K. Życzkowski, “Thirty-six Entangled Officers of Euler: Quantum Solution to a Classically Impossible Problem”, Physical Review Letters 128, (2022) arXiv:2104.05122 DOI. Appears in: Perfect-tensor code, $((3,6,2))_{\mathbb{Z}_6}$ Euler code
R. Raussendorf and H. J. Briegel, “A One-Way Quantum Computer”, Physical Review Letters 86, 5188 (2001) DOI. Appears in: Cluster-state code, Symmetry-protected topological (SPT) code, Square-lattice cluster-state code, Lattice stabilizer code
R. Raussendorf, D. Browne, and H. Briegel, “The one-way quantum computer--a non-network model of quantum computation”, Journal of Modern Optics 49, 1299 (2002) arXiv:quant-ph/0108118 DOI. Appears in: Cluster-state code, Symmetry-protected topological (SPT) code, Square-lattice cluster-state code, Lattice stabilizer code
R. Raussendorf and H. Briegel, “Computational model underlying the one-way quantum computer”, (2002) arXiv:quant-ph/0108067. Appears in: Cluster-state code
R. Raussendorf, D. E. Browne, and H. J. Briegel, “Measurement-based quantum computation on cluster states”, Physical Review A 68, (2003) arXiv:quant-ph/0301052 DOI. Appears in: Cluster-state code, Symmetry-protected topological (SPT) code, Lattice stabilizer code
R. Raussendorf, S. Bravyi, and J. Harrington, “Long-range quantum entanglement in noisy cluster states”, Physical Review A 71, (2005) arXiv:quant-ph/0407255 DOI. Appears in: Raussendorf-Bravyi-Harrington (RBH) cluster-state code
R. Raussendorf, J. Harrington, and K. Goyal, “A fault-tolerant one-way quantum computer”, Annals of Physics 321, 2242 (2006) arXiv:quant-ph/0510135 DOI. Appears in: Cluster-state code, Raussendorf-Bravyi-Harrington (RBH) cluster-state code, Kitaev surface code
R. Raussendorf, J. Harrington, and K. Goyal, “Topological fault-tolerance in cluster state quantum computation”, New Journal of Physics 9, 199 (2007) arXiv:quant-ph/0703143 DOI. Appears in: Cluster-state code, Raussendorf-Bravyi-Harrington (RBH) cluster-state code, Symmetry-protected topological (SPT) code, Kitaev surface code, Lattice stabilizer code
R. Raussendorf and J. Harrington, “Fault-Tolerant Quantum Computation with High Threshold in Two Dimensions”, Physical Review Letters 98, (2007) arXiv:quant-ph/0610082 DOI. Appears in: Cluster-state code, Raussendorf-Bravyi-Harrington (RBH) cluster-state code, Kitaev surface code
R. Raussendorf, “Key ideas in quantum error correction”, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370, 4541 (2012) DOI. Appears in: $[[15,1,3]]$ quantum Reed-Muller code, $[[7,1,3]]$ Steane code
R. Raussendorf, C. Okay, D.-S. Wang, D. T. Stephen, and H. P. Nautrup, “Computationally Universal Phase of Quantum Matter”, Physical Review Letters 122, (2019) arXiv:1803.00095 DOI. Appears in: Cluster-state code, Symmetry-protected topological (SPT) code, Square-lattice cluster-state code, Lattice stabilizer code
A. Ravagnani, “Rank-metric codes and their duality theory”, (2015) arXiv:1410.1333. Appears in: Gabidulin code, Rank-metric code
N. Raveendran and B. Vasić, “Trapping Sets of Quantum LDPC Codes”, Quantum 5, 562 (2021) arXiv:2012.15297 DOI. Appears in: Quantum LDPC (QLDPC) code
N. Raveendran, N. Rengaswamy, F. Rozpędek, A. Raina, L. Jiang, and B. Vasić, “Finite Rate QLDPC-GKP Coding Scheme that Surpasses the CSS Hamming Bound”, Quantum 6, 767 (2022) arXiv:2111.07029 DOI. Appears in: Abelian LP code, Concatenated GKP code, Gottesman-Kitaev-Preskill (GKP) code, Quasi-cyclic LDPC (QC-LDPC) code
N. Raveendran, N. Rengaswamy, A. K. Pradhan, and B. Vasić, “Soft Syndrome Decoding of Quantum LDPC Codes for Joint Correction of Data and Syndrome Errors”, (2022) arXiv:2205.02341. Appears in: Quantum LDPC (QLDPC) code
G. S. Ravi, J. M. Baker, A. Fayyazi, S. F. Lin, A. Javadi-Abhari, M. Pedram, and F. T. Chong, “Better Than Worst-Case Decoding for Quantum Error Correction”, (2022) arXiv:2208.08547. Appears in: Kitaev surface code
A. S. Rawat, Z. Song, A. G. Dimakis, and A. Gal, “Batch Codes Through Dense Graphs Without Short Cycles”, IEEE Transactions on Information Theory 62, 1592 (2016) DOI. Appears in: Batch code
P. Raynal, A. Kalev, J. Suzuki, and B.-G. Englert, “Encoding many qubits in a rotor”, Physical Review A 81, (2010) arXiv:1003.1201 DOI. Appears in: Rotor GKP code
R. Raz and S. Safra, “A sub-constant error-probability low-degree test, and a sub-constant error-probability PCP characterization of NP”, Proceedings of the twenty-ninth annual ACM symposium on Theory of computing - STOC ’97 475 (1997) DOI. Appears in: Generalized RM (GRM) code, $q$-ary linear LTC
N. Read, “Topological phases and quasiparticle braiding”, Physics Today 65, 38 (2012) DOI. Appears in: Hamiltonian-based code
I. S. Reed and G. Solomon, “Polynomial Codes Over Certain Finite Fields”, Journal of the Society for Industrial and Applied Mathematics 8, 300 (1960) DOI. Appears in: Narrow-sense RS code, Reed-Solomon (RS) code
I. Reed, “A class of multiple-error-correcting codes and the decoding scheme”, Transactions of the IRE Professional Group on Information Theory 4, 38 (1954) DOI. Appears in: Reed-Muller (RM) code
I. Reed, R. Scholtz, Treiu-Kien Truong, and L. Welch, “The fast decoding of Reed-Solomon codes using Fermat theoretic transforms and continued fractions”, IEEE Transactions on Information Theory 24, 100 (1978) DOI. Appears in: Reed-Solomon (RS) code
M. D. Reed, L. DiCarlo, S. E. Nigg, L. Sun, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, “Realization of three-qubit quantum error correction with superconducting circuits”, Nature 482, 382 (2012) arXiv:1109.4948 DOI. Appears in: Quantum repetition code
G. Reeves and H. D. Pfister, “Achieving Capacity on Non-Binary Channels with Generalized Reed-Muller Codes”, (2023) arXiv:2305.07779. Appears in: Generalized RM (GRM) code
G. Reeves and H. D. Pfister, “Reed–Muller Codes on BMS Channels Achieve Vanishing Bit-Error Probability for all Rates Below Capacity”, IEEE Transactions on Information Theory 70, 920 (2024) arXiv:2110.14631 DOI. Appears in: Reed-Muller (RM) code
F.-M. L. Régent, C. Berdou, Z. Leghtas, J. Guillaud, and M. Mirrahimi, “High-performance repetition cat code using fast noisy operations”, Quantum 7, 1198 (2023) arXiv:2212.11927 DOI. Appears in: Concatenated cat code, Cat-repetition code, Quantum repetition code
O. Regev, “On lattices, learning with errors, random linear codes, and cryptography”, Journal of the ACM 56, 1 (2009) DOI. Appears in: Quantum lattice code, Random code
U. Réglade et al., “Quantum control of a cat qubit with bit-flip times exceeding ten seconds”, Nature 629, 778 (2024) arXiv:2307.06617 DOI. Appears in: Two-component cat code
B. W. Reichardt, “Improved ancilla preparation scheme increases fault-tolerant threshold”, (2004) arXiv:quant-ph/0406025. Appears in: Concatenated Steane code
B. W. Reichardt, “Quantum Universality from Magic States Distillation Applied to CSS Codes”, Quantum Information Processing 4, 251 (2005) arXiv:quant-ph/0411036 DOI. Appears in: $[[23, 1, 7]]$ Quantum Golay code
B. W. Reichardt, “Error-detection-based quantum fault tolerance against discrete Pauli noise”, (2006) arXiv:quant-ph/0612004. Appears in: $[[23, 1, 7]]$ Quantum Golay code
B. W. Reichardt, “Fault-tolerant quantum error correction for Steane’s seven-qubit color code with few or no extra qubits”, Quantum Science and Technology 6, 015007 (2020) DOI. Appears in: $[[7,1,3]]$ Steane code
B. W. Reichardt et al., “Logical computation demonstrated with a neutral atom quantum processor”, (2024) arXiv:2411.11822. Appears in: $[[9,1,3,3]]$ Nine-qubit Bacon-Shor code, $[[4,2,2]]$ Four-qubit code
B. W. Reichardt et al., “Demonstration of quantum computation and error correction with a tesseract code”, (2024) arXiv:2409.04628. Appears in: $[[16,6,4]]$ Tesseract color code, $[[4,2,2]]$ Four-qubit code, $[[8,3,2]]$ Smallest interesting color code
B. Reichardt, “Postselection threshold against biased noise”, 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS’06) 420 (2006) arXiv:quant-ph/0608018 DOI. Appears in: Concatenated qubit code, $[[4,2,2]]$ Four-qubit code, $[[6,2,2]]$ $C_6$ code
B. Reichardt and Y. Ouyang. Unpublished (2006).. Appears in: $[[23, 1, 7]]$ Quantum Golay code
M. Reichert, L. W. Tessler, M. Bergmann, P. van Loock, and T. Byrnes, “Nonlinear quantum error correction”, Physical Review A 105, (2022) arXiv:2112.01858 DOI. Appears in: Approximate quantum error-correcting code (AQECC)
B. Reid, “A simple method for compiling quantum stabilizer circuits”, (2024) arXiv:2404.19408. Appears in: Qubit stabilizer code
C. Reimer et al., “High-dimensional one-way quantum processing implemented on d-level cluster states”, Nature Physics 15, 148 (2018) DOI. Appears in: Modular-qudit cluster-state code
M. Reimpell and R. F. Werner, “Iterative Optimization of Quantum Error Correcting Codes”, Physical Review Letters 94, (2005) arXiv:quant-ph/0307138 DOI. Appears in: Approximate quantum error-correcting code (AQECC), Qudit-into-oscillator code
P. Reinhold, S. Rosenblum, W.-L. Ma, L. Frunzio, L. Jiang, and R. J. Schoelkopf, “Error-corrected gates on an encoded qubit”, Nature Physics 16, 822 (2020) arXiv:1907.12327 DOI. Appears in: Binomial code
F. Reiter, A. S. Sørensen, P. Zoller, and C. A. Muschik, “Dissipative quantum error correction and application to quantum sensing with trapped ions”, Nature Communications 8, (2017) arXiv:1702.08673 DOI. Appears in: Quantum repetition code
Y. Ren, A. T. Kristensen, Y. Shen, A. Balatsoukas-Stimming, C. Zhang, and A. Burg, “A Sequence Repetition Node-Based Successive Cancellation List Decoder for 5G Polar Codes: Algorithm and Implementation”, IEEE Transactions on Signal Processing 70, 5592 (2022) arXiv:2205.08857 DOI. Appears in: Polar code
Y. Ren, N. Tantivasadakarn, and D. J. Williamson, “Efficient Preparation of Solvable Anyons with Adaptive Quantum Circuits”, (2024) arXiv:2411.04985. Appears in: String-net code
J. M. Renes, R. Blume-Kohout, A. J. Scott, and C. M. Caves, “Symmetric informationally complete quantum measurements”, Journal of Mathematical Physics 45, 2171 (2004) arXiv:quant-ph/0310075 DOI. Appears in: $t$-design
J. M. Renes and J.-C. Boileau, “Physical underpinnings of privacy”, Physical Review A 78, (2008) arXiv:0803.3096 DOI. Appears in: Quantum polar code
J. M. Renes, F. Dupuis, and R. Renner, “Efficient Polar Coding of Quantum Information”, Physical Review Letters 109, (2012) arXiv:1109.3195 DOI. Appears in: Quantum polar code
J. M. Renes, D. Sutter, F. Dupuis, and R. Renner, “Efficient Quantum Polar Codes Requiring No Preshared Entanglement”, IEEE Transactions on Information Theory 61, 6395 (2015) arXiv:1307.1136 DOI. Appears in: EA qubit stabilizer code, Quantum polar code, Qubit CSS code
J. M. Renes, “Belief propagation decoding of quantum channels by passing quantum messages”, New Journal of Physics 19, 072001 (2017) arXiv:1607.04833 DOI. Appears in: Qubit c-q code
J. M. Renes, “Duality of Channels and Codes”, IEEE Transactions on Information Theory 64, 577 (2018) arXiv:1701.05583 DOI. Appears in: Qubit c-q code
J. M. Renes, “Achievable error exponents of data compression with quantum side information and communication over symmetric classical-quantum channels”, 2023 IEEE Information Theory Workshop (ITW) 170 (2023) arXiv:2207.08899 DOI. Appears in: Classical-quantum (c-q) code
N. Rengaswamy, R. Calderbank, H. D. Pfister, and S. Kadhe, “Synthesis of Logical Clifford Operators via Symplectic Geometry”, 2018 IEEE International Symposium on Information Theory (ISIT) (2018) arXiv:1803.06987 DOI. Appears in: $[[2m,2m-2,2]]$ error-detecting code, Single parity-check (SPC) code, Qubit stabilizer code, Repetition code, $[[6,4,2]]$ error-detecting code
N. Rengaswamy, R. Calderbank, and H. D. Pfister, “Unifying the Clifford hierarchy via symmetric matrices over rings”, Physical Review A 100, (2019) arXiv:1902.04022 DOI. Appears in: Qubit code
N. Rengaswamy, R. Calderbank, M. Newman, and H. D. Pfister, “On Optimality of CSS Codes for Transversal T”, IEEE Journal on Selected Areas in Information Theory 1, 499 (2020) arXiv:1910.09333 DOI. Appears in: CSS-T code, $[[2^D,D,2]]$ hypercube quantum code, Quantum Reed-Muller code, Triorthogonal code
N. Rengaswamy, R. Calderbank, S. Kadhe, and H. D. Pfister, “Logical Clifford Synthesis for Stabilizer Codes”, IEEE Transactions on Quantum Engineering 1, 1 (2020) arXiv:1907.00310 DOI. Appears in: Qubit stabilizer code, $[[6,4,2]]$ error-detecting code
N. Rengaswamy, R. Calderbank, M. Newman, and H. D. Pfister, “Classical Coding Problem from Transversal T Gates”, 2020 IEEE International Symposium on Information Theory (ISIT) (2020) arXiv:2001.04887 DOI. Appears in: CSS-T code
N. Rengaswamy, R. Calderbank, M. Newman, and H. D. Pfister, “On Optimality of CSS Codes for Transversal T”, IEEE Journal on Selected Areas in Information Theory 1, 499 (2020) DOI. Appears in: $[[16,6,4]]$ Tesseract color code
N. Rengaswamy, K. P. Seshadreesan, S. Guha, and H. D. Pfister, “Belief propagation with quantum messages for quantum-enhanced classical communications”, npj Quantum Information 7, (2021) arXiv:2003.04356 DOI. Appears in: Qubit c-q code
N. Rengaswamy, A. Raina, N. Raveendran, and B. Vasić, “Distilling GHZ States using Stabilizer Codes”, (2022) arXiv:2109.06248. Appears in: Qubit stabilizer code
N. Rengaswamy, N. Raveendran, A. Raina, and B. Vasić, “Entanglement Purification with Quantum LDPC Codes and Iterative Decoding”, Quantum 8, 1233 (2024) arXiv:2210.14143 DOI. Appears in: Quantum LDPC (QLDPC) code
S.-J. Rey and F. Sugino, “A Nonperturbative Proposal for Nonabelian Tensor Gauge Theory and Dynamical Quantum Yang-Baxter Maps”, (2010) arXiv:1002.4636. Appears in: Two-gauge theory code
T. J. Richardson, M. A. Shokrollahi, and R. L. Urbanke, “Design of capacity-approaching irregular low-density parity-check codes”, IEEE Transactions on Information Theory 47, 619 (2001) DOI. Appears in: Irregular LDPC code, Low-density parity-check (LDPC) code
T. J. Richardson and R. L. Urbanke, “Efficient encoding of low-density parity-check codes”, IEEE Transactions on Information Theory 47, 638 (2001) DOI. Appears in: Low-density parity-check (LDPC) code
T. J. Richardson and R. L. Urbanke, “The capacity of low-density parity-check codes under message-passing decoding”, IEEE Transactions on Information Theory 47, 599 (2001) DOI. Appears in: Low-density parity-check (LDPC) code
T. Richardson and R. Urbanke, “The renaissance of gallager’s low-density parity-check codes”, IEEE Communications Magazine 41, 126 (2003) DOI. Appears in: Low-density parity-check (LDPC) code
T. Richardson and R. Urbanke, Modern Coding Theory (Cambridge University Press, 2008) DOI. Appears in: Luby transform (LT) code
T. Richardson and S. Kudekar, “Design of Low-Density Parity Check Codes for 5G New Radio”, IEEE Communications Magazine 56, 28 (2018) DOI. Appears in: Quasi-cyclic LDPC (QC-LDPC) code
Richardson, Tom, and Rüdiger Urbanke. "Multi-edge type LDPC codes." Workshop honoring Prof. Bob McEliece on his 60th birthday, California Institute of Technology, Pasadena, California. 2002.. Appears in: Irregular LDPC code, Multi-edge LDPC code
G. Richter and S. Plass, “Fast decoding of rank-codes with rank errors and column erasures”, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings. 398 DOI. Appears in: Rank-metric code
A.-E. Riet, V. Skachek, and E. K. Thomas, “Batch Codes for Asynchronous Recovery of Data”, IEEE Transactions on Information Theory 68, 1545 (2022) DOI. Appears in: Batch code, Locally recoverable code (LRC)
S. Rietsch, A. Y. Dubey, C. Ufrecht, M. Periyasamy, A. Plinge, C. Mutschler, and D. D. Scherer, “Unitary Synthesis of Clifford+T Circuits with Reinforcement Learning”, 2024 IEEE International Conference on Quantum Computing and Engineering (QCE) 824 (2024) arXiv:2404.14865 DOI. Appears in: Qubit code
A. Rigby, J. C. Olivier, and P. Jarvis, “Heuristic construction of codeword stabilized codes”, Physical Review A 100, (2019) arXiv:1907.04537 DOI. Appears in: $((5+2r,3\times 2^{2r+1},2))$ Rains code
F. van Riggelen, W. I. L. Lawrie, M. Russ, N. W. Hendrickx, A. Sammak, M. Rispler, B. M. Terhal, G. Scappucci, and M. Veldhorst, “Phase flip code with semiconductor spin qubits”, (2022) arXiv:2202.11530. Appears in: Quantum repetition code
L. Riguang and M. Zhi, “Non-binary Entanglement-assisted Stabilizer Quantum Codes”, (2011) arXiv:1105.5872. Appears in: EA Galois-qudit stabilizer code, Galois-qudit stabilizer code
D. Ristè, S. Poletto, M.-Z. Huang, A. Bruno, V. Vesterinen, O.-P. Saira, and L. DiCarlo, “Detecting bit-flip errors in a logical qubit using stabilizer measurements”, Nature Communications 6, (2015) arXiv:1411.5542 DOI. Appears in: Quantum repetition code
Hörmann, F., Bartz, H., & Horlemann, A. L. (2022). Security considerations for Mceliece-like cryptosystems based on linearized Reed-Solomon codes in the sum-rank metric.. Appears in: Linearized RS code
S. Roberts, B. Yoshida, A. Kubica, and S. D. Bartlett, “Symmetry-protected topological order at nonzero temperature”, Physical Review A 96, (2017) arXiv:1611.05450 DOI. Appears in: Cluster-state code, Raussendorf-Bravyi-Harrington (RBH) cluster-state code, Symmetry-protected topological (SPT) code, Lattice stabilizer code
S. Roberts and S. D. Bartlett, “Symmetry-Protected Self-Correcting Quantum Memories”, Physical Review X 10, (2020) arXiv:1805.01474 DOI. Appears in: 3D subsystem color code, Raussendorf-Bravyi-Harrington (RBH) cluster-state code, Symmetry-protected topological (SPT) code, Symmetry-protected self-correcting quantum code
S. Roberts and D. J. Williamson, “3-Fermion Topological Quantum Computation”, PRX Quantum 5, (2024) arXiv:2011.04693 DOI. Appears in: Raussendorf-Bravyi-Harrington (RBH) cluster-state code, Three-fermion (3F) subsystem code, Three-fermion (3F) Walker-Wang model code, Walker-Wang model code
A. Robertson, C. Granade, S. D. Bartlett, and S. T. Flammia, “Tailored Codes for Small Quantum Memories”, Physical Review Applied 8, (2017) arXiv:1703.08179 DOI. Appears in: Asymmetric quantum code, Twisted XZZX toric code
B. Rodatz, B. Poór, and A. Kissinger, “Floquetifying stabiliser codes with distance-preserving rewrites”, (2024) arXiv:2410.17240. Appears in: Hastings-Haah Floquet code, Ladder Floquet code, Qubit stabilizer code, $[[4,2,2]]$ Four-qubit code
F. Rodier, “Codes from flag varieties over a finite field”, Journal of Pure and Applied Algebra 178, 203 (2003) DOI. Appears in: Flag-variety code
P. S. Rodriguez et al., “Experimental Demonstration of Logical Magic State Distillation”, (2024) arXiv:2412.15165. Appears in: Square-octagon (4.8.8) color code
J. Roffe, D. Headley, N. Chancellor, D. Horsman, and V. Kendon, “Protecting quantum memories using coherent parity check codes”, Quantum Science and Technology 3, 035010 (2018) arXiv:1709.01866 DOI. Appears in: Coherent-parity-check (CPC) code, $[[4,2,2]]$ Four-qubit code
J. Roffe, “Quantum error correction: an introductory guide”, Contemporary Physics 60, 226 (2019) arXiv:1907.11157 DOI. Appears in: Quantum error-correcting code (QECC)
J. Roffe, D. R. White, S. Burton, and E. Campbell, “Decoding across the quantum low-density parity-check code landscape”, Physical Review Research 2, (2020) arXiv:2005.07016 DOI. Appears in: Low-density parity-check (LDPC) code, Quantum LDPC (QLDPC) code, Toric code
J. Roffe, L. Z. Cohen, A. O. Quintavalle, D. Chandra, and E. T. Campbell, “Bias-tailored quantum LDPC codes”, Quantum 7, 1005 (2023) arXiv:2202.01702 DOI. Appears in: Abelian LP code, Asymmetric quantum code
Roffe, Joschka. "LDPC: Python tools for low density parity check codes." (2022).. Appears in: Low-density parity-check (LDPC) code, Quantum LDPC (QLDPC) code
C. A. Rogers, “A note on coverings”, Mathematika 4, 1 (1957) DOI. Appears in: Sphere packing
C. A. Rogers, “The Packing of Equal Spheres”, Proceedings of the London Mathematical Society s3-8, 609 (1958) DOI. Appears in: Sphere packing
I. Rojkov, M. Simoni, E. Zapusek, F. Reiter, and J. Home, “Stabilization of cat-state manifolds using nonlinear reservoir engineering”, (2024) arXiv:2407.18087. Appears in: Squeezed cat code
L. Rokach, Pattern Classification Using Ensemble Methods (WORLD SCIENTIFIC, 2009) DOI. Appears in: Error-correcting output code (ECOC), One-hot code, One-versus-one (OVO) code
Ronghui Peng and Rong-Rong Chen, “Application of Nonbinary LDPC Cycle Codes to MIMO Channels”, IEEE Transactions on Wireless Communications 7, 2020 (2008) DOI. Appears in: Cycle LDPC code
M. Rosati, A. Mari, and V. Giovannetti, “Narrow bounds for the quantum capacity of thermal attenuators”, Nature Communications 9, (2018) arXiv:1801.04731 DOI. Appears in: Gottesman-Kitaev-Preskill (GKP) code
M. Rosati, “Performance of Coherent Frequency-Shift Keying for Classical Communication on Quantum Channels”, 2021 IEEE International Symposium on Information Theory (ISIT) (2021) arXiv:2203.09822 DOI. Appears in: Coherent-state c-q code, Coherent FSK (CFSK) c-q code
S. Rosenblum, P. Reinhold, M. Mirrahimi, L. Jiang, L. Frunzio, and R. J. Schoelkopf, “Fault-tolerant detection of a quantum error”, Science 361, 266 (2018) arXiv:1803.00102 DOI. Appears in: Cat code
J. Rosenthal and P. O. Vontobel, “Constructions of regular and irregular LDPC codes using Ramanujan graphs and ideas from Margulis”, Proceedings. 2001 IEEE International Symposium on Information Theory (IEEE Cat. No.01CH37252) DOI. Appears in: Margulis LDPC code
M. Rossi, M. Huber, D. Bruß, and C. Macchiavello, “Quantum hypergraph states”, New Journal of Physics 15, 113022 (2013) arXiv:1211.5554 DOI. Appears in: Cluster-state code, Qubit stabilizer code, XP stabilizer code
R. M. Roth and A. Lempel, “A construction of non-Reed-Solomon type MDS codes”, IEEE Transactions on Information Theory 35, 655 (1989) DOI. Appears in: Roth-Lempel code
R. M. Roth, “Maximum-rank array codes and their application to crisscross error correction”, IEEE Transactions on Information Theory 37, 328 (1991) DOI. Appears in: Gabidulin code, Maximum-rank distance (MRD) code
R. M. Roth and G. Ruckenstein, “Efficient decoding of Reed-Solomon codes beyond half the minimum distance”, IEEE Transactions on Information Theory 46, 246 (2000) DOI. Appears in: Reed-Solomon (RS) code
R. Roth, Introduction to Coding Theory (Cambridge University Press, 2006) DOI. Appears in: Alternant code, Berlekamp code, Maximum distance separable (MDS) code, Reed-Solomon (RS) code
B. Röthlisberger, J. R. Wootton, R. M. Heath, J. K. Pachos, and D. Loss, “Incoherent dynamics in the toric code subject to disorder”, Physical Review A 85, (2012) arXiv:1112.1613 DOI. Appears in: Asymmetric quantum code, Twisted XZZX toric code
A. Roumy, S. Guemghar, G. Caire, and S. Verdu, “Design Methods for Irregular Repeat–Accumulate Codes”, IEEE Transactions on Information Theory 50, 1711 (2004) DOI. Appears in: Irregular repeat-accumulate (IRA) code
E. Rowell, R. Stong, and Z. Wang, “On classification of modular tensor categories”, (2009) arXiv:0712.1377. Appears in: Three-fermion (3F) subsystem code
A. Roy and A. J. Scott, “Unitary designs and codes”, Designs, Codes and Cryptography 53, 13 (2009) arXiv:0809.3813 DOI. Appears in: $t$-design, Twisted $1$-group code
A. Roy and S. Suda, “Complex spherical designs and codes”, (2011) arXiv:1104.4692. Appears in: Hessian polyhedron code, Spherical design
A. Roy and D. P. DiVincenzo, “Topological Quantum Computing”, (2017) arXiv:1701.05052. Appears in: Fermion-into-qubit code, Kitaev honeycomb code
V. P. Roychowdhury and F. Vatan, “On the Structure of Additive Quantum Codes and the Existence of Nonadditive Codes”, (1997) arXiv:quant-ph/9710031. Appears in: Galois-qudit USt code, Union stabilizer (USt) code
A. Royer, “Wigner function as the expectation value of a parity operator”, Physical Review A 15, 449 (1977) DOI. Appears in: Bosonic code
B. Royer, S. Singh, and S. M. Girvin, “Stabilization of Finite-Energy Gottesman-Kitaev-Preskill States”, Physical Review Letters 125, (2020) arXiv:2009.07941 DOI. Appears in: Square-lattice GKP code, Gottesman-Kitaev-Preskill (GKP) code
B. Royer, S. Singh, and S. M. Girvin, “Encoding Qubits in Multimode Grid States”, PRX Quantum 3, (2022) arXiv:2201.12337 DOI. Appears in: $D_4$ hyper-diamond GKP code, Concatenated GKP code, Gottesman-Kitaev-Preskill (GKP) code, Quantum repetition code
Á. Rozgonyi and G. Széchenyi, “Break-even point of the phase-flip error correcting code”, New Journal of Physics 25, 103004 (2023) arXiv:2303.17810 DOI. Appears in: Quantum repetition code
D. Ruano, “On the Parameters of r-dimensional Toric Codes”, (2005) arXiv:math/0512285. Appears in: Hansen toric code
R. Rubinfeld and M. Sudan, “Robust Characterizations of Polynomials with Applications to Program Testing”, SIAM Journal on Computing 25, 252 (1996) DOI. Appears in: Locally testable code (LTC)
Rudolf Schürer and Wolfgang Ch. Schmid. “Cyclic Codes (BCH-Bound).” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2015-09-03. https://mint.sbg.ac.at/desc_CCyclic-BCHBound.html. Appears in: Binary BCH code, Bose–Chaudhuri–Hocquenghem (BCH) code
Rudolf Schürer and Wolfgang Ch. Schmid. “Denniston Codes.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2015-09-03. https://mint.sbg.ac.at/desc_CDenniston.html. Appears in: Denniston code, Hyperoval code, Projective two-weight code
Rudolf Schürer and Wolfgang Ch. Schmid. “Extended Reed–Solomon Code.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2015-09-03. https://mint.sbg.ac.at/desc_CReedSolomon-extended.html. Appears in: Extended GRS code, $q$-ary parity-check code, Reed-Solomon (RS) code
Rudolf Schürer and Wolfgang Ch. Schmid. “Hexacode.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2015-09-03. https://mint.sbg.ac.at/desc_CHexa.html. Appears in: Hexacode
Rudolf Schürer and Wolfgang Ch. Schmid. “Kerdock Codes.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2015-09-03. https://mint.sbg.ac.at/desc_CKerdock.html. Appears in: Kerdock code
Rudolf Schürer and Wolfgang Ch. Schmid. “Preparata Codes.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2015-09-03. https://mint.sbg.ac.at/desc_CPreparata.html. Appears in: Preparata code
Rudolf Schürer and Wolfgang Ch. Schmid. “Reed–Solomon Code.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2015-09-03. https://mint.sbg.ac.at/desc_CReedSolomon.html. Appears in: Reed-Solomon (RS) code
Rudolf Schürer and Wolfgang Ch. Schmid. “Reed-Solomon Codes for OOAs.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2024-09-05. https://mint.sbg.ac.at/desc_OReedSolomon.html. Appears in: Reed-Solomon (RS) code, RS NRT code
Rudolf Schürer and Wolfgang Ch. Schmid. “Simplex Code.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2015-09-03. https://mint.sbg.ac.at/desc_CSimplex.html. Appears in: Extended GRS code, $q$-ary simplex code, $[2^m-1,m,2^{m-1}]$ simplex code
Rudolf Schürer and Wolfgang Ch. Schmid. “Tetracode.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2015-09-03. https://mint.sbg.ac.at/desc_CTetra.html. Appears in: Tetracode
L. Rudolph, “A class of majority logic decodable codes (Corresp.)”, IEEE Transactions on Information Theory 13, 305 (1967) DOI. Appears in: Incidence-matrix projective code
L. Rudolph and C. Hartmann, “Decoding by sequential code reduction”, IEEE Transactions on Information Theory 19, 549 (1973) DOI. Appears in: Reed-Muller (RM) code
A. Rudra and M. Wootters, “Average-radius list-recovery of random linear codes: it really ties the room together”, (2017) arXiv:1704.02420. Appears in: Linear $q$-ary code
D. Ruiz, R. Gautier, J. Guillaud, and M. Mirrahimi, “Two-photon driven Kerr quantum oscillator with multiple spectral degeneracies”, Physical Review A 107, (2023) arXiv:2211.03689 DOI. Appears in: Two-component cat code
D. Ruiz, J. Guillaud, A. Leverrier, M. Mirrahimi, and C. Vuillot, “LDPC-cat codes for low-overhead quantum computing in 2D”, (2024) arXiv:2401.09541. Appears in: Concatenated cat code, Low-density parity-check (LDPC) code
F. J. R. Ruiz et al., “Quantum Circuit Optimization with AlphaTensor”, (2024) arXiv:2402.14396. Appears in: Qubit code
C. Ruiz-Gonzalez, S. Arlt, J. Petermann, S. Sayyad, T. Jaouni, E. Karimi, N. Tischler, X. Gu, and M. Krenn, “Digital Discovery of 100 diverse Quantum Experiments with PyTheus”, Quantum 7, 1204 (2023) arXiv:2210.09980 DOI. Appears in: Perfect-tensor code, Neural network quantum code
P. Ruján, “Finite temperature error-correcting codes”, Physical Review Letters 70, 2968 (1993) DOI. Appears in: Convolutional code
J. J. Rushanan, Topics in Integral Matrices and Abelian Group Codes, California Institute of Technology, 1986 DOI. Appears in: $q$-ary duadic code
M. B. Ruskai, “Pauli Exchange Errors in Quantum Computation”, Physical Review Letters 85, 194 (2000) arXiv:quant-ph/9906114 DOI. Appears in: $((9,2,3))$ Ruskai code, $[[9,1,3]]$ Shor code
C. T. Ryan and K. M. Ryan, “The minimum weight of the Grassmann codes C(k,n),”, Discrete Applied Mathematics 28, 149 (1990) DOI. Appears in: Grassmannian code
C. Ryan-Anderson et al., “Realization of real-time fault-tolerant quantum error correction”, (2021) arXiv:2107.07505. Appears in: $[[7,1,3]]$ Steane code
C. Ryan-Anderson et al., “Implementing Fault-tolerant Entangling Gates on the Five-qubit Code and the Color Code”, (2022) arXiv:2208.01863. Appears in: Five-qubit perfect code, $[[7,1,3]]$ Steane code
C. Ryan-Anderson et al., “High-fidelity and Fault-tolerant Teleportation of a Logical Qubit using Transversal Gates and Lattice Surgery on a Trapped-ion Quantum Computer”, (2024) arXiv:2404.16728. Appears in: $[[7,1,3]]$ Steane code
C. T. Ryan, An application of Grassmannian varieties to coding theory. Congr. Numer. 57 (1987) 257–271.. Appears in: Grassmannian code
C.T. Ryan, Projective codes based on Grassmann varieties, Congr. Numer. 57, 273–279 (1987).. Appears in: Grassmannian code
M. Rymarz, S. Bosco, A. Ciani, and D. P. DiVincenzo, “Hardware-Encoding Grid States in a Nonreciprocal Superconducting Circuit”, Physical Review X 11, (2021) arXiv:2002.07718 DOI. Appears in: Square-lattice GKP code
S. S. Ryshkov, E. P. Baranovskii, “Solution of the problem of least dense lattice covering of five-dimensional space by equal spheres”, Dokl. Akad. Nauk SSSR, 222:1 (1975), 39–42. Appears in: $A_n^{\perp}$ lattice
S. S. Ryshkov, E. P. Baranovskii, “C-types of n-dimensional lattices and 5-dimensional primitive parallelohedra (with application to the theory of coverings)”, Trudy Mat. Inst. Steklov., 137, 1976, 3–131; Proc. Steklov Inst. Math., 137 (1976), 1–140. Appears in: $A_n^{\perp}$ lattice
S. Ryu, “Three-dimensional topological phase on the diamond lattice”, Physical Review B 79, (2009) arXiv:0811.2036 DOI. Appears in: 3D fermionic surface code
E. Sabo, A. B. Aloshious, and K. R. Brown, “Trellis Decoding For Qudit Stabilizer Codes And Its Application To Qubit Topological Codes”, (2022) arXiv:2106.08251. Appears in: Modular-qudit stabilizer code
E. Sabo, L. G. Gunderman, B. Ide, M. Vasmer, and G. Dauphinais, “Weight Reduced Stabilizer Codes with Lower Overhead”, (2024) arXiv:2402.05228. Appears in: Distance-balanced code, GKP CV-cluster-state code
S. Sachdev and J. Ye, “Gapless spin-fluid ground state in a random quantum Heisenberg magnet”, Physical Review Letters 70, 3339 (1993) arXiv:cond-mat/9212030 DOI. Appears in: SYK code
S. Sachdev, “The quantum phases of matter”, (2012) arXiv:1203.4565. Appears in: Hamiltonian-based code
S. Sachdev, Quantum Phases of Matter (Cambridge University Press, 2023) DOI. Appears in: Hamiltonian-based code
H. R. Sadjadpour, “<title>Maximum a posteriori decoding algorithms for turbo codes</title>”, SPIE Proceedings (2000) DOI. Appears in: Turbo code
H. R. Sadjadpour, N. J. A. Sloane, M. Salehi, and G. Nebe, “Interleaver design for turbo codes”, IEEE Journal on Selected Areas in Communications 19, 831 (2001) DOI. Appears in: Turbo code
Sae-Young Chung, G. D. Forney, T. J. Richardson, and R. Urbanke, “On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit”, IEEE Communications Letters 5, 58 (2001) DOI. Appears in: Irregular LDPC code
Sae-Young Chung, T. J. Richardson, and R. L. Urbanke, “Analysis of sum-product decoding of low-density parity-check codes using a Gaussian approximation”, IEEE Transactions on Information Theory 47, 657 (2001) DOI. Appears in: Irregular LDPC code
E. B. Saff and A. B. J. Kuijlaars, “Distributing many points on a sphere”, The Mathematical Intelligencer 19, 5 (1997) DOI. Appears in: Spherical code, Universally optimal spherical code
K. Sahay and B. J. Brown, “Decoder for the Triangular Color Code by Matching on a Möbius Strip”, PRX Quantum 3, (2022) arXiv:2108.11395 DOI. Appears in: Honeycomb (6.6.6) color code
K. Sahay, Y. Lin, S. Huang, K. R. Brown, and S. Puri, “Error correction of transversal CNOT gates for scalable surface code computation”, (2024) arXiv:2408.01393. Appears in: Kitaev surface code
K. Saints and C. Heegard, “On hyperbolic cascaded Reed-Solomon codes”, Lecture Notes in Computer Science 291 (1993) DOI. Appears in: Hyperbolic evaluation code, Reed-Solomon (RS) code
S. Sakata, “Finding a minimal set of linear recurring relations capable of generating a given finite two-dimensional array”, Journal of Symbolic Computation 5, 321 (1988) DOI. Appears in: Evaluation AG code, Hermitian code
S. Sakata, “Extension of the Berlekamp-Massey algorithm to N dimensions”, Information and Computation 84, 207 (1990) DOI. Appears in: Evaluation AG code
S. Sakata, “Decoding binary 2-D cyclic codes by the 2-D Berlekamp-Massey algorithm”, IEEE Transactions on Information Theory 37, 1200 (1991) DOI. Appears in: Evaluation AG code
P. Sala and R. Verresen, “Stability and Loop Models from Decohering Non-Abelian Topological Order”, (2024) arXiv:2409.12230. Appears in: Quantum-double code
P. Sala, J. Alicea, and R. Verresen, “Decoherence and wavefunction deformation of $D_4$ non-Abelian topological order”, (2024) arXiv:2409.12948. Appears in: Quantum-double code, Dihedral $G=D_m$ quantum-double code
P. J. Salas, “Simple fault-tolerant encoding over q-ary CSS quantum codes”, (2007) arXiv:0712.3223. Appears in: Galois-qudit CSS code
A. Samorodnitsky, “Low-degree tests at large distances”, (2006) arXiv:math/0604353. Appears in: Binary linear LTC, Reed-Muller (RM) code
A. Samorodnitsky, “One more proof of the first linear programming bound for binary codes and two conjectures”, (2021) arXiv:2104.14587. Appears in: Binary code
B. C. Sanders, S. D. Bartlett, T. Rudolph, and P. L. Knight, “Photon-number superselection and the entangled coherent-state representation”, Physical Review A 68, (2003) arXiv:quant-ph/0306076 DOI. Appears in: Bosonic code
B. C. Sanders, “Review of entangled coherent states”, Journal of Physics A: Mathematical and Theoretical 45, 244002 (2012) arXiv:1112.1778 DOI. Appears in: Bosonic code
S. Sang, Y. Zou, and T. H. Hsieh, “Mixed-state Quantum Phases: Renormalization and Quantum Error Correction”, (2023) arXiv:2310.08639. Appears in: Kitaev surface code
S. Sang, T. H. Hsieh, and Y. Zou, “Approximate quantum error correcting codes from conformal field theory”, (2024) arXiv:2406.09555. Appears in: Conformal-field theory (CFT) code
S. Sang and T. H. Hsieh, “Stability of mixed-state quantum phases via finite Markov length”, (2024) arXiv:2404.07251. Appears in: Kitaev surface code
Sanjeev Arora. Probabilistic checking of proofs and hardness of approximation problems. UC Berkeley, 1994.. Appears in: Locally testable code (LTC)
G. Sansoni, S. Corini, S. Lazzari, R. Rodella, and F. Docchio, “Three-dimensional imaging based on Gray-code light projection: characterization of the measuring algorithm and development of a measuring system for industrial applications”, Applied Optics 36, 4463 (1997) DOI. Appears in: Gray code
D. F. G. Santiago and G. S. S. Otoni, “A new approach to codeword stabilized quantum codes using the algebraic structure of modules”, (2015) arXiv:1505.00283. Appears in: Modular-qudit CWS code, Modular-qudit stabilizer code
S. Santos, V. Niculae, D. McNamee, and A. F. T. Martins, “Sparse and Structured Hopfield Networks”, (2024) arXiv:2402.13725. Appears in: Spherical code
B. Sarac and D. Acar, “A Construction of Quantum Stabilizer Codes from Classical Codes and Butson Hadamard Matrices”, (2024) arXiv:2407.13527. Appears in: Complex Hadamard spherical code, Hermitian Galois-qudit code
L. Sari, “Effects of Puncturing Patterns on Punctured Convolutional Codes”, TELKOMNIKA (Telecommunication, Computing, Electronics and Control) 10, (2012) DOI. Appears in: Convolutional code
R. Sarkar and T. J. Yoder, “A graph-based formalism for surface codes and twists”, Quantum 8, 1416 (2024) arXiv:2101.09349 DOI. Appears in: Rotated surface code, Five-qubit perfect code, Kitaev surface code, Twist-defect surface code, Twisted XZZX toric code, XZZX surface code
R. Sarkar and T. J. Yoder, “The qudit Pauli group: non-commuting pairs, non-commuting sets, and structure theorems”, Quantum 8, 1307 (2024) arXiv:2302.07966 DOI. Appears in: Modular-qudit code
G. Sarma and H. Mabuchi, “Gauge subsystems, separability and robustness in autonomous quantum memories”, New Journal of Physics 15, 035014 (2013) arXiv:1212.3564 DOI. Appears in: Bacon-Shor code
E. Sarmiento, M. V. Pinto, and R. H. Villarreal, “The minimum distance of parameterized codes on projective tori”, (2011) arXiv:1009.4966. Appears in: Hansen toric code
M. Sarovar, C. Ahn, K. Jacobs, and G. J. Milburn, “Practical scheme for error control using feedback”, Physical Review A 69, (2004) arXiv:quant-ph/0402017 DOI. Appears in: Qubit stabilizer code
M. Sarovar and G. J. Milburn, “Continuous quantum error correction by cooling”, Physical Review A 72, (2005) arXiv:quant-ph/0501038 DOI. Appears in: Finite-dimensional quantum error-correcting code
M. Sarovar and G. J. Milburn, “Continuous quantum error correction”, SPIE Proceedings 5842, 158 (2005) arXiv:quant-ph/0501049 DOI. Appears in: Quantum repetition code
P. K. Sarvepalli and A. Klappenecker, “Nonbinary Quantum Reed-Muller Codes”, (2005) arXiv:quant-ph/0502001. Appears in: Galois-qudit quantum RM code, Prime-qudit RM code
P. K. Sarvepalli, A. Klappenecker, and M. Rotteler, “Asymmetric quantum LDPC codes”, 2008 IEEE International Symposium on Information Theory (2008) arXiv:0804.4316 DOI. Appears in: Asymmetric quantum code, Finite-geometry LDPC (FG-LDPC) code
P. K. Sarvepalli, “Quantum stabilizer codes and beyond”, (2008) arXiv:0810.2574. Appears in: Galois-qudit BCH code, Qubit code, Subsystem qubit stabilizer code
P. K. Sarvepalli and A. Klappenecker, “Encoding Subsystem Codes”, (2008) arXiv:0806.4954. Appears in: Subsystem qubit stabilizer code
P. K. Sarvepalli, A. Klappenecker, and M. Rötteler, “Asymmetric quantum codes: constructions, bounds and performance”, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, 1645 (2009) DOI. Appears in: Asymmetric quantum code, Galois-qudit BCH code, Subsystem Galois-qudit stabilizer code, Finite-geometry LDPC (FG-LDPC) code, Quantum maximum-distance-separable (MDS) code, Quantum Reed-Muller code
P. K. Sarvepalli, A. Klappenecker, and M. Rotteler, “New decoding algorithms for a class of subsystem codes and generalized shor codes”, 2009 IEEE International Symposium on Information Theory 804 (2009) DOI. Appears in: Generalized Shor code, Subsystem hypergraph product (SHP) code
P. Sarvepalli and A. Klappenecker, “Degenerate quantum codes and the quantum Hamming bound”, Physical Review A 81, (2010) arXiv:0812.2674 DOI. Appears in: Galois-qudit CSS code, Griesmer code
P. Sarvepalli, “Topological color codes over higher alphabet”, 2010 IEEE Information Theory Workshop 1 (2010) DOI. Appears in: Galois-qudit color code
P. Sarvepalli and R. Raussendorf, “Efficient decoding of topological color codes”, Physical Review A 85, (2012) arXiv:1111.0831 DOI. Appears in: Honeycomb (6.6.6) color code
P. Sarvepalli and K. R. Brown, “Topological subsystem codes from graphs and hypergraphs”, Physical Review A 86, (2012) arXiv:1207.0479 DOI. Appears in: 2D subsystem color code, Color code, Generalized five-squares code, Sarvepalli-Brown subsystem code
D. V. Sarwate and M. B. Pursley, “Crosscorrelation properties of pseudorandom and related sequences”, Proceedings of the IEEE 68, 593 (1980) DOI. Appears in: Gold code, Kasami code
D. V. Sarwate and N. R. Shanbhag, “High-speed architectures for Reed-Solomon decoders”, IEEE Transactions on Very Large Scale Integration (VLSI) Systems 9, 641 (2001) DOI. Appears in: Reed-Solomon (RS) code
B. Sasidharan and E. Viterbo, “Private Data Access in Blockchain Systems Employing Coded Sharding”, 2021 IEEE International Symposium on Information Theory (ISIT) 2684 (2021) DOI. Appears in: Private information retrieval (PIR) code, Reed-Solomon (RS) code
K. J. Satzinger et al., “Realizing topologically ordered states on a quantum processor”, Science 374, 1237 (2021) arXiv:2104.01180 DOI. Appears in: Kitaev surface code
C. Savage, “A Survey of Combinatorial Gray Codes”, SIAM Review 39, 605 (1997) DOI. Appears in: Gray code
N. P. D. Sawaya and J. Huh, “Quantum Algorithm for Calculating Molecular Vibronic Spectra”, The Journal of Physical Chemistry Letters 10, 3586 (2019) arXiv:1812.10495 DOI. Appears in: One-hot quantum code
N. P. D. Sawaya, T. Menke, T. H. Kyaw, S. Johri, A. Aspuru-Guzik, and G. G. Guerreschi, “Resource-efficient digital quantum simulation of d-level systems for photonic, vibrational, and spin-s Hamiltonians”, npj Quantum Information 6, (2020) arXiv:1909.12847 DOI. Appears in: Gray code, One-hot quantum code, Qubit code
H. Sayginel, S. Koutsioumpas, M. Webster, A. Rajput, and Dan E Browne, “Fault-Tolerant Logical Clifford Gates from Code Automorphisms”, (2024) arXiv:2409.18175. Appears in: Two-block group-algebra (2BGA) codes, Qubit stabilizer code
L. Schatzki, G. Liu, M. Cerezo, and E. Chitambar, “Hierarchy of multipartite correlations based on concentratable entanglement”, Physical Review Research 6, (2024) arXiv:2209.07607 DOI. Appears in: Modular-qudit code
P. Schindler, J. T. Barreiro, T. Monz, V. Nebendahl, D. Nigg, M. Chwalla, M. Hennrich, and R. Blatt, “Experimental Repetitive Quantum Error Correction”, Science 332, 1059 (2011) DOI. Appears in: Quantum repetition code
S. G. Schirmer and X. Wang, “Stabilizing open quantum systems by Markovian reservoir engineering”, Physical Review A 81, (2010) arXiv:0909.1596 DOI. Appears in: Amplitude-damping (AD) code
D. S. Schlegel, F. Minganti, and V. Savona, “Quantum error correction using squeezed Schrödinger cat states”, Physical Review A 106, (2022) arXiv:2201.02570 DOI. Appears in: Squeezed cat code, Two-component cat code
Schläfli, L. (1901). Theorie der vielfachen Kontinuität (Vol. 38). Zürcher & Furrer.. Appears in: 24-cell code, Witting polytope code
D. Schlingemann and R. F. Werner, “Quantum error-correcting codes associated with graphs”, Physical Review A 65, (2001) arXiv:quant-ph/0012111 DOI. Appears in: $[[5,1,3]]_q$ Galois-qudit code, Galois-qudit stabilizer code, Graph quantum code, $[[10,1,4]]_{G}$ tenfold code, $[[5,1,3]]_{\mathbb{Z}_q}$ modular-qudit code, Modular-qudit stabilizer code, Five-qubit perfect code
D. Schlingemann, “Stabilizer codes can be realized as graph codes”, (2001) arXiv:quant-ph/0111080. Appears in: Cluster-state code, Galois-qudit stabilizer code, Graph quantum code, Qubit stabilizer code, Modular-qudit cluster-state code, Modular-qudit stabilizer code, Stabilizer code
L. Schmid, T. Peham, L. Berent, M. Müller, and R. Wille, “Deterministic Fault-Tolerant State Preparation for Near-Term Quantum Error Correction: Automatic Synthesis Using Boolean Satisfiability”, (2025) arXiv:2501.05527. Appears in: Qubit stabilizer code
A. T. Schmitz, H. Ma, R. M. Nandkishore, and S. A. Parameswaran, “Recoverable information and emergent conservation laws in fracton stabilizer codes”, Physical Review B 97, (2018) arXiv:1712.02375 DOI. Appears in: Lattice stabilizer code
A. T. Schmitz, “Thermal Stability of Dynamical Phase Transitions in Higher Dimensional Stabilizer Codes”, (2020) arXiv:2002.11733. Appears in: Bacon-Shor code, Qubit CSS code
J. Schnheim, “On linear and nonlinear single-error-correcting q-nary perfect codes”, Information and Control 12, 23 (1968) DOI. Appears in: Perfect code
C. P. Schnorr and M. Euchner, “Lattice basis reduction: Improved practical algorithms and solving subset sum problems”, Mathematical Programming 66, 181 (1994) DOI. Appears in: Lattice-based code
D. Schomaker and M. Wirtz, “On binary cyclic codes of odd lengths from 101 to 127”, IEEE Transactions on Information Theory 38, 516 (1992) DOI. Appears in: Cyclic linear binary code
A. Schotte, G. Zhu, L. Burgelman, and F. Verstraete, “Quantum error correction thresholds for the universal Fibonacci Turaev-Viro code”, (2021) arXiv:2012.04610. Appears in: Fibonacci string-net code
A. Schotte, L. Burgelman, and G. Zhu, “Fault-tolerant error correction for a universal non-Abelian topological quantum computer at finite temperature”, (2022) arXiv:2301.00054. Appears in: Fibonacci string-net code
K. A. Schouhamer Immink and J. H. Weber, “Very Efficient Balanced Codes”, IEEE Journal on Selected Areas in Communications 28, 188 (2010) DOI. Appears in: Balanced code
Schoute, P. H. (1903). Mehrdimensionale Geometrie, Vol. 2 (Die Polytope).. Appears in: 120-cell code, 24-cell code, 600-cell code
Schoute, P. H. "On the relation between the vertices of a definite six-dimensional polytope and the lines of a cubic surface." Proc. Roy. Acad. Amsterdam. Vol. 13. 1910.. Appears in: Hessian polyhedron code
K. M. Schreiter, A. Pasieka, R. Kaltenbaek, K. J. Resch, and D. W. Kribs, “Optical implementation of a unitarily correctable code”, Physical Review A 80, (2009) arXiv:0909.1584 DOI. Appears in: Subsystem QECC
B. Schroeder, E. Pinheiro, and W.-D. Weber, “DRAM errors in the wild”, Communications of the ACM 54, 100 (2011) DOI. Appears in: Error-correcting code (ECC)
N. Schuch, D. Pérez-García, and I. Cirac, “Classifying quantum phases using matrix product states and projected entangled pair states”, Physical Review B 84, (2011) arXiv:1010.3732 DOI. Appears in: Magnon code, Symmetry-protected topological (SPT) code, Valence-bond-solid (VBS) code
A. Schuckert, E. Crane, A. V. Gorshkov, M. Hafezi, and M. J. Gullans, “Fermion-qubit fault-tolerant quantum computing”, (2024) arXiv:2411.08955. Appears in: Constant-excitation (CE) code, Fermion code, Fermion-into-qubit code, Kitaev chain code, Majorana stabilizer code, Quantum repetition code
B. Schumacher and M. A. Nielsen, “Quantum data processing and error correction”, Physical Review A 54, 2629 (1996) arXiv:quant-ph/9604022 DOI. Appears in: Haar-random qubit code, Finite-dimensional quantum error-correcting code
B. Schumacher and M. D. Westmoreland, “Sending classical information via noisy quantum channels”, Physical Review A 56, 131 (1997) DOI. Appears in: Classical-quantum (c-q) code
T. Schuster, N. Tantivasadakarn, A. Vishwanath, and N. Y. Yao, “A holographic view of topological stabilizer codes”, (2023) arXiv:2312.04617. Appears in: 2D lattice stabilizer code, Holographic code
T. Schuster, J. Haferkamp, and H.-Y. Huang, “Random unitaries in extremely low depth”, (2025) arXiv:2407.07754. Appears in: Hamiltonian-based code
K. Schütte and B. L. van der Waerden, “Das Problem der dreizehn Kugeln”, Mathematische Annalen 125, 325 (1952) DOI. Appears in: Cubeoctahedron code
M. Schwartz and A. Vardy, “On the stopping distance and the stopping redundancy of codes”, IEEE Transactions on Information Theory 52, 922 (2006) DOI. Appears in: Low-density parity-check (LDPC) code
J. Schwinger, Quantum Kinematics and Dynamics (CRC Press, 2018) DOI. Appears in: Modular-qudit code
A. J. Scott, “Multipartite entanglement, quantum-error-correcting codes, and entangling power of quantum evolutions”, Physical Review A 69, (2004) arXiv:quant-ph/0310137 DOI. Appears in: Perfect-tensor code, Galois-qudit RS code, Hexacode, Quantum maximum-distance-separable (MDS) code, Modular-qudit code, Five-qubit perfect code, Hermitian qubit code
A. J. Scott, “Probabilities of Failure for Quantum Error Correction”, Quantum Information Processing 4, 399 (2005) DOI. Appears in: Dodecacode, $[[11,1,5]]$ quantum dodecacode
A. J. Scott, “Probabilities of Failure for Quantum Error Correction”, Quantum Information Processing 4, 399 (2005) arXiv:quant-ph/0406063 DOI. Appears in: Qubit code, $[[11,1,5]]$ quantum dodecacode
A. J. Scott, “Optimizing quantum process tomography with unitary2-designs”, Journal of Physics A: Mathematical and Theoretical 41, 055308 (2008) arXiv:0711.1017 DOI. Appears in: $t$-design
T. R. Scruby, D. E. Browne, P. Webster, and M. Vasmer, “Numerical Implementation of Just-In-Time Decoding in Novel Lattice Slices Through the Three-Dimensional Surface Code”, Quantum 6, 721 (2022) arXiv:2012.08536 DOI. Appears in: Kitaev surface code
T. R. Scruby and K. Nemoto, “Local Probabilistic Decoding of a Quantum Code”, Quantum 7, 1093 (2023) arXiv:2212.06985 DOI. Appears in: 3D surface code
T. R. Scruby, T. Hillmann, and J. Roffe, “High-threshold, low-overhead and single-shot decodable fault-tolerant quantum memory”, (2024) arXiv:2406.14445. Appears in: Abelian LP code, Generalized bicycle (GB) code, Quasi-cyclic LDPC (QC-LDPC) code, Single-shot code
T. R. Scruby, A. Pesah, and M. Webster, “Quantum Rainbow Codes”, (2024) arXiv:2408.13130. Appears in: Hypergraph product (HGP) code, Quantum pin code, Quantum rainbow code, Triorthogonal code, Quasi-hyperbolic color code, Generalized homological-product qubit CSS code
T. R. Scruby and Z. Cai, “Fault-tolerant Quantum Computation without Distillation on a 2D Device”, (2024) arXiv:2412.12529. Appears in: Kitaev surface code
J. R. Seddon and E. T. Campbell, “Quantifying magic for multi-qubit operations”, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, 20190251 (2019) arXiv:1901.03322 DOI. Appears in: Qubit stabilizer code
C. N. Self, M. Benedetti, and D. Amaro, “Protecting expressive circuits with a quantum error detection code”, Nature Physics 20, 219 (2024) arXiv:2211.06703 DOI. Appears in: $[[2m,2m-2,2]]$ error-detecting code
P. Selinger, “Generators and relations for n-qubit Clifford operators”, Logical Methods in Computer Science Volume 11, Issue 2, (2015) arXiv:1310.6813 DOI. Appears in: Qubit code
N. V. Semakov, V. A. Zinovev, Complete and Quasi-complete Balanced Codes, Probl. Peredachi Inf., 5:2 (1969), 14–18; Problems Inform. Transmission, 5:2 (1969), 11–13. Appears in: Nordstrom-Robinson (NR) code
N. V. Semakov, V. A. Zinov'ev, G. V. Zaitsev, “Uniformly Packed Codes”, Probl. Peredachi Inf., 7:1 (1971), 38–50; Problems Inform. Transmission, 7:1 (1971), 30–39. Appears in: Nearly perfect code, Uniformly packed code
N. V. Semakov, V. A. Zinoviev, “Equidistant q-ary Codes with Maximal Distance and Resolvable Balanced Incomplete Block Designs”, Probl. Peredachi Inf., 4:2 (1968), 3–10; Problems Inform. Transmission, 4:2 (1968), 1–7. Appears in: $ED_m$ code
N. V. Semakov, V. A. Zinoviev, G. V. Zaitsev, “A Class of Maximum Equidistant Codes”, Probl. Peredachi Inf., 5:2 (1969), 84–87; Problems Inform. Transmission, 5:2 (1969), 65–68. Appears in: Semakov-Zinoviev-Zaitsev (SZZ) equidistant code
G. Semeghini et al., “Probing topological spin liquids on a programmable quantum simulator”, Science 374, 1242 (2021) arXiv:2104.04119 DOI. Appears in: Kitaev surface code
A. Serafini, O. C. O. Dahlsten, D. Gross, and M. B. Plenio, “Canonical and micro-canonical typical entanglement of continuous variable systems”, Journal of Physics A: Mathematical and Theoretical 40, 9551 (2007) arXiv:quant-ph/0701051 DOI. Appears in: Bosonic code
A. Serafini, “Quantum Continuous Variables”, (2017) DOI. Appears in: Bosonic code
G. Seroussi and A. Lempel, “Factorization of Symmetric Matrices and Trace-Orthogonal Bases in Finite Fields”, SIAM Journal on Computing 9, 758 (1980) DOI. Appears in: Reed-Muller (RM) code
K. Setia, S. Bravyi, A. Mezzacapo, and J. D. Whitfield, “Superfast encodings for fermionic quantum simulation”, Physical Review Research 1, (2019) arXiv:1810.05274 DOI. Appears in: Bravyi-Kitaev superfast (BKSF) code
F. Setiawan and C. McLauchlan, “Tailoring Dynamical Codes for Biased Noise: The X$^3$Z$^3$ Floquet Code”, (2024) arXiv:2411.04974. Appears in: Asymmetric quantum code, Hastings-Haah Floquet code
P. D. Seymour and T. Zaslavsky, “Averaging sets: A generalization of mean values and spherical designs”, Advances in Mathematics 52, 213 (1984) DOI. Appears in: $t$-design
R. A. Shaikh, L. Yeh, and S. Gogioso, “The Focked-up ZX Calculus: Picturing Continuous-Variable Quantum Computation”, (2024) arXiv:2406.02905. Appears in: Bosonic code
I. Shakeel, M. O. Hasna, A. Abu-Dayya, and A. Ghrayeb, “Reed-Solomon coding for cooperative wireless communication”, 21st Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications 1021 (2010) DOI. Appears in: Reed-Solomon (RS) code
C. Shangguan, X. Wang, G. Ge, and Y. Miao, “New Bounds For Frameproof Codes”, (2014) arXiv:1411.5782. Appears in: Frameproof (FP) code
C. E. Shannon, “A Mathematical Theory of Communication”, Bell System Technical Journal 27, 379 (1948) DOI. Appears in: Error-correcting code (ECC), Finite-dimensional error-correcting code (ECC), $[2^r,2^r-r-1,4]$ Extended Hamming code, $[7,4,3]$ Hamming code, $[8,4,4]$ extended Hamming code, $q$-ary simplex code, Random code, $[2^m-1,m,2^{m-1}]$ simplex code
C. E. Shannon, “A Mathematical Theory of Communication”, Bell System Technical Journal 27, 623 (1948) DOI. Appears in: Binary PSK (BPSK) code
C. E. Shannon, “Communication in the Presence of Noise”, Proceedings of the IRE 37, 10 (1949) DOI. Appears in: Sphere packing
C. E. Shannon, “Probability of Error for Optimal Codes in a Gaussian Channel”, Bell System Technical Journal 38, 611 (1959) DOI. Appears in: Block code, Sphere packing
C. E. Shannon, R. G. Gallager, and E. R. Berlekamp, “Lower bounds to error probability for coding on discrete memoryless channels. I”, Information and Control 10, 65 (1967) DOI. Appears in: Block code
H. S. Shapiro and D. L. Slotnick, “On the Mathematical Theory of Error-Correcting Codes”, IBM Journal of Research and Development 3, 25 (1959) DOI. Appears in: Perfect code
J. H. Shapiro, “The Quantum Theory of Optical Communications”, IEEE Journal of Selected Topics in Quantum Electronics 15, 1547 (2009) DOI. Appears in: Bosonic c-q code
Y. Sharf, D. G. Cory, S. S. Somaroo, T. F. Havel, E. Knill, R. Laflamme, and W. H. Zurek, “A study of quantum error correction by geometric algebra and liquid-state NMR spectroscopy”, Molecular Physics 98, 1347 (2000) arXiv:quant-ph/0004030 DOI. Appears in: Quantum repetition code
A. K. Sharma and S. S. Garani, “Fault-Tolerant Quantum LDPC Encoders”, (2024) arXiv:2405.07242. Appears in: EA qubit stabilizer code, Quantum LDPC (QLDPC) code
K. Sharma, M. M. Wilde, S. Adhikari, and M. Takeoka, “Bounding the energy-constrained quantum and private capacities of phase-insensitive bosonic Gaussian channels”, New Journal of Physics 20, 063025 (2018) arXiv:1708.07257 DOI. Appears in: Gottesman-Kitaev-Preskill (GKP) code
B. A. Shaw, “Quantum Steganography and Quantum Error-Correction”, (2010) arXiv:1008.0425. Appears in: $[[6,1,3]]$ Six-qubit stabilizer code, Subsystem qubit stabilizer code
B. Shaw, M. M. Wilde, O. Oreshkov, I. Kremsky, and D. A. Lidar, “Encoding one logical qubit into six physical qubits”, Physical Review A 78, (2008) arXiv:0803.1495 DOI. Appears in: EA qubit stabilizer code, Five-qubit perfect code, $[[6,1,3]]$ Six-qubit stabilizer code, $[[7,1,3]]$ Steane code, Subsystem qubit stabilizer code
M. H. Shaw and B. M. Terhal, “Lowering Connectivity Requirements For Bivariate Bicycle Codes Using Morphing Circuits”, (2024) arXiv:2407.16336. Appears in: $[[144,12,12]]$ gross code, Bivariate bicycle (BB) code
M. L. Shcherbatenko, M. S. Elezov, G. N. Goltsman, and D. V. Sych, “Sub-shot-noise-limited fiber-optic quantum receiver”, Physical Review A 101, (2020) arXiv:1911.08932 DOI. Appears in: BPSK c-q code
R. Shen, Y. Wang, and C. Cao, “Quantum Lego and XP Stabilizer Codes”, (2023) arXiv:2310.19538. Appears in: Tensor-network code, $[[15,1,3]]$ quantum Reed-Muller code, XP stabilizer code
S. Sheng-Ju, “Implementation of Cyclic Redundancy Check in Data Communication”, 2015 International Conference on Computational Intelligence and Communication Networks (CICN) (2015) DOI. Appears in: Cyclic redundancy check (CRC) code
N. Shental et al., “Efficient high-throughput SARS-CoV-2 testing to detect asymptomatic carriers”, Science Advances 6, (2020) DOI. Appears in: Reed-Solomon (RS) code
F. Shi, M.-S. Li, L. Chen, and X. Zhang, “k -uniform quantum information masking”, Physical Review A 104, (2021) arXiv:2009.12497 DOI. Appears in: Perfect-tensor code
M. Shi, D. Lu, A. Armario, R. Egan, F. Ozbudak, and P. Solé, “Butson Hadamard matrices, bent sequences, and spherical codes”, (2023) arXiv:2311.00354. Appears in: Complex Hadamard spherical code
M. Shi, H. Lu, J.-L. Kim, and P. Sole, “Triorthogonal Codes and Self-dual Codes”, (2024) arXiv:2408.09685. Appears in: Triorthogonal code, Self-dual linear code
Y. Shi, “Both Toffoli and Controlled-NOT need little help to do universal quantum computation”, (2002) arXiv:quant-ph/0205115. Appears in: Qubit code
Y. Shi, A. Patil, and S. Guha, “Stabilizer Entanglement Distillation and Efficient Fault-Tolerant Encoder”, (2024) arXiv:2408.06299. Appears in: Linear binary code, Quantum LDPC (QLDPC) code, Qubit stabilizer code
T. Shibayama and M. Hagiwara, “Permutation-Invariant Quantum Codes for Deletion Errors”, 2021 IEEE International Symposium on Information Theory (ISIT) 1493 (2021) arXiv:2102.03015 DOI. Appears in: Block quantum code, Permutation-invariant (PI) code
T. Shibayama and Y. Ouyang, “The equivalence between correctability of deletions and insertions of separable states in quantum codes”, 2021 IEEE Information Theory Workshop (ITW) 1 (2021) arXiv:2105.07214 DOI. Appears in: Block quantum code
T. Shibayama, “Necessary and sufficient condition for constructing a single qudit insertion/deletion code and its decoding algorithm”, (2025) arXiv:2501.07027. Appears in: Block quantum code
K. Shimizu, T. Ishikawa, N. Togawa, T. Ikenaga, and S. Goto, “A parallel LSI architecture for LDPC decoder improving message-passing schedule”, 2006 IEEE International Symposium on Circuits and Systems DOI. Appears in: Low-density parity-check (LDPC) code
J. Shin, J. Heo, and T. A. Brun, “Entanglement-assisted codeword stabilized quantum codes”, Physical Review A 84, (2011) arXiv:1109.3358 DOI. Appears in: Codeword stabilized (CWS) code, EA qubit code
M. Shinoda, “Existence of phase transition of percolation on Sierpiński carpet lattices”, Journal of Applied Probability 39, 1 (2002) DOI. Appears in: Fractal surface code, Self-correcting quantum code
K. Shiraishi, H. Yamasaki, and M. Murao, “Efficient local operations and classical communication extraction of quantum information encoded in stabilizer codes”, Physical Review A 110, (2024) arXiv:2308.14054 DOI. Appears in: Qubit stabilizer code
W. Shirley, K. Slagle, and X. Chen, “Foliated fracton order from gauging subsystem symmetries”, SciPost Physics 6, (2019) arXiv:1806.08679 DOI. Appears in: 2D color code, 3D color code, 3D subsystem color code, 3D surface code, Color code, Cubic theory code, Double-semion stabilizer code, Homological code, Abelian quantum-double stabilizer code, Dihedral $G=D_m$ quantum-double code, Concatenated qubit code, Subsystem modular-qudit stabilizer code, Modular-qudit surface code, Kitaev surface code, Abelian TQD stabilizer code, Two-foliated fracton code, Two-gauge theory code
W. Shirley, K. Slagle, and X. Chen, “Foliated fracton order in the checkerboard model”, Physical Review B 99, (2019) arXiv:1806.08633 DOI. Appears in: Checkerboard model code, Fracton stabilizer code, X-cube model code
W. Shirley, K. Slagle, and X. Chen, “Fractional excitations in foliated fracton phases”, Annals of Physics 410, 167922 (2019) arXiv:1806.08625 DOI. Appears in: Two-foliated fracton code, X-cube model code
W. Shirley, K. Slagle, and X. Chen, “Universal entanglement signatures of foliated fracton phases”, SciPost Physics 6, (2019) arXiv:1803.10426 DOI. Appears in: Fracton stabilizer code, X-cube model code
W. Shirley, “Fractonic order and emergent fermionic gauge theory”, (2020) arXiv:2002.12026. Appears in: Bosonization code
W. Shirley, Y.-A. Chen, A. Dua, T. D. Ellison, N. Tantivasadakarn, and D. J. Williamson, “Three-Dimensional Quantum Cellular Automata from Chiral Semion Surface Topological Order and beyond”, PRX Quantum 3, (2022) arXiv:2202.05442 DOI. Appears in: Chiral semion Walker-Wang model code, Chiral semion subsystem code, Abelian topological code, Abelian TQD stabilizer code, Walker-Wang model code
A. Shokrollahi, “LDPC Codes: An Introduction”, Coding, Cryptography and Combinatorics 85 (2004) DOI. Appears in: Low-density parity-check (LDPC) code
A. Shokrollahi, “Raptor codes”, IEEE Transactions on Information Theory 52, 2551 (2006) DOI. Appears in: Fountain code, Low-density parity-check (LDPC) code, Raptor (RAPid TORnado) code, Tornado code
M. A. Shokrollahi and H. Wasserman, “List decoding of algebraic-geometric codes”, IEEE Transactions on Information Theory 45, 432 (1999) DOI. Appears in: Evaluation AG code
P. W. Shor, “Scheme for reducing decoherence in quantum computer memory”, Physical Review A 52, R2493 (1995) DOI. Appears in: Bacon-Shor code, $[[4,1,1,2]]$ Four-qubit subsystem code, $[[9,1,3,3]]$ Nine-qubit Bacon-Shor code, Quantum parity code (QPC), $[[9,1,3]]$ Shor code
P. W. Shor, “Fault-tolerant quantum computation”, (1997) arXiv:quant-ph/9605011. Appears in: Quantum data-syndrome (QDS) code, Qubit CSS code, Qubit stabilizer code, $[[7,1,3]]$ Steane code, Subsystem spacetime circuit code
P. W. Shor and J. Preskill, “Simple Proof of Security of the BB84 Quantum Key Distribution Protocol”, Physical Review Letters 85, 441 (2000) arXiv:quant-ph/0003004 DOI. Appears in: Qubit CSS code
P. W. Shor, G. Smith, J. A. Smolin, and B. Zeng, “High performance single-error-correcting quantum codes for amplitude damping”, (2009) arXiv:0907.5149. Appears in: Amplitude-damping (AD) code, Amplitude-damping CWS code, Constantin-Rao (CR) code, Self-complementary qubit code
P. Shor and R. Laflamme, “Quantum MacWilliams Identities”, (1996) arXiv:quant-ph/9610040. Appears in: Qubit code
Shruti Puri, QEC when the noise is biased, 2019.. Appears in: Two-component cat code
O. Shtanko, Y.-J. Liu, S. Lieu, A. V. Gorshkov, and V. V. Albert, “Bounds on Autonomous Quantum Error Correction”, (2023) arXiv:2308.16233. Appears in: Qubit stabilizer code
S. K. Shukla, T. D. Ellison, and L. Fidkowski, “Tensor network approach to two-dimensional bosonization”, Physical Review B 101, (2020) arXiv:1909.10552 DOI. Appears in: 2D bosonization code
N. Shutty and C. Chamberland, “Decoding Merged Color-Surface Codes and Finding Fault-Tolerant Clifford Circuits Using Solvers for Satisfiability Modulo Theories”, Physical Review Applied 18, (2022) arXiv:2201.12450 DOI. Appears in: Color code, Homological code
N. Shutty, M. Newman, and B. Villalonga, “Efficient near-optimal decoding of the surface code through ensembling”, (2024) arXiv:2401.12434. Appears in: Kitaev surface code
I. Siap, T. Abualrub, N. Aydin, and P. Seneviratne, “Skew cyclic codes of arbitrary length”, International Journal of Information and Coding Theory 2, 10 (2011) DOI. Appears in: Quasi-cyclic code, Skew-cyclic code
T. Sidana and N. Kashyap, “Entanglement-Assisted Quantum Error-Correcting Codes over Local Frobenius Rings”, (2023) arXiv:2202.00248. Appears in: EA Galois-qudit stabilizer code, Concatenated quantum code
V. M. Sidelnikov, “On a finite group of matrices generating orbit codes on Euclidean sphere”, Proceedings of IEEE International Symposium on Information Theory 436 DOI. Appears in: Barnes-Wall (BW) lattice, Real-Clifford subgroup-orbit code
V. M. SIDELNIKOV and S. O. SHESTAKOV, “On insecurity of cryptosystems based on generalized Reed-Solomon codes”, Discrete Mathematics and Applications 2, (1992) DOI. Appears in: Generalized RS (GRS) code
V. M. Sidelnikov, Journal of Algebraic Combinatorics 10, 279 (1999) DOI. Appears in: Real-Clifford subgroup-orbit code, Spherical design
V. M. Sidelnikov, On a finite group of matrices and codes on the Euclidean sphere (in Russian), Probl. Peredach. Inform. 33 (1997), 35–54 (1997); English translation in Problems Inform. Transmission 33 (1997), 29–44. Appears in: Barnes-Wall (BW) lattice, Real-Clifford subgroup-orbit code
V. M. Sidelnikov, “Orbital spherical 11-designs in which the initial point is a root of an invariant polynomial”, Algebra i Analiz, 11:4 (1999), 183–203; St. Petersburg Math. J., 11:4 (2000), 673–686. Appears in: Real-Clifford subgroup-orbit code, Spherical design
J. S. Sidhu, M. S. Bullock, S. Guha, and C. Lupo, “Linear optics and photodetection achieve near-optimal unambiguous coherent state discrimination”, Quantum 7, 1025 (2023) arXiv:2109.00008 DOI. Appears in: Coherent-state c-q code
A. Siegel, A. Strikis, T. Flatters, and S. Benjamin, “Adaptive surface code for quantum error correction in the presence of temporary or permanent defects”, Quantum 7, 1065 (2023) arXiv:2211.08468 DOI. Appears in: Kitaev surface code
D. Silva and F. R. Kschischang, “Rank-Metric Codes for Priority Encoding Transmission with Network Coding”, 2007 10th Canadian Workshop on Information Theory (CWIT) 81 (2007) DOI. Appears in: Rank-metric code
D. Silva, F. R. Kschischang, and R. Koetter, “A Rank-Metric Approach to Error Control in Random Network Coding”, IEEE Transactions on Information Theory 54, 3951 (2008) arXiv:0711.0708 DOI. Appears in: Maximum-rank distance (MRD) code
D. Silva, F. R. Kschischang, and R. Koetter, “A Rank-Metric Approach to Error Control in Random Network Coding”, IEEE Transactions on Information Theory 54, 3951 (2008) DOI. Appears in: Rank-metric code, Subspace code
D. Silva and F. R. Kschischang, “Fast encoding and decoding of Gabidulin codes”, 2009 IEEE International Symposium on Information Theory 2858 (2009) arXiv:0901.2483 DOI. Appears in: Gabidulin code
D. Silva and F. R. Kschischang, “On Metrics for Error Correction in Network Coding”, IEEE Transactions on Information Theory 55, 5479 (2009) arXiv:0805.3824 DOI. Appears in: Subspace code
E. B. da Silva, M. Firer, S. R. Costa, and R. Palazzo Jr., “Signal constellations in the hyperbolic plane: A proposal for new communication systems”, Journal of the Franklin Institute 343, 69 (2006) DOI. Appears in: Hyperbolic sphere packing
E. B. da Silva and W. S. Soares Junior, “Construction of color codes from polygons”, Journal of Physics Communications 2, 095011 (2018) DOI. Appears in: Square-octagon (4.8.8) color code
E. B. da Silva and W. S. Soares Jr, “Hyperbolic quantum color codes”, (2018) arXiv:1804.06382. Appears in: Hyperbolic color code
M. Silva, “Erasure Thresholds for Efficient Linear Optics Quantum Computation”, (2004) arXiv:quant-ph/0405112. Appears in: Concatenated Steane code, Dual-rail quantum code, Concatenated bosonic code, $[[7,1,3]]$ Steane code
M. Silva, M. Rötteler, and C. Zalka, “Thresholds for linear optics quantum computing with photon loss at the detectors”, Physical Review A 72, (2005) arXiv:quant-ph/0502101 DOI. Appears in: Concatenated Steane code, Dual-rail quantum code, Concatenated bosonic code, $[[7,1,3]]$ Steane code
N. de Silva and O. Lautsch, “The Clifford hierarchy for one qubit or qudit”, (2025) arXiv:2501.07939. Appears in: Qubit code, Modular-qudit code
Silva, E. B., R. Palazzo Jr, and M. Firer. "Performance analysis of QAM-like constellations in hyperbolic space." 2000 International Symposium on Information Theory and its Applications, Honolulu, USA. 2000.. Appears in: Hyperbolic sphere packing, Quadrature-amplitude modulation (QAM) code
Silva, E. B., and R. Palazzo Jr. "M-PSK signal constellations in hyperbolic space achieving better performance than the M-PSK signal constellations in Euclidean space." 1999 IEEE Information Theory Workshop, Metsovo, Greece. 1999.. Appears in: Hyperbolic sphere packing, Phase-shift keying (PSK) code
R. Silverman and M. Balser, “Coding for constant-data-rate systems”, Transactions of the IRE Professional Group on Information Theory 4, 50 (1954) DOI. Appears in: Single parity-check (SPC) code
Ilya. A. Simakov and Ilya. S. Besedin, “Low-overhead quantum error correction codes with a cyclic topology”, (2024) arXiv:2211.03094. Appears in: $(5,1,2)$-convolutional code, Five-qubit perfect code
R. Simon, E. C. G. Sudarshan, and N. Mukunda, “Gaussian pure states in quantum mechanics and the symplectic group”, Physical Review A 37, 3028 (1988) DOI. Appears in: Bosonic code
T. Singal, C. Chiang, E. Hsu, E. Kim, H.-S. Goan, and M.-H. Hsieh, “Counting stabiliser codes for arbitrary dimension”, Quantum 7, 1048 (2023) arXiv:2209.01449 DOI. Appears in: Modular-qudit stabilizer code
D. Singh and S. Prakash, “Fault-Tolerant Implementation of the Deutsch-Jozsa Algorithm”, (2024) arXiv:2412.04791. Appears in: $[[4,2,2]]$ Four-qubit code
P. Singkanipa, Z. Xia, and D. A. Lidar, “Families of $d=2$ 2D subsystem stabilizer codes for universal Hamiltonian quantum computation with two-body interactions”, (2025) arXiv:2412.06744. Appears in: $[[2m,2m-2,2]]$ error-detecting code, Trapezoid subsystem code
R. Singleton, “Maximum distance&lt;tex&gt;q&lt;/tex&gt;-nary codes”, IEEE Transactions on Information Theory 10, 116 (1964) DOI. Appears in: Maximum distance separable (MDS) code
M. Sipser and D. A. Spielman, “Expander codes”, IEEE Transactions on Information Theory 42, 1710 (1996) DOI. Appears in: Expander code, Regular binary Tanner code
R. M. Siqueira and S. I. R. Costa, “Flat tori, lattices and bounds for commutative group codes”, Designs, Codes and Cryptography 49, 307 (2008) DOI. Appears in: Slepian group-orbit code
V. V. Sivak et al., “Real-time quantum error correction beyond break-even”, Nature 616, 50 (2023) arXiv:2211.09116 DOI. Appears in: Binomial code, Square-lattice GKP code
V. Skachek, “Batch and PIR Codes and Their Connections to Locally Repairable Codes”, (2017) arXiv:1611.09914. Appears in: Batch code, Locally recoverable code (LRC), Private information retrieval (PIR) code
V. Skachek, “Batch and PIR Codes and Their Connections to Locally Repairable Codes”, Signals and Communication Technology 427 (2018) DOI. Appears in: Batch code, Locally recoverable code (LRC)
B. Skinner, J. Ruhman, and A. Nahum, “Measurement-Induced Phase Transitions in the Dynamics of Entanglement”, Physical Review X 9, (2019) DOI. Appears in: Monitored random-circuit code
B. Sklar, “A primer on turbo code concepts”, IEEE Communications Magazine 35, 94 (1997) DOI. Appears in: Turbo code
L. Skoric, D. E. Browne, K. M. Barnes, N. I. Gillespie, and E. T. Campbell, “Parallel window decoding enables scalable fault tolerant quantum computation”, Nature Communications 14, (2023) arXiv:2209.08552 DOI. Appears in: Kitaev surface code
A. N. Skorobogatov and S. G. Vladut, “On the decoding of algebraic-geometric codes”, IEEE Transactions on Information Theory 36, 1051 (1990) DOI. Appears in: Plane-curve code
D. Slepian, “A Class of Binary Signaling Alphabets”, Bell System Technical Journal 35, 203 (1956) DOI. Appears in: Binary group-orbit code
D. Slepian, “Some Further Theory of Group Codes”, Bell System Technical Journal 39, 1219 (1960) DOI. Appears in: Binary group-orbit code, Linear binary code
D. Slepian, “Bounds on Communication”, Bell System Technical Journal 42, 681 (1963) DOI. Appears in: Sphere packing
D. Slepian, “Permutation modulation”, Proceedings of the IEEE 53, 228 (1965) DOI. Appears in: Permutation spherical code
D. Slepian, “Group Codes for the Gaussian Channel”, Bell System Technical Journal 47, 575 (1968) DOI. Appears in: Slepian group-orbit code
N. J. A. Sloane, R. H. Hardin, and P. Cara, “Spherical designs in four dimensions”, Proceedings 2003 IEEE Information Theory Workshop (Cat. No.03EX674) DOI. Appears in: Disphenoidal 288-cell code, Spherical design
N. J. A. Sloane and J. J. Seidel, “A NEW FAMILY OF NONLINEAR CODES OBTAINED FROM CONFERENCE MATRICES”, Annals of the New York Academy of Sciences 175, 363 (1970) DOI. Appears in: Conference code
N. J. A. Sloane and J. Stufken, “A linear programming bound for orthogonal arrays with mixed levels”, Journal of Statistical Planning and Inference 56, 295 (1996) DOI. Appears in: Mixed code, Orthogonal array (OA)
N. J. A. Sloane, “On Single-Deletion-Correcting Codes”, (2002) arXiv:math/0207197. Appears in: Editing code, Varshamov-Tenengolts (VT) code
N. Sloane and D. Whitehead, “New family of single-error correcting codes”, IEEE Transactions on Information Theory 16, 717 (1970) DOI. Appears in: Binary quadratic-residue (QR) code, Sloane-Whitehead code, $(u|u+v)$-construction code
N. Sloane, “Is there a (72,36) d = 16 self-dual code? (Corresp.)”, IEEE Transactions on Information Theory 19, 251 (1973) DOI. Appears in: Self-dual linear code
N. Sloane, “Tables of sphere packings and spherical codes”, IEEE Transactions on Information Theory 27, 327 (1981) DOI. Appears in: Lattice-shell code
Sloane, N. J. A., R. H. Hardin, and W. D. Smith. "Tables of spherical codes." collaboration with R. H. Hardin, W. D. Smith and others. Published electronically at https://neilsloane.com/packings/ (2004).. Appears in: Smith $40$-point code
Sloane, N. J. A., R. H. Hardin, and W. D. Smith. "Tables of spherical codes." collaboration with RH Hardin, WD Smith and others. Published electronically at https://neilsloane.com/packings/ (2004).. Appears in: Spherical code
S. Slussarenko and G. J. Pryde, “Photonic quantum information processing: A concise review”, Applied Physics Reviews 6, (2019) arXiv:1907.06331 DOI. Appears in: Cluster-state code, Dual-rail quantum code
R. Smarandache and P. O. Vontobel, “Quasi-Cyclic LDPC Codes: Influence of Proto- and Tanner-Graph Structure on Minimum Hamming Distance Upper Bounds”, IEEE Transactions on Information Theory 58, 585 (2012) DOI. Appears in: Quasi-cyclic LDPC (QC-LDPC) code
M. Smid, “Duadic codes (Corresp.)”, IEEE Transactions on Information Theory 33, 432 (1987) DOI. Appears in: $q$-ary duadic code
A. Smith, O. Golan, and Z. Ringel, “Intrinsic sign problems in topological quantum field theories”, Physical Review Research 2, (2020) arXiv:2005.05343 DOI. Appears in: Double-semion stabilizer code
D. H. Smith, L. A. Hughes, and S. Perkins, “A New Table of Constant Weight Codes of Length Greater than 28”, The Electronic Journal of Combinatorics 13, (2006) DOI. Appears in: Constant-weight code
G. S. B. Smith, Upper and Lower Bounds on Quantum Codes, California Institute of Technology, 2006 DOI. Appears in: Block quantum code
G. Smith and J. A. Smolin, “Degenerate Quantum Codes for Pauli Channels”, Physical Review Letters 98, (2007) arXiv:quant-ph/0604107 DOI. Appears in: Qubit stabilizer code
G. Smith, J. A. Smolin, and A. Winter, “The Quantum Capacity With Symmetric Side Channels”, IEEE Transactions on Information Theory 54, 4208 (2008) arXiv:quant-ph/0607039 DOI. Appears in: Qubit code
S. C. Smith, B. J. Brown, and S. D. Bartlett, “Local Predecoder to Reduce the Bandwidth and Latency of Quantum Error Correction”, Physical Review Applied 19, (2023) arXiv:2208.04660 DOI. Appears in: Kitaev surface code
S. C. Smith, B. J. Brown, and S. D. Bartlett, “Mitigating errors in logical qubits”, Communications Physics 7, (2024) arXiv:2405.03766 DOI. Appears in: Kitaev surface code
J. A. Smolin, G. Smith, and S. Wehner, “Simple Family of Nonadditive Quantum Codes”, Physical Review Letters 99, (2007) arXiv:quant-ph/0701065 DOI. Appears in: Binary code, Self-complementary qubit code, Smolin-Smith-Wehner (SSW) code
Snover, S. L. (1973). THE UNIQUENESS OF THE NORDSTROM-ROBINSON AND THE GOLAY BINARY-CODES. Michigan State University.. Appears in: Nordstrom-Robinson (NR) code
S. L. Sobolev, “Cubature Formulas on the Sphere Invariant under Finite Groups of Rotations”, Selected Works of S.L. Sobolev 461 DOI. Appears in: Slepian group-orbit code, Spherical design
L. Sok, “On linear codes with one-dimensional Euclidean hull and their applications to EAQECCs”, (2021) arXiv:2101.06461. Appears in: Algebraic-geometry (AG) code, EA Galois-qudit stabilizer code
H. M. Solanki and P. Kiran Sarvepalli, “Correcting Erasures with Topological Subsystem Color Codes”, 2020 IEEE Information Theory Workshop (ITW) 1 (2021) DOI. Appears in: 2D subsystem color code, Subsystem color code
H. M. Solanki and P. K. Sarvepalli, “Decoding Topological Subsystem Color Codes Over the Erasure Channel using Gauge Fixing”, (2022) arXiv:2111.14594. Appears in: 2D subsystem color code, Subsystem color code
H. M. Solanki and P. K. Sarvepalli, “Decoding Topological Subsystem Color Codes Over the Erasure Channel Using Gauge Fixing”, IEEE Transactions on Communications 71, 4181 (2023) DOI. Appears in: 2D subsystem color code
E. Soljanin and E. Offer, “LDPC codes: a group algebra formulation”, Electronic Notes in Discrete Mathematics 6, 148 (2001) DOI. Appears in: Tanner code
G. Solomon and J. J. Stiffler, “Algebraically punctured cyclic codes”, Information and Control 8, 170 (1965) DOI. Appears in: Griesmer code
G. Solomon and H. C. A. Tilborg, “A Connection Between Block and Convolutional Codes”, SIAM Journal on Applied Mathematics 37, 358 (1979) DOI. Appears in: Convolutional code, Quasi-cyclic code
F. I. Solov'eva, S. T. Topalova, “On Automorphism Groups of Perfect Binary Codes and Steiner Triple Systems”, Probl. Peredachi Inf., 36:4 (2000), 53–58; Problems Inform. Transmission, 36:4 (2000), 331–335. Appears in: Perfect binary code
F. I. Solov'eva, S. T. Topalova, “Perfect binary codes and Steiner triple systems with maximum orders of automorphism groups”, Diskretn. Anal. Issled. Oper., Ser. 1, 7:4 (2000), 101–110. Appears in: Perfect binary code
R. D. Somma, “Quantum Computation, Complexity, and Many-Body Physics”, (2005) arXiv:quant-ph/0512209. Appears in: One-hot quantum code
R. Somma, G. Ortiz, J. E. Gubernatis, E. Knill, and R. Laflamme, “Simulating physical phenomena by quantum networks”, Physical Review A 65, (2002) arXiv:quant-ph/0108146 DOI. Appears in: Jordan-Wigner transformation code
G. M. Sommers, D. A. Huse, and M. J. Gullans, “Crystalline Quantum Circuits”, PRX Quantum 4, (2023) arXiv:2210.10808 DOI. Appears in: Crystalline-circuit qubit code
G. M. Sommers, D. A. Huse, and M. J. Gullans, “Dynamically generated concatenated codes and their phase diagrams”, (2024) arXiv:2409.13801. Appears in: Quantum parity code (QPC)
W. Son, L. Amico, and V. Vedral, “Topological order in 1D Cluster state protected by symmetry”, Quantum Information Processing 11, 1961 (2011) arXiv:1111.7173 DOI. Appears in: Cluster-state code, Symmetry-protected topological (SPT) code, Lattice stabilizer code
H. Song, A. Prem, S.-J. Huang, and M. A. Martin-Delgado, “Twisted fracton models in three dimensions”, Physical Review B 99, (2019) arXiv:1805.06899 DOI. Appears in: Checkerboard model code
H. Song, J. Schönmeier-Kromer, K. Liu, O. Viyuela, L. Pollet, and M. A. Martin-Delgado, “Optimal Thresholds for Fracton Codes and Random Spin Models with Subsystem Symmetry”, Physical Review Letters 129, (2022) arXiv:2112.05122 DOI. Appears in: Checkerboard model code, X-cube model code
Z. Song, A. Dua, W. Shirley, and D. J. Williamson, “Topological Defect Network Representations of Fracton Stabilizer Codes”, PRX Quantum 4, (2023) arXiv:2112.14717 DOI. Appears in: Fracton stabilizer code, Topological code
Z. Song and G. Zhu, “Magic Boundaries of 3D Color Codes”, (2024) arXiv:2404.05033. Appears in: 3D color code, 3D surface code
A. B. Sorensen, “Projective Reed-Muller codes”, IEEE Transactions on Information Theory 37, 1567 (1991) DOI. Appears in: Projective RM (PRM) code
N. Sourlas, “Spin-glass models as error-correcting codes”, Nature 339, 693 (1989) DOI. Appears in: Block code
A. M. Souza, J. Zhang, C. A. Ryan, and R. Laflamme, “Experimental magic state distillation for fault-tolerant quantum computing”, Nature Communications 2, (2011) arXiv:1103.2178 DOI. Appears in: Five-qubit perfect code
L. Spagnoli, A. Roggero, and N. Wiebe, “Fault-tolerant simulation of Lattice Gauge Theories with gauge covariant codes”, (2024) arXiv:2405.19293. Appears in: Fermion-into-qubit code, Gauss' law code, Concatenated qubit code, Abelian topological code
F. M. Spedalieri and V. P. Roychowdhury, “Latency in local, two-dimensional, fault-tolerant quantum computing”, (2008) arXiv:0805.4213. Appears in: $[[9,1,3,3]]$ Nine-qubit Bacon-Shor code
D. A. Spielman, “Linear-time encodable and decodable error-correcting codes”, IEEE Transactions on Information Theory 42, 1723 (1996) DOI. Appears in: Expander code, Regular binary Tanner code
J. J. SPILKER Jr., “GPS Signal Structure and Performance Characteristics”, Navigation 25, 121 (1978) DOI. Appears in: Gold code
B. Srivastava, A. Frisk Kockum, and M. Granath, “The XYZ2 hexagonal stabilizer code”, Quantum 6, 698 (2022) arXiv:2112.06036 DOI. Appears in: XYZ$^2$ hexagonal stabilizer code
T. M. Stace, S. D. Barrett, and A. C. Doherty, “Thresholds for Topological Codes in the Presence of Loss”, Physical Review Letters 102, (2009) arXiv:0904.3556 DOI. Appears in: Toric code
T. M. Stace and S. D. Barrett, “Error correction and degeneracy in surface codes suffering loss”, Physical Review A 81, (2010) arXiv:0912.1159 DOI. Appears in: Toric code
B. C. Stacey, “Sporadic SICs and Exceptional Lie Algebras”, (2019) arXiv:1911.05809. Appears in: Hessian polyhedron code
J. N. Staddon, D. R. Stinson, and Ruizhong Wei, “Combinatorial properties of frameproof and traceability codes”, IEEE Transactions on Information Theory 47, 1042 (2001) DOI. Appears in: Frameproof (FP) code, Identifiable parent property (IPP) code, $q$-ary code, Traceability code
M. P. Stafford and N. C. Menicucci, “Biased Gottesman-Kitaev-Preskill repetition code”, Physical Review A 108, (2023) arXiv:2212.11397 DOI. Appears in: Concatenated GKP code, Quantum repetition code
C. Stahl, “Self-Correction from Higher-Form Symmetry Protection on a Boundary”, PRX Quantum 4, (2023) arXiv:2206.05294 DOI. Appears in: Symmetry-protected self-correcting quantum code
C. Stahl, “Single-shot quantum error correction in intertwined toric codes”, Physical Review B 110, (2024) arXiv:2307.08118 DOI. Appears in: 3D subsystem surface code, Single-shot code
C. Stark, L. Pollet, A. Imamoğlu, and R. Renner, “Localization of Toric Code Defects”, Physical Review Letters 107, (2011) arXiv:1101.6028 DOI. Appears in: Self-correcting quantum code, Kitaev surface code
A. M. Steane, “Simple quantum error-correcting codes”, Physical Review A 54, 4741 (1996) arXiv:quant-ph/9605021 DOI. Appears in: Asymmetric quantum code, $[2^m,m+1,2^{m-1}]$ First-order RM code, $[[2m,2m-2,2]]$ error-detecting code, Qubit BCH code, $[[2^r, 2^r-r-2, 3]]$ Gottesman code, $[[2^r-1, 2^r-2r-1, 3]]$ quantum Hamming code, Qubit CSS code, $[[23, 1, 7]]$ Quantum Golay code, $[[15, 7, 3]]$ quantum Hamming code, $[[6,4,2]]$ error-detecting code, $[[8, 3, 3]]$ Eight-qubit Gottesman code
A. M. Steane, “Error Correcting Codes in Quantum Theory”, Physical Review Letters 77, 793 (1996) DOI. Appears in: Galois-qudit CSS code, Qubit CSS code, Modular-qudit CSS code
A. M. Steane, “Active Stabilization, Quantum Computation, and Quantum State Synthesis”, Physical Review Letters 78, 2252 (1997) arXiv:quant-ph/9611027 DOI. Appears in: Qubit CSS code
A. M. Steane, “Space, Time, Parallelism and Noise Requirements for Reliable Quantum Computing”, Fortschritte der Physik 46, 443 (1998) arXiv:quant-ph/9708021 DOI. Appears in: Quantum divisible code, Quasi-cyclic code, Qubit stabilizer code
A. M. Steane, “Enlargement of Calderbank Shor Steane quantum codes”, (1998) arXiv:quant-ph/9802061. Appears in: Qubit BCH code, Qubit CSS code
A. M. Steane, “Efficient fault-tolerant quantum computing”, Nature 399, 124 (1999) arXiv:quant-ph/9809054 DOI. Appears in: Concatenated Steane code
A. M. Steane, “Overhead and noise threshold of fault-tolerant quantum error correction”, Physical Review A 68, (2003) arXiv:quant-ph/0207119 DOI. Appears in: Concatenated Steane code, Qubit BCH code, $[[23, 1, 7]]$ Quantum Golay code
A. M. Steane, “Quantum Computing and Error Correction”, (2003) arXiv:quant-ph/0304016. Appears in: Qubit stabilizer code
A. M. Steane, “Fast fault-tolerant filtering of quantum codewords”, (2004) arXiv:quant-ph/0202036. Appears in: Qubit CSS code
A. Steane, “Quantum Reed-Muller Codes”, (1996) arXiv:quant-ph/9608026. Appears in: Quantum Reed-Muller code, $[[15,1,3]]$ quantum Reed-Muller code
Stefan Krastanov et al., QuantumSavory/QuantumClifford.Jl: V0.9.16 (Zenodo, 2024) DOI. Appears in: Qubit stabilizer code
S. Stein et al., “Architectures for Heterogeneous Quantum Error Correction Codes”, (2024) arXiv:2411.03202. Appears in: $[[144,12,12]]$ gross code, Kitaev surface code
M. Steinberg, S. Feld, and A. Jahn, “Holographic codes from hyperinvariant tensor networks”, Nature Communications 14, (2023) arXiv:2304.02732 DOI. Appears in: Hyperinvariant tensor-network (HTN) code
M. Steinberg, J. Fan, R. J. Harris, D. Elkouss, S. Feld, and A. Jahn, “Far from Perfect: Quantum Error Correction with (Hyperinvariant) Evenbly Codes”, (2024) arXiv:2407.11926. Appears in: Hyperinvariant tensor-network (HTN) code
J. F. Steiner and F. von Oppen, “Readout of Majorana qubits”, Physical Review Research 2, (2020) arXiv:2004.02124 DOI. Appears in: Majorana box qubit
D. T. Stephen, H. P. Nautrup, J. Bermejo-Vega, J. Eisert, and R. Raussendorf, “Subsystem symmetries, quantum cellular automata, and computational phases of quantum matter”, Quantum 3, 142 (2019) arXiv:1806.08780 DOI. Appears in: Cluster-state code, Symmetry-protected topological (SPT) code, Square-lattice cluster-state code, Lattice stabilizer code
A. M. Stephens, Z. W. E. Evans, S. J. Devitt, and L. C. L. Hollenberg, “Asymmetric quantum error correction via code conversion”, Physical Review A 77, (2008) arXiv:0708.3969 DOI. Appears in: Asymmetric quantum code
A. M. Stephens, A. G. Fowler, and L. C. L. Hollenberg, “Universal fault tolerant quantum computation on bilinear nearest neighbor arrays”, (2008) arXiv:quant-ph/0702201. Appears in: Concatenated Steane code
A. M. Stephens and Z. W. E. Evans, “Accuracy threshold for concatenated error detection in one dimension”, Physical Review A 80, (2009) arXiv:0902.2658 DOI. Appears in: Concatenated qubit code, $[[4,2,2]]$ Four-qubit code
A. M. Stephens, W. J. Munro, and K. Nemoto, “High-threshold topological quantum error correction against biased noise”, Physical Review A 88, (2013) arXiv:1308.4776 DOI. Appears in: Asymmetric quantum code, Cluster-state code, XZZX surface code
A. M. Stephens, “Efficient fault-tolerant decoding of topological color codes”, (2014) arXiv:1402.3037. Appears in: 2D color code, Square-octagon (4.8.8) color code
A. M. Stephens, “Fault-tolerant thresholds for quantum error correction with the surface code”, Physical Review A 89, (2014) arXiv:1311.5003 DOI. Appears in: Kitaev surface code
P. R. J. Östergård, "Construction and Classification of Codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI. Appears in: Binary code, Maximum distance separable (MDS) code, Orthogonal array (OA), $q$-ary code
M. Steudtner and S. Wehner, “Fermion-to-qubit mappings with varying resource requirements for quantum simulation”, New Journal of Physics 20, 063010 (2018) arXiv:1712.07067 DOI. Appears in: Auxiliary qubit mapping (AQM) code
M. Steudtner and S. Wehner, “Quantum codes for quantum simulation of fermions on a square lattice of qubits”, Physical Review A 99, (2019) arXiv:1810.02681 DOI. Appears in: Auxiliary qubit mapping (AQM) code
G. W. Stewart, “The Efficient Generation of Random Orthogonal Matrices with an Application to Condition Estimators”, SIAM Journal on Numerical Analysis 17, 403 (1980) DOI. Appears in: Haar-random qubit code
S. Stiassny, “Mathematical analysis of various superimposed coding methods”, American Documentation 11, 155 (1960) DOI. Appears in: Superimposed code
H. Stichtenoth and C. Xing, “Excellent Nonlinear Codes From Algebraic Function Fields”, IEEE Transactions on Information Theory 51, 4044 (2005) DOI. Appears in: Nonlinear AG code
H. Stichtenoth, Algebraic Function Fields and Codes (Springer Berlin Heidelberg, 2009) DOI. Appears in: Evaluation code
D. R. Stinson, T. van Trung, and R. Wei, “Secure frameproof codes, key distribution patterns, group testing algorithms and related structures”, Journal of Statistical Planning and Inference 86, 595 (2000) DOI. Appears in: Frameproof (FP) code
D. Stoler, B. E. A. Saleh, and M. C. Teich, “Binomial States of the Quantized Radiation Field”, Optica Acta: International Journal of Optics 32, 345 (1985) DOI. Appears in: Binomial code
E. C. Stone, “The Voyager 2 encounter with Uranus”, Journal of Geophysical Research: Space Physics 92, 14873 (1987) DOI. Appears in: $[24, 12, 8]$ Extended Golay code
L. Storme, "Coding Theory and Galois Geometries." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI. Appears in: Extended GRS code, Griesmer code, Incidence-matrix projective code, Narrow-sense RS code, Projective geometry code, Projective RM (PRM) code
V. Strassen, “Asymptotische Absch¨atzungen in Shannons Informationstheorie,” Trans. Third Prague Conference on Information Theory, Prague, 689–723, (1962). Appears in: Error-correcting code (ECC)
Stroud, Arthur H. Approximate calculation of multiple integrals. Prentice Hall, 1971.. Appears in: $t$-design
D. Su, C. R. Myers, and K. K. Sabapathy, “Conversion of Gaussian states to non-Gaussian states using photon-number-resolving detectors”, Physical Review A 100, (2019) arXiv:1902.02323 DOI. Appears in: Cat code, Square-lattice GKP code
K. Su, Z. Yang, and C.-M. Jian, “Tapestry of dualities in decohered quantum error correction codes”, Physical Review B 110, (2024) arXiv:2401.17359 DOI. Appears in: 2D lattice stabilizer code
V. P. Su, C. Cao, H.-Y. Hu, Y. Yanay, C. Tahan, and B. Swingle, “Discovery of Optimal Quantum Error Correcting Codes via Reinforcement Learning”, (2023) arXiv:2305.06378. Appears in: Asymmetric quantum code, Tensor-network code, Neural network quantum code
M. Suchara, S. Bravyi, and B. Terhal, “Constructions and noise threshold of topological subsystem codes”, Journal of Physics A: Mathematical and Theoretical 44, 155301 (2011) arXiv:1012.0425 DOI. Appears in: Generalized five-squares code, Kitaev honeycomb code, Subsystem modular-qudit stabilizer code, $\mathbb{Z}_q^{(1)}$ subsystem code, Kitaev surface code
M. Sudan, “Decoding of Reed Solomon Codes beyond the Error-Correction Bound”, Journal of Complexity 13, 180 (1997) DOI. Appears in: Reed-Solomon (RS) code
M. Sudan, L. Trevisan, and S. Vadhan, “Pseudorandom generators without the XOR Lemma (extended abstract)”, Proceedings of the thirty-first annual ACM symposium on Theory of Computing (1999) DOI. Appears in: Locally decodable code (LDC)
M. Sudan, “Invariance in Property Testing”, Lecture Notes in Computer Science 211 (2010) DOI. Appears in: Cyclic linear binary code, Binary linear LTC, Cyclic linear $q$-ary code, $q$-ary linear LTC
S. Sudevan, S. Das, T. Aswanth, N. Patanker, and N. Kashyap, “Sequentially Encodable Codeword Stabilized Codes”, (2024) arXiv:2405.06142. Appears in: Codeword stabilized (CWS) code
Y. Sugiyama, M. Kasahara, S. Hirasawa, and T. Namekawa, “A modification of the constructive asymptotically good codes of Justesen for low rates”, Information and Control 25, 341 (1974) DOI. Appears in: Justesen code
Y. Sugiyama, M. Kasahara, S. Hirasawa, and T. Namekawa, “A method for solving key equation for decoding goppa codes”, Information and Control 27, 87 (1975) DOI. Appears in: Binary BCH code, Goppa code, Bose–Chaudhuri–Hocquenghem (BCH) code
Y. Sugiyama, M. Kasahara, S. Hirasawa, and T. Namekawa, “A new class of asymptotically good codes beyond the Zyablov bound”, IEEE Transactions on Information Theory 24, 198 (1978) DOI. Appears in: Justesen code
J. Sullivan, R. Wen, and A. C. Potter, “Floquet codes and phases in twist-defect networks”, (2023) arXiv:2303.17664. Appears in: Honeycomb Floquet code
M. Sullivan, “Code conversion with the quantum Golay code for a universal transversal gate set”, Physical Review A 109, (2024) arXiv:2307.14425 DOI. Appears in: Triorthogonal code, $[[23, 1, 7]]$ Quantum Golay code
L. Sun et al., “Tracking photon jumps with repeated quantum non-demolition parity measurements”, Nature 511, 444 (2014) arXiv:1311.2534 DOI. Appears in: Cat code
N. Sundaresan, T. J. Yoder, Y. Kim, M. Li, E. H. Chen, G. Harper, T. Thorbeck, A. W. Cross, A. D. Córcoles, and M. Takita, “Demonstrating multi-round subsystem quantum error correction using matching and maximum likelihood decoders”, Nature Communications 14, (2023) arXiv:2203.07205 DOI. Appears in: Heavy-hexagon code
K. J. Sung, M. J. Rančić, O. T. Lanes, and N. T. Bronn, “Simulating Majorana zero modes on a noisy quantum processor”, Quantum Science and Technology 8, 025010 (2023) arXiv:2206.00563 DOI. Appears in: Kitaev chain code
Sur les formes quadratiques positives. (Zus. Mit S. Zolotareff) Korkine in: Mathematische Annalen. Appears in: $D_n$ checkerboard lattice
L. Susskind and J. Glogower, “Quantum mechanical phase and time operator”, Physics Physique Fizika 1, 49 (1964) DOI. Appears in: Bosonic code
L. Susskind, “Computational Complexity and Black Hole Horizons”, (2014) arXiv:1402.5674. Appears in: Approximate quantum error-correcting code (AQECC)
E. Sutcliffe, B. Jonnadula, C. Le Gall, A. E. Moylett, and C. M. Westoby, “Distributed quantum error correction based on hyperbolic Floquet codes”, (2025) arXiv:2501.14029. Appears in: Hyperbolic Floquet code
D. Suter and G. A. Álvarez, “Colloquium: Protecting quantum information against environmental noise”, Reviews of Modern Physics 88, (2016) DOI. Appears in: Quantum error-correcting code (QECC)
B. Sutherland, “Two-Dimensional Hydrogen Bonded Crystals without the Ice Rule”, Journal of Mathematical Physics 11, 3183 (1970) DOI. Appears in: Quantum-inspired classical block code, X-cube model code
J. Svigals, “IBM 7070 data processing system”, Papers presented at the the March 3-5, 1959, western joint computer conference on XX - IRE-AIEE-ACM ’59 (Western) 222 (1959) DOI. Appears in: Weight-two code
K. M. Svore, B. M. Terhal, and D. P. DiVincenzo, “Local fault-tolerant quantum computation”, Physical Review A 72, (2005) arXiv:quant-ph/0410047 DOI. Appears in: Concatenated Steane code, Concatenated qubit code, Qubit code
K. M. Svore, D. P. DiVincenzo, and B. M. Terhal, “Noise Threshold for a Fault-Tolerant Two-Dimensional Lattice Architecture”, (2006) arXiv:quant-ph/0604090. Appears in: Concatenated Steane code, Concatenated qubit code, Qubit code
E. Swaroop, T. Jochym-O’Connor, and T. J. Yoder, “Universal adapters between quantum LDPC codes”, (2024) arXiv:2410.03628. Appears in: Quantum LDPC (QLDPC) code
R. Sweke, M. S. Kesselring, E. P. L. van Nieuwenburg, and J. Eisert, “Reinforcement learning decoders for fault-tolerant quantum computation”, Machine Learning: Science and Technology 2, 025005 (2020) arXiv:1810.07207 DOI. Appears in: Kitaev surface code
B. Swingle and J. McGreevy, “Renormalization group constructions of topological quantum liquids and beyond”, Physical Review B 93, (2016) arXiv:1407.8203 DOI. Appears in: Topological code
D. Sych and G. Leuchs, “Practical Receiver for Optimal Discrimination of Binary Coherent Signals”, Physical Review Letters 117, (2016) arXiv:1404.5033 DOI. Appears in: BPSK c-q code
D. V. Sychev, A. E. Ulanov, E. S. Tiunov, A. A. Pushkina, A. Kuzhamuratov, V. Novikov, and A. I. Lvovsky, “Entanglement and teleportation between polarization and wave-like encodings of an optical qubit”, Nature Communications 9, (2018) arXiv:1712.10206 DOI. Appears in: Hybrid cat code
Sylvester, James Joseph. The Collected Mathematical Papers of James Joseph Sylvester... Vol. 3. University Press, 1909.. Appears in: Modular-qudit code
A. Ta-Shma, “Explicit, almost optimal, epsilon-balanced codes”, Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing (2017) DOI. Appears in: Ta-Shma zigzag code
W. Tadej and K. Zyczkowski, “A concise guide to complex Hadamard matrices”, (2006) arXiv:quant-ph/0512154. Appears in: Complex Hadamard spherical code
K. Takeda and H. Nishimori, “Self-dual random-plaquette gauge model and the quantum toric code”, Nuclear Physics B 686, 377 (2004) arXiv:hep-th/0310279 DOI. Appears in: Loop toric code
K. Takeda, T. Sasamoto, and H. Nishimori, “Exact location of the multicritical point for finite-dimensional spin glasses: a conjecture”, Journal of Physics A: Mathematical and General 38, 3751 (2005) arXiv:cond-mat/0501372 DOI. Appears in: Cluster-state code
K. Takeda, A. Noiri, T. Nakajima, T. Kobayashi, and S. Tarucha, “Quantum error correction with silicon spin qubits”, Nature 608, 682 (2022) arXiv:2201.08581 DOI. Appears in: Quantum repetition code
M. Takeoka, M. Sasaki, P. van Loock, and N. Lütkenhaus, “Implementation of projective measurements with linear optics and continuous photon counting”, Physical Review A 71, (2005) arXiv:quant-ph/0410133 DOI. Appears in: PSK c-q code
M. Takeoka and M. Sasaki, “Discrimination of the binary coherent signal: Gaussian-operation limit and simple non-Gaussian near-optimal receivers”, Physical Review A 78, (2008) arXiv:0706.1038 DOI. Appears in: BPSK c-q code
M. Takeoka, H. Krovi, and S. Guha, “Achieving the Holevo capacity of a pure state classical-quantum channel via unambiguous state discrimination”, 2013 IEEE International Symposium on Information Theory 166 (2013) DOI. Appears in: Classical-quantum (c-q) code
M. Takeoka, S. Guha, and M. M. Wilde, “The Squashed Entanglement of a Quantum Channel”, IEEE Transactions on Information Theory 60, 4987 (2014) arXiv:1310.0129 DOI. Appears in: Bosonic code
M. Takeoka, S. Guha, and M. M. Wilde, “Fundamental rate-loss tradeoff for optical quantum key distribution”, Nature Communications 5, (2014) arXiv:1504.06390 DOI. Appears in: Bosonic code
Y. Takeuchi, T. Morimae, and M. Hayashi, “Quantum computational universality of hypergraph states with Pauli-X and Z basis measurements”, Scientific Reports 9, (2019) DOI. Appears in: Cluster-state code, XP stabilizer code
M. Takita, A. W. Cross, A. D. Córcoles, J. M. Chow, and J. M. Gambetta, “Experimental Demonstration of Fault-Tolerant State Preparation with Superconducting Qubits”, Physical Review Letters 119, (2017) arXiv:1705.09259 DOI. Appears in: Heavy-hexagon code, $[[4,2,2]]$ Four-qubit code
I. Tal and A. Vardy, “List Decoding of Polar Codes”, IEEE Transactions on Information Theory 61, 2213 (2015) DOI. Appears in: Cyclic redundancy check (CRC) code, Polar code
J. Talbot, editor , Sphere Packings (Springer New York, 1999) DOI. Appears in: Lattice-based code
T. H. Taminiau, J. Cramer, T. van der Sar, V. V. Dobrovitski, and R. Hanson, “Universal control and error correction in multi-qubit spin registers in diamond”, Nature Nanotechnology 9, 171 (2014) arXiv:1309.5452 DOI. Appears in: Quantum repetition code
S. Tamiya, M. Koashi, and H. Yamasaki, “Polylog-time- and constant-space-overhead fault-tolerant quantum computation with quantum low-density parity-check codes”, (2024) arXiv:2411.03683. Appears in: Concatenated Steane code, Quantum LDPC (QLDPC) code, Concatenated qubit code, Qubit code
I. Tamo, Z. Wang, and J. Bruck, “Zigzag Codes: MDS Array Codes With Optimal Rebuilding”, IEEE Transactions on Information Theory 59, 1597 (2013) arXiv:1112.0371 DOI. Appears in: B-code, EVENODD code, MDS array code, X-code, Zigzag code
I. Tamo and A. Barg, “A Family of Optimal Locally Recoverable Codes”, IEEE Transactions on Information Theory 60, 4661 (2014) arXiv:1311.3284 DOI. Appears in: Tamo-Barg code
I. Tamo, A. Barg, and A. Frolov, “Bounds on the Parameters of Locally Recoverable Codes”, IEEE Transactions on Information Theory 62, 3070 (2016) DOI. Appears in: Locally recoverable code (LRC)
A. K. Tan, M. H. Ho, and I. L. Chuang, “Reliable Computation by Large-Alphabet Formulas in the Presence of Noise”, IEEE Transactions on Information Theory 70, 9152 (2024) arXiv:2306.13262 DOI. Appears in: $q$-ary code
P. Tan and J. Li, “Efficient Quantum Stabilizer Codes: LDPC and LDPC-Convolutional Constructions”, IEEE Transactions on Information Theory 56, 476 (2010) DOI. Appears in: Quasi-cyclic LDPC (QC-LDPC) code, Quasi-cyclic QLDPC (QC-QLDPC) code
S. J. S. Tan and L. Stambler, “Effective Distance of Higher Dimensional HGPs and Weight-Reduced Quantum LDPC Codes”, (2024) arXiv:2409.02193. Appears in: Distance-balanced code, Hypergraph product (HGP) code, Quantum LDPC (QLDPC) code
X. Tan, F. Zhang, R. Chao, Y. Shi, and J. Chen, “Scalable surface code decoders with parallelization in time”, (2022) arXiv:2209.09219. Appears in: Kitaev surface code
Y. Tan, B. Roberts, N. Tantivasadakarn, B. Yoshida, and N. Y. Yao, “Fracton models from product codes”, (2024) arXiv:2312.08462. Appears in: Hypergraph product (HGP) code, Newman-Moore code, Repetition code, Sierpinsky fractal spin-liquid (SFSL) code
Y. Tanaka, Y. Mori, Y. Shingu, A. Yamaguchi, T. Yamamoto, and Y. Matsuzaki, “Single-qubit rotations on a binomial code without ancillary qubits”, (2024) arXiv:2408.12968. Appears in: Binomial code
T. Tanamoto, V. M. Stojanović, C. Bruder, and D. Becker, “Strategy for implementing stabilizer-based codes on solid-state qubits”, Physical Review A 87, (2013) arXiv:1301.4796 DOI. Appears in: Five-qubit perfect code, $[[7,1,3]]$ Steane code
C. Tang and C. Ding, “An infinite family of linear codes supporting 4-designs”, (2020) arXiv:2001.00158. Appears in: Binary BCH code, Combinatorial design
Y. Tang, S. Zhu, X. Kai, and J. Ding, “New quantum codes from dual-containing cyclic codes over finite rings”, (2016) arXiv:1608.06674. Appears in: Galois-qudit CSS code, Cyclic linear $q$-ary code
A. Tanggara, M. Gu, and K. Bharti, “Strategic Code: A Unified Spatio-Temporal Framework for Quantum Error-Correction”, (2024) arXiv:2405.17567. Appears in: Quantum error-correcting code (QECC), Finite-dimensional quantum error-correcting code
A. Tanggara, M. Gu, and K. Bharti, “Simple Construction of Qudit Floquet Codes on a Family of Lattices”, (2025) arXiv:2410.02022. Appears in: Modular-qudit honeycomb Floquet code
R. M. Tanner, “Minimum-distance bounds by graph analysis”, IEEE Transactions on Information Theory 47, 808 (2001) DOI. Appears in: Regular binary Tanner code
R. M. Tanner, D. Sridhara, A. Sridharan, T. E. Fuja, and D. J. Costello, “LDPC Block and Convolutional Codes Based on Circulant Matrices”, IEEE Transactions on Information Theory 50, 2966 (2004) DOI. Appears in: LDPC convolutional code (LDPC-CC), Quasi-cyclic LDPC (QC-LDPC) code
R. M. Tanner, D. Sridhara, A. Sridharan, T. E. Fuja, and D. J. Costello, “LDPC Block and Convolutional Codes Based on Circulant Matrices”, IEEE Transactions on Information Theory 50, 2966 (2004) DOI. Appears in: Cycle LDPC code, Quasi-cyclic LDPC (QC-LDPC) code, Regular LDPC code
R. Tanner, “A recursive approach to low complexity codes”, IEEE Transactions on Information Theory 27, 533 (1981) DOI. Appears in: Regular binary Tanner code, Tanner code
Tanner, R. Michael, Deepak Sridhara, and Tom Fuja. "A class of group-structured LDPC codes." Proc. ISTA. 2001.. Appears in: Algebraic LDPC code, Quasi-cyclic LDPC (QC-LDPC) code, Tanner-Sridhara-Fuja (TSF) code
Tanner, R. Michael. "On quasi-cyclic repeat-accumulate codes." Proc. 37th Allerton Conf., Monticello, IL, Sept. 1999. 1999.. Appears in: Repeat-accumulate (RA) code
M. R. Tanner, "On quasi-cyclic repeat-accumulate codes." PROCEEDINGS OF THE ANNUAL ALLERTON CONFERENCE ON COMMUNICATION CONTROL AND COMPUTING. Vol. 37. The University; 1998, 1999.. Appears in: Quasi-cyclic LDPC (QC-LDPC) code, Repeat-accumulate (RA) code
T. Tansuwannont, C. Chamberland, and D. Leung, “Flag fault-tolerant error correction, measurement, and quantum computation for cyclic Calderbank-Shor-Steane codes”, Physical Review A 101, (2020) arXiv:1803.09758 DOI. Appears in: Qubit CSS code
T. Tansuwannont and D. Leung, “Achieving Fault Tolerance on Capped Color Codes with Few Ancillas”, PRX Quantum 3, (2022) arXiv:2106.02649 DOI. Appears in: Capped color code (CCC)
T. Tansuwannont, B. Pato, and K. R. Brown, “Adaptive syndrome measurements for Shor-style error correction”, Quantum 7, 1075 (2023) arXiv:2208.05601 DOI. Appears in: Qubit stabilizer code
T. Tansuwannont and A. Nemec, “Synchronizable hybrid subsystem codes”, (2024) arXiv:2409.11312. Appears in: Quantum synchronizable code, Operator-algebra (OA) qubit stabilizer code
N. Tantivasadakarn, “Jordan-Wigner dualities for translation-invariant Hamiltonians in any dimension: Emergent fermions in fracton topological order”, Physical Review Research 2, (2020) arXiv:2002.11345 DOI. Appears in: Bosonization code
N. Tantivasadakarn and A. Vishwanath, “Symmetric Finite-Time Preparation of Cluster States via Quantum Pumps”, Physical Review Letters 129, (2022) arXiv:2107.04019 DOI. Appears in: Cluster-state code, Symmetry-protected topological (SPT) code, Lattice stabilizer code
N. Tantivasadakarn, A. Vishwanath, and R. Verresen, “Hierarchy of Topological Order From Finite-Depth Unitaries, Measurement, and Feedforward”, PRX Quantum 4, (2023) arXiv:2209.06202 DOI. Appears in: Fibonacci string-net code, Quantum-double code, Twisted quantum double (TQD) code
N. Tantivasadakarn, R. Verresen, and A. Vishwanath, “Shortest Route to Non-Abelian Topological Order on a Quantum Processor”, Physical Review Letters 131, (2023) arXiv:2209.03964 DOI. Appears in: Topological code
N. Tantivasadakarn, R. Thorngren, A. Vishwanath, and R. Verresen, “Long-Range Entanglement from Measuring Symmetry-Protected Topological Phases”, Physical Review X 14, (2024) arXiv:2112.01519 DOI. Appears in: Quantum-double code
R. E. Tarjan and J. van Leeuwen, “Worst-case Analysis of Set Union Algorithms”, Journal of the ACM 31, 245 (1984) DOI. Appears in: Kitaev surface code
H. Tarnanen, “Upper Bounds on Permutation Codes via Linear Programming”, European Journal of Combinatorics 20, 101 (1999) DOI. Appears in: Code in permutations
V. Tarokh, N. Seshadri, and A. R. Calderbank, “Space-time codes for high data rate wireless communication: performance criterion and code construction”, IEEE Transactions on Information Theory 44, 744 (1998) DOI. Appears in: Spacetime code (STC)
V. Tarokh, H. Jafarkhani, and A. R. Calderbank, “Space-time block coding for wireless communications: performance results”, IEEE Journal on Selected Areas in Communications 17, 451 (1999) DOI. Appears in: Orthogonal Spacetime Block Code (OSTBC)
H. Tasaki, Physics and Mathematics of Quantum Many-Body Systems (Springer International Publishing, 2020) DOI. Appears in: Hamiltonian-based code
K. Tatwawadi and S. Chandak, “Tutorial on algebraic deletion correction codes”, (2019) arXiv:1906.07887. Appears in: Editing code, Varshamov-Tenengolts (VT) code
Taussky, Olga, and John Todd. "Covering theorems for groups." Bulletin of the American Mathematical Society. Vol. 54. No. 3. 201 CHARLES ST, PROVIDENCE, RI 02940-2213: AMER MATHEMATICAL SOC, 1948.. Appears in: Maximum distance separable (MDS) code, $q$-ary Hamming code
M. Taylor and C. Woodward, “Holography, cellulations and error correcting codes”, (2023) arXiv:2112.12468. Appears in: Pastawski-Yoshida-Harlow-Preskill (HaPPY) code
L. Teirlinck, “Non-trivial t-designs without repeated blocks exist for all t”, Discrete Mathematics 65, 301 (1987) DOI. Appears in: Combinatorial design, $t$-design
E. Telatar, “Capacity of Multi‐antenna Gaussian Channels”, European Transactions on Telecommunications 10, 585 (1999) DOI. Appears in: Spacetime code (STC)
K. Temme, “Thermalization time bounds for Pauli stabilizer Hamiltonians”, (2016) arXiv:1412.2858. Appears in: Self-correcting quantum code
G. Tenengolts, “Nonbinary codes, correcting single deletion or insertion (Corresp.)”, IEEE Transactions on Information Theory 30, 766 (1984) DOI. Appears in: Varshamov-Tenengolts (VT) code
G. M. Tenengolts, Class of codes correcting bit loss and errors in the preceding bit (translated to English), Automation and Remote Control, 37(5), 797–802 (1976).. Appears in: Varshamov-Tenengolts (VT) code
J. C. Y. Teo, A. Roy, and X. Chen, “Unconventional fusion and braiding of topological defects in a lattice model”, Physical Review B 90, (2014) arXiv:1306.1538 DOI. Appears in: Twist-defect color code
Y. S. Teo, S. U. Shringarpure, S. Cho, and H. Jeong, “Linear-optical protocols for mitigating and suppressing noise in bosonic systems”, (2024) arXiv:2411.11313. Appears in: Cat code
J. D. Teoh et al., “Dual-rail encoding with superconducting cavities”, Proceedings of the National Academy of Sciences 120, (2023) arXiv:2212.12077 DOI. Appears in: Dual-rail quantum code
B. M. Terhal and D. P. DiVincenzo, “Classical simulation of noninteracting-fermion quantum circuits”, Physical Review A 65, (2002) arXiv:quant-ph/0108010 DOI. Appears in: Fermion code
B. M. Terhal and G. Burkard, “Fault-tolerant quantum computation for local non-Markovian noise”, Physical Review A 71, (2005) arXiv:quant-ph/0402104 DOI. Appears in: Qubit code
B. M. Terhal, F. Hassler, and D. P. DiVincenzo, “From Majorana fermions to topological order”, Physical Review Letters 108, (2012) arXiv:1201.3757 DOI. Appears in: XZZX surface code
B. M. Terhal, “Quantum error correction for quantum memories”, Reviews of Modern Physics 87, 307 (2015) arXiv:1302.3428 DOI. Appears in: Analog surface code, Bacon-Shor code, Quantum error-correcting code (QECC), Qubit stabilizer code, Subsystem surface code
B. M. Terhal and D. Weigand, “Encoding a qubit into a cavity mode in circuit QED using phase estimation”, Physical Review A 93, (2016) arXiv:1506.05033 DOI. Appears in: Approximate quantum error-correcting code (AQECC), Square-lattice GKP code
B. M. Terhal, J. Conrad, and C. Vuillot, “Towards scalable bosonic quantum error correction”, Quantum Science and Technology 5, 043001 (2020) arXiv:2002.11008 DOI. Appears in: Square-lattice GKP code, Gottesman-Kitaev-Preskill (GKP) code, Bosonic code
An Introduction to Mathematical Cryptography (Springer New York, 2008) DOI. Appears in: Lattice-based code
Classification Algorithms for Codes and Designs (Springer-Verlag, 2006) DOI. Appears in: Binary code
Combinatorial Designs (Springer-Verlag, 2004) DOI. Appears in: Combinatorial design, Orthogonal array (OA), Reed-Muller (RM) code
Encyclopedia of Computer Science and Technology, Second Edition Volume I (CRC Press, 2017) DOI. Appears in: One-hot code, Single parity-check (SPC) code
Self-Dual Codes and Invariant Theory (Springer-Verlag, 2006) DOI. Appears in: Cyclic code, Dodecacode, $[8,4,4]$ extended Hamming code, Hexacode, Octacode, Quadratic-residue (QR) code, Self-dual linear code, Unimodular lattice, $[[8, 3, 3]]$ Eight-qubit Gottesman code
A. V. Thapliyal, Multipartite maximally entangled states, minimal entanglement generating states and entropic inequalities unpublished presentation (2003).. Appears in: Perfect-tensor code, Maximum distance separable (MDS) code, Modular-qudit cluster-state code
The LMFDB Collaboration, The L-functions and modular forms database, https://www.lmfdb.org, 2024.. Appears in: Evaluation code, Lattice-based code
“The Solovay–Kitaev theorem”, Quantum Computation and Quantum Information 617 (2012) DOI. Appears in: Qubit code
L. E. Thomas, “Bound on the mass gap for finite volume stochastic ising models at low temperature”, Communications in Mathematical Physics 126, 1 (1989) DOI. Appears in: Repetition code, Self-correcting quantum code
Thomas A. Gulliver, Construction of quasi-cyclic codes, Thesis, University of New Brunswick, 1989.. Appears in: Quasi-cyclic code
C. Thommesen, “The existence of binary linear concatenated codes with Reed - Solomon outer codes which asymptotically meet the Gilbert- Varshamov bound”, IEEE Transactions on Information Theory 29, 850 (1983) DOI. Appears in: Concatenated code, Generalized RS (GRS) code, Linear $q$-ary code, Random code
A. Thompson and R. Calderbank, “Compressed Neighbour Discovery using Sparse Kerdock Matrices”, (2018) arXiv:1801.04537. Appears in: Delsarte-Goethals (DG) code
T. Thompson, From Error-Correcting Codes Through Sphere Packings to Simple Groups (American Mathematical Society, 1983) DOI. Appears in: Ternary Golay code, Weight-two code
F. Thomsen, M. S. Kesselring, S. D. Bartlett, and B. J. Brown, “Low-overhead quantum computing with the color code”, Physical Review Research 6, (2024) arXiv:2201.07806 DOI. Appears in: Square-octagon (4.8.8) color code, Honeycomb (6.6.6) color code
Thorpe, Jeremy. "Low-density parity-check (LDPC) codes constructed from protographs." IPN progress report 42.154 (2003): 42-154.. Appears in: Protograph LDPC code
K. T. Tian and Z. Wang, “Generalized Haah Codes and Fracton Models”, (2019) arXiv:1902.04543. Appears in: Haah cubic code (CC)
K. T. Tian, E. Samperton, and Z. Wang, “Haah codes on general three-manifolds”, Annals of Physics 412, 168014 (2020) arXiv:1812.02101 DOI. Appears in: Two-block group-algebra (2BGA) codes, Haah cubic code (CC)
F. Ticozzi and L. Viola, “Analysis and synthesis of attractive quantum Markovian dynamics”, (2008) arXiv:0809.0613. Appears in: Frustration-free Hamiltonian code
F. Ticozzi and L. Viola, “Stabilizing entangled states with quasi-local quantum dynamical semigroups”, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370, 5259 (2012) arXiv:1112.4860 DOI. Appears in: Frustration-free Hamiltonian code
H. Tiersma, “Remarks on codes from Hermitian curves (Corresp.)”, IEEE Transactions on Information Theory 33, 605 (1987) DOI. Appears in: Hermitian code
R. Tiew and N. P. Breuckmann, “Low-Overhead Entangling Gates from Generalised Dehn Twists”, (2024) arXiv:2411.03302. Appears in: Balanced product (BP) code, Hypergraph product (HGP) code, Bivariate bicycle (BB) code
A. Tikku and I. H. Kim, “Circuit depth versus energy in topologically ordered systems”, (2022) arXiv:2210.06796. Appears in: Kitaev surface code
J.-P. Tillich and G. Zemor, “Quantum LDPC Codes With Positive Rate and Minimum Distance Proportional to the Square Root of the Blocklength”, IEEE Transactions on Information Theory 60, 1193 (2014) arXiv:0903.0566 DOI. Appears in: Generalized Shor code, Hypergraph product (HGP) code, Low-density generator-matrix (LDGM) code, Quantum LDPC (QLDPC) code, Subsystem hypergraph product (SHP) code
K. Tiurev, A. Pesah, P.-J. H. S. Derks, J. Roffe, J. Eisert, M. S. Kesselring, and J.-M. Reiner, “Domain Wall Color Code”, Physical Review Letters 133, (2024) arXiv:2307.00054 DOI. Appears in: XYZ color code
J. A. Todd, “A Combinatorial Problem”, Journal of Mathematics and Physics 12, 321 (1933) DOI. Appears in: Combinatorial design, Hadamard code
J. Tolar, “On Clifford groups in quantum computing”, Journal of Physics: Conference Series 1071, 012022 (2018) arXiv:1810.10259 DOI. Appears in: Qubit code
M. Tomamichel and V. Y. F. Tan, “Second-Order Asymptotics for the Classical Capacity of Image-Additive Quantum Channels”, Communications in Mathematical Physics 338, 103 (2015) arXiv:1308.6503 DOI. Appears in: Classical-quantum (c-q) code
M. Tomba, S. Wei, B. Hungar, D. Wallick, K. Kawagoe, C. Y. Chuah, and D. Penneys, “Boundary algebras of the Kitaev Quantum Double model”, (2023) arXiv:2309.13440. Appears in: Quantum-double code
T. Tomesh, P. Gokhale, V. Omole, G. S. Ravi, K. N. Smith, J. Viszlai, X.-C. Wu, N. Hardavellas, M. R. Martonosi, and F. T. Chong, “SupermarQ: A Scalable Quantum Benchmark Suite”, (2022) arXiv:2202.11045. Appears in: Quantum repetition code
Y. Tomita and K. M. Svore, “Low-distance surface codes under realistic quantum noise”, Physical Review A 90, (2014) arXiv:1404.3747 DOI. Appears in: Rotated surface code, $[[9,1,3]]$ Surface-17 code
M. Tomlinson, C. J. Tjhai, M. A. Ambroze, M. Ahmed, and M. Jibril, Error-Correction Coding and Decoding (Springer International Publishing, 2017) DOI. Appears in: Evaluation AG code
V. D. Tonchev, “Binary codes derived from the Hoffman-Singleton and Higman-Sims graphs”, IEEE Transactions on Information Theory 43, 1021 (1997) DOI. Appears in: Combinatorial design, Graph-adjacency code, Higman-Sims graph-adjacency code, Hoffman-Singleton cycle code, Hoffman-Singleton graph-adjacency code
V. D. Tonchev, “Error-correcting codes from graphs”, Discrete Mathematics 257, 549 (2002) DOI. Appears in: Graph-adjacency code, Higman-Sims graph-adjacency code, Hoffman-Singleton cycle code, Hoffman-Singleton graph-adjacency code, Hermitian qubit code
V. D. Tonchev, "Codes and designs." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI. Appears in: Combinatorial design, Dual linear code, $[7,4,3]$ Hamming code, Perfect code, Cyclic linear $q$-ary code, Reed-Muller (RM) code, Self-dual linear code
Y. Tong, V. V. Albert, J. R. McClean, J. Preskill, and Y. Su, “Provably accurate simulation of gauge theories and bosonic systems”, Quantum 6, 816 (2022) arXiv:2110.06942 DOI. Appears in: Bosonic code
Toom, Andrei L. "Stable and attractive trajectories in multicomponent systems." Multicomponent random systems 6 (1980): 549-575.. Appears in: Loop toric code, Repetition code
A. L. Toom, “Nonergodic Multidimensional System of Automata”, Probl. Peredachi Inf., 10:3 (1974), 70–79; Problems Inform. Transmission, 10:3 (1974), 239–246. Appears in: Loop toric code, Repetition code
C. Torezzan, S. I. R. Costa, and V. A. Vaishampayan, “Spherical codes on torus layers”, 2009 IEEE International Symposium on Information Theory 2033 (2009) DOI. Appears in: Torus-layer spherical code (TLSC)
G. Torlai and R. G. Melko, “Neural Decoder for Topological Codes”, Physical Review Letters 119, (2017) arXiv:1610.04238 DOI. Appears in: Kitaev surface code
A. D. C. Tosta, T. O. Maciel, and L. Aolita, “Grand Unification of continuous-variable codes”, (2022) arXiv:2206.01751. Appears in: Square-lattice GKP code, Number-phase code
S. Totey, A. Kyle, S. Liu, P. J. Barge, N. Lordi, and J. Combes, “The performance of random bosonic rotation codes”, (2023) arXiv:2311.16089. Appears in: Bosonic rotation code, Random quantum code
L. F. Tóth, Lagerungen in Der Ebene Auf Der Kugel Und Im Raum (Springer Berlin Heidelberg, 1972) DOI. Appears in: $D_3$ face-centered cubic (fcc) lattice, $A_2$ triangular lattice
S. Touzard et al., “Coherent Oscillations inside a Quantum Manifold Stabilized by Dissipation”, Physical Review X 8, (2018) arXiv:1705.02401 DOI. Appears in: Two-component cat code
R. Townsend and E. Weldon, “Self-orthogonal quasi-cyclic codes”, IEEE Transactions on Information Theory 13, 183 (1967) DOI. Appears in: Quasi-cyclic code
A. Townsend-Teague, J. Magdalena de la Fuente, and M. Kesselring, “Floquetifying the Colour Code”, Electronic Proceedings in Theoretical Computer Science 384, 265 (2023) arXiv:2307.11136 DOI. Appears in: Hastings-Haah Floquet code, Ladder Floquet code, Qubit stabilizer code, $[[4,2,2]]$ Four-qubit code
S. Trebst, P. Werner, M. Troyer, K. Shtengel, and C. Nayak, “Breakdown of a Topological Phase: Quantum Phase Transition in a Loop Gas Model with Tension”, Physical Review Letters 98, (2007) arXiv:cond-mat/0609048 DOI. Appears in: Kitaev surface code
M. A. Tremblay, N. Delfosse, and M. E. Beverland, “Constant-Overhead Quantum Error Correction with Thin Planar Connectivity”, Physical Review Letters 129, (2022) arXiv:2109.14609 DOI. Appears in: Quantum LDPC (QLDPC) code
M. Tremblay, G. Duclos-Cianci, and S. Kourtis, “Finite-rate sparse quantum codes aplenty”, Quantum 7, 985 (2023) arXiv:2207.03562 DOI. Appears in: Quantum LDPC (QLDPC) code, Random stabilizer code
C. C. Trinca, J. C. Interlando, R. Palazzo Jr., A. A. de Andrade, and R. A. Watanabe, “On the Construction of New Toric Quantum Codes and Quantum Burst-Error Correcting Codes”, (2022) arXiv:2205.13582. Appears in: $D$-dimensional twisted toric code
C. J. Trout and K. R. Brown, “Magic state distillation and gate compilation in quantum algorithms for quantum chemistry”, International Journal of Quantum Chemistry 115, 1296 (2015) DOI. Appears in: Qubit stabilizer code
C. J. Trout, M. Li, M. Gutiérrez, Y. Wu, S.-T. Wang, L. Duan, and K. R. Brown, “Simulating the performance of a distance-3 surface code in a linear ion trap”, New Journal of Physics 20, 043038 (2018) arXiv:1710.01378 DOI. Appears in: $[[9,1,3]]$ Surface-17 code
D. Truhachev, M. Lentmaier, O. Wintzell, and K. Sh. Zigangirov, “On the minimum distance of turbo codes”, Proceedings IEEE International Symposium on Information Theory, 84 DOI. Appears in: Turbo code
M. A. Tsfasman, S. G. Vlădutx, and Th. Zink, “Modular curves, Shimura curves, and Goppa codes, better than Varshamov‐Gilbert bound”, Mathematische Nachrichten 109, 21 (1982) DOI. Appears in: Algebraic-geometry (AG) code, Tsfasman-Vladut-Zink (TVZ) code
M. A. Tsfasman and S. G. Vlăduţ, Algebraic-Geometric Codes (Springer Netherlands, 1991) DOI. Appears in: Algebraic-geometry (AG) code, Cyclic linear binary code, Elliptic code, Evaluation AG code, Polynomial evaluation code, Evaluation code, Generalized RM (GRM) code, Generalized RS (GRS) code, Group-algebra code, Klein-quartic code, Maximum distance separable (MDS) code, Plane-curve code, Cyclic linear $q$-ary code, $q$-ary Hamming code, $[[2^r-1, 2^r-2r-1, 3]]_p$ quantum Hamming code, Prime-qudit RM code, Reed-Muller (RM) code, Residue AG code
M. Tsfasman, S. Vlǎduţ, and D. Nogin. Algebraic geometric codes: basic notions. Vol. 139. American Mathematical Society, 2022.. Appears in: Algebraic-geometry (AG) code, Cyclic linear binary code, Elliptic code, Evaluation AG code, Evaluation code, Generalized RM (GRM) code, Generalized RS (GRS) code, Hermitian code, Maximum distance separable (MDS) code, Linear $q$-ary code, Reed-Muller (RM) code, Residue AG code
L. Tsui and X.-G. Wen, “Lattice models that realize Zn -1 symmetry-protected topological states for even n”, Physical Review B 101, (2020) arXiv:1908.02613 DOI. Appears in: Cubic theory code
K. Tsujino, D. Fukuda, G. Fujii, S. Inoue, M. Fujiwara, M. Takeoka, and M. Sasaki, “Sub-shot-noise-limit discrimination of on-off keyed coherent signals via a quantum receiver with a superconducting transition edge sensor”, Optics Express 18, 8107 (2010) DOI. Appears in: On-off keyed (OOK) c-q code
K. Tsujino, D. Fukuda, G. Fujii, S. Inoue, M. Fujiwara, M. Takeoka, and M. Sasaki, “Quantum Receiver beyond the Standard Quantum Limit of Coherent Optical Communication”, Physical Review Letters 106, (2011) arXiv:1103.5592 DOI. Appears in: BPSK c-q code
T. Tsunoda, J. D. Teoh, W. D. Kalfus, S. J. de Graaf, B. J. Chapman, J. C. Curtis, N. Thakur, S. M. Girvin, and R. J. Schoelkopf, “Error-detectable bosonic entangling gates with a noisy ancilla”, (2022) arXiv:2212.11196. Appears in: Binomial code, Cat code, Dual-rail quantum code
M. Tuchler, “Design of Serially Concatenated Systems Depending on the Block Length”, IEEE Transactions on Communications 52, 209 (2004) DOI. Appears in: Irregular convolutional code (IRCC)
M. Tuchler and J. Hagenauer, “EXIT charts of irregular codes,” in Proc. 36th Annual Conference on Information Sciences and Systems (CDROM), Princeton, NJ, USA, Mar. 2002.. Appears in: Irregular convolutional code (IRCC)
D. K. Tuckett, S. D. Bartlett, and S. T. Flammia, “Ultrahigh Error Threshold for Surface Codes with Biased Noise”, Physical Review Letters 120, (2018) arXiv:1708.08474 DOI. Appears in: Asymmetric quantum code, XY surface code, XZZX surface code
D. K. Tuckett, A. S. Darmawan, C. T. Chubb, S. Bravyi, S. D. Bartlett, and S. T. Flammia, “Tailoring Surface Codes for Highly Biased Noise”, Physical Review X 9, (2019) arXiv:1812.08186 DOI. Appears in: XY surface code
D. K. Tuckett, S. D. Bartlett, S. T. Flammia, and B. J. Brown, “Fault-Tolerant Thresholds for the Surface Code in Excess of 5% Under Biased Noise”, Physical Review Letters 124, (2020) arXiv:1907.02554 DOI. Appears in: XY surface code, XZZX surface code
I. S. Tupitsyn, A. Kitaev, N. V. Prokof’ev, and P. C. E. Stamp, “Topological multicritical point in the phase diagram of the toric code model and three-dimensional lattice gauge Higgs model”, Physical Review B 82, (2010) arXiv:0804.3175 DOI. Appears in: Kitaev surface code
J. Tyson, “Two-sided bounds on minimum-error quantum measurement, on the reversibility of quantum dynamics, and on maximum overlap using directional iterates”, Journal of Mathematical Physics 51, (2010) arXiv:0907.3386 DOI. Appears in: Approximate quantum error-correcting code (AQECC)
N. Tzanakis and J. Wolfskill, “The diophantine equation x2 = 4qa2 + 4q + 1, with an application to coding theory”, Journal of Number Theory 26, 96 (1987) DOI. Appears in: Ovoid code, Hyperoval code, Projective two-weight code, Ternary Golay code
I. Tzitrin, J. E. Bourassa, N. C. Menicucci, and K. K. Sabapathy, “Progress towards practical qubit computation using approximate Gottesman-Kitaev-Preskill codes”, Physical Review A 101, (2020) arXiv:1910.03673 DOI. Appears in: Square-lattice GKP code
I. Tzitrin, T. Matsuura, R. N. Alexander, G. Dauphinais, J. E. Bourassa, K. K. Sabapathy, N. C. Menicucci, and I. Dhand, “Fault-Tolerant Quantum Computation with Static Linear Optics”, PRX Quantum 2, (2021) arXiv:2104.03241 DOI. Appears in: GKP CV-cluster-state code
M. Ueda, “Probability-density-functional description of quantum photodetection processes”, Quantum Optics: Journal of the European Optical Society Part B 1, 131 (1989) DOI. Appears in: Amplitude-damping (AD) code
D. Ueno and R. Matsumoto, “Explicit method to make shortened stabilizer EAQECC from stabilizer QECC”, (2022) arXiv:2205.13732. Appears in: EA qubit stabilizer code, Qubit stabilizer code
Y. Ueno, M. Kondo, M. Tanaka, Y. Suzuki, and Y. Tabuchi, “NEO-QEC: Neural Network Enhanced Online Superconducting Decoder for Surface Codes”, (2022) arXiv:2208.05758. Appears in: Kitaev surface code
T. Unden et al., “Quantum Metrology Enhanced by Repetitive Quantum Error Correction”, Physical Review Letters 116, (2016) arXiv:1602.07144 DOI. Appears in: Error-corrected sensing code
W. G. Unruh, “Maintaining coherence in quantum computers”, Physical Review A 51, 992 (1995) arXiv:hep-th/9406058 DOI. Appears in: Quantum error-correcting code (QECC)
R. Urbanke and B. Rimoldi, “Lattice codes can achieve capacity on the AWGN channel”, IEEE Transactions on Information Theory 44, 273 (1998) DOI. Appears in: Lattice-based code
R. Urbanke, LdpcOpt - a fast and accurate degree distribution optimizer for LDPC code ensembles (2001).. Appears in: Irregular LDPC code
W. Utschick and W. Weichselberger, “Stochastic Organization of Output Codes in Multiclass Learning Problems”, Neural Computation 13, 1065 (2001) DOI. Appears in: Error-correcting output code (ECOC), One-hot code
T. Utsumi and Y. Nakata, “Explicit decoders using fixed-point amplitude amplification based on QSVT”, (2024) arXiv:2405.06051. Appears in: Approximate quantum error-correcting code (AQECC)
M.-S. Vaezi, G. Ortiz, and Z. Nussinov, “Robust topological degeneracy of classical theories”, Physical Review B 93, (2016) arXiv:1511.07867 DOI. Appears in: Classical topological code
L. Vaidman, Y. Aharonov, and D. Z. Albert, “How to ascertain the values ofsigmax,σy, andσzof a spin-1/2particle”, Physical Review Letters 58, 1385 (1987) DOI. Appears in: $[[2m,2m-2,2]]$ error-detecting code, Finite-dimensional quantum error-correcting code
L. Vaidman, L. Goldenberg, and S. Wiesner, “Error prevention scheme with four particles”, Physical Review A 54, R1745 (1996) arXiv:quant-ph/9603031 DOI. Appears in: $[[4,2,2]]$ Four-qubit code
P. du Val, “On the Directrices of a Set of Points in a Plane”, Proceedings of the London Mathematical Society s2-35, 23 (1933) DOI. Appears in: $3_{21}$ polytope code, Hessian polyhedron code, Witting polytope code
C. H. Valahu, M. P. Stafford, Z. Huang, V. G. Matsos, M. J. Millican, T. Chalermpusitarak, N. C. Menicucci, J. Combes, B. Q. Baragiola, and T. R. Tan, “Quantum-Enhanced Multi-Parameter Sensing in a Single Mode”, (2024) arXiv:2412.04865. Appears in: Square-lattice GKP code, Number-phase code
L. G. Valiant, “Quantum computers that can be simulated classically in polynomial time”, Proceedings of the thirty-third annual ACM symposium on Theory of computing 114 (2001) DOI. Appears in: Fermion code
P. Valiant, “The Tensor Product of Two Codes Is Not Necessarily Robustly Testable”, Lecture Notes in Computer Science 472 (2005) DOI. Appears in: Tensor-product code
M. Van den Nest, J. Dehaene, and B. De Moor, “Graphical description of the action of local Clifford transformations on graph states”, Physical Review A 69, (2004) arXiv:quant-ph/0308151 DOI. Appears in: Cluster-state code, Codeword stabilized (CWS) code, Galois-qudit stabilizer code, Graph quantum code, Qubit stabilizer code, Modular-qudit cluster-state code, Modular-qudit stabilizer code, Stabilizer code
M. Van den Nest, J. Dehaene, and B. De Moor, “Local invariants of stabilizer codes”, Physical Review A 70, (2004) arXiv:quant-ph/0404106 DOI. Appears in: Qubit stabilizer code
M. Van den Nest, J. Dehaene, and B. De Moor, “Finite set of invariants to characterize local Clifford equivalence of stabilizer states”, Physical Review A 72, (2005) arXiv:quant-ph/0410165 DOI. Appears in: Qubit stabilizer code
R. D. Van Meter III, “Architecture of a Quantum Multicomputer Optimized for Shor’s Factoring Algorithm”, (2006) arXiv:quant-ph/0607065. Appears in: $[[23, 1, 7]]$ Quantum Golay code
R. Van Meter, K. Nemoto, and W. Munro, “Communication Links for Distributed Quantum Computation”, IEEE Transactions on Computers 56, 1643 (2007) arXiv:quant-ph/0701043 DOI. Appears in: $[[23, 1, 7]]$ Quantum Golay code
R. R. Vandermolen and D. Wright, “Graph-theoretic approach to quantum error correction”, Physical Review A 105, (2022) arXiv:2110.08414 DOI. Appears in: Galois-qudit CSS code
van Emde Boas, P. (1981). Another NP-complete problem and the complexity of computing short vectors in a lattice. Tecnical Report, Department of Mathmatics, University of Amsterdam.. Appears in: Lattice-based code
van Emde, Boas P. "Another NP-complete partition problem and the complexity of computing short vectors in lattices." TR (1981).. Appears in: Lattice-based code
H. C. A. van Tilborg. Uniformly packed codes. Technische Hogeschool Eindhoven, 1976.. Appears in: Uniformly packed code
B. M. Varbanov, F. Battistel, B. M. Tarasinski, V. P. Ostroukh, T. E. O’Brien, L. DiCarlo, and B. M. Terhal, “Leakage detection for a transmon-based surface code”, npj Quantum Information 6, (2020) arXiv:2002.07119 DOI. Appears in: $[[9,1,3]]$ Surface-17 code
A. Vardy and Y. Be’ery, “Bit-level soft-decision decoding of Reed-Solomon codes”, IEEE Transactions on Communications 39, 440 (1991) DOI. Appears in: Bose–Chaudhuri–Hocquenghem (BCH) code, Reed-Solomon (RS) code
A. Vardy, “Even more efficient bounded-distance decoding of the hexacode, the Golay code, and the Leech lattice”, IEEE Transactions on Information Theory 41, 1495 (1995) DOI. Appears in: $[23, 12, 7]$ Golay code, Hexacode
A. Vardy, “The intractability of computing the minimum distance of a code”, IEEE Transactions on Information Theory 43, 1757 (1997) DOI. Appears in: Linear binary code
M. Varnava, D. E. Browne, and T. Rudolph, “Loss Tolerance in One-Way Quantum Computation via Counterfactual Error Correction”, Physical Review Letters 97, (2006) arXiv:quant-ph/0507036 DOI. Appears in: Tree cluster-state code
R. Varshamov, “A class of codes for asymmetric channels and a problem from the additive theory of numbers”, IEEE Transactions on Information Theory 19, 92 (1973) DOI. Appears in: $q$-ary code
R. R. Varshamov, On the general theory of linear coding, Ph.D. Thesis, Moscow State University, 1959.. Appears in: Griesmer code
R. R. Varshamov, Estimate of the number of signals in error correcting codes, Dokl. Akad. Nauk SSSR Soviet Math. - Doklady 117 (1957), 739–741.. Appears in: $q$-ary code
Varshamov, R. R. "Some features of linear codes that correct asymmetric errors." Soviet Physics Doklady. Vol. 9. 1965.. Appears in: Linear binary code, $q$-ary code
R. R. Varshamov and G. M. Tenengolts, Codes which correct single asymmetric errors (translated to English), Autom. Remote Control, 26(2), 286-290 (1965). Appears in: Varshamov-Tenengolts (VT) code
J. J. Vartiainen, M. Möttönen, and M. M. Salomaa, “Efficient Decomposition of Quantum Gates”, Physical Review Letters 92, (2004) arXiv:quant-ph/0312218 DOI. Appears in: Gray code, Qubit code
B. Vasic, “Combinatorial constructions of low-density parity check codes for iterative decoding”, Proceedings IEEE International Symposium on Information Theory, DOI. Appears in: Quasi-cyclic LDPC (QC-LDPC) code
B. Vasic and O. Milenkovic, “Combinatorial Constructions of Low-Density Parity-Check Codes for Iterative Decoding”, IEEE Transactions on Information Theory 50, 1156 (2004) DOI. Appears in: Algebraic LDPC code
B. Vasic and E. M. Kurtas, editors , Coding and Signal Processing for Magnetic Recording Systems (CRC Press, 2004) DOI. Appears in: Low-density parity-check (LDPC) code
J. L. Vasilyev On nongroup close-packed codes (in Russian), Probl. Kibernet., 8 (1962), 337-339, translated in Probleme der Kibernetik 8 (1965), 375-378.. Appears in: Perfect code, Perfect binary code, Vasilyev code
M. Vasmer and D. E. Browne, “Three-dimensional surface codes: Transversal gates and fault-tolerant architectures”, Physical Review A 100, (2019) arXiv:1801.04255 DOI. Appears in: 3D color code, 3D surface code, Concatenated qubit code
M. Vasmer and A. Kubica, “Morphing Quantum Codes”, PRX Quantum 3, (2022) arXiv:2112.01446 DOI. Appears in: Ball color code, Color code, Homological code, $[[2^D,D,2]]$ hypercube quantum code, $[[2m,2m-2,2]]$ error-detecting code, $[[10,1,2]]$ CSS code, $[[15,1,3]]$ quantum Reed-Muller code, $[[5,1,2]]$ rotated surface code, $[[6,4,2]]$ error-detecting code, $[[8,3,2]]$ Smallest interesting color code, $[[7,1,3]]$ Steane code
F. Vatan, V. P. Roychowdhury, and M. P. Anantram, “Spatially Correlated Qubit Errors and Burst-Correcting Quantum Codes”, (1997) arXiv:quant-ph/9704019. Appears in: $[[13,1,5]]$ cyclic code, Hermitian qubit code
F. Vatan, V. P. Roychowdhury, and M. P. Anantram, “Spatially correlated qubit errors and burst-correcting quantum codes”, IEEE Transactions on Information Theory 45, 1703 (1999) DOI. Appears in: Block quantum code
Veikkaus-Lotto (Veikkaaja) magazine, issues 27, 28, and 33, August-September 1947.. Appears in: Ternary Golay code
V. Veitch, N. Wiebe, C. Ferrie, and J. Emerson, “Efficient simulation scheme for a class of quantum optics experiments with non-negative Wigner representation”, New Journal of Physics 15, 013037 (2013) arXiv:1210.1783 DOI. Appears in: Bosonic code, Stabilizer code
B. B. Venkov. Even unimodular extremal lattices, algebraic geometry and its applications. Trudy Mat. Inst. Steklov., 165:43–48, 1984.. Appears in: Lattice-shell code, Spherical design
B. Venkov. Réseaux et designs sphériques. In Réseaux euclidiens, designs sphériques et formes modulaires, volume 37 of Monogr. Enseign. Math., pages 10–86. Enseignement Math., Geneva, 2001.. Appears in: Lattice-shell code, Spherical design
S. Veroni, A. Paler, and G. Giudice, “Universal quantum computation via scalable measurement-free error correction”, (2025) arXiv:2412.15187. Appears in: Bacon-Shor code
R. Verresen, N. Tantivasadakarn, and A. Vishwanath, “Efficiently preparing Schrödinger’s cat, fractons and non-Abelian topological order in quantum devices”, (2022) arXiv:2112.03061. Appears in: $[[2m,2m-2,2]]$ error-detecting code, Quantum-double code, Quantum repetition code
R. Versluis, S. Poletto, N. Khammassi, B. Tarasinski, N. Haider, D. J. Michalak, A. Bruno, K. Bertels, and L. DiCarlo, “Scalable Quantum Circuit and Control for a Superconducting Surface Code”, Physical Review Applied 8, (2017) arXiv:1612.08208 DOI. Appears in: $[[9,1,3]]$ Surface-17 code
F. Verstraete and J. I. Cirac, “Mapping local Hamiltonians of fermions to local Hamiltonians of spins”, Journal of Statistical Mechanics: Theory and Experiment 2005, P09012 (2005) arXiv:cond-mat/0508353 DOI. Appears in: Ball-Verstraete-Cirac (BVC) code
F. Verstraete, M. M. Wolf, and J. I. Cirac, “Quantum computation, quantum state engineering, and quantum phase transitions driven by dissipation”, (2008) arXiv:0803.1447. Appears in: Frustration-free Hamiltonian code
Vetchinkin, N. M. "Uniqueness of classes of positive quadratic forms, on which values of Hermite constants are reached for 6≤n≤8." Trudy Matematicheskogo Instituta imeni VA Steklova 152 (1980): 34-86.. Appears in: $E_6$ root lattice
Vetchinkin, N. M. "Uniqueness of classes of positive quadratic and highest kissing number of 240 in eight dimensions". Appears in: $E_8$ Gosset lattice
Vetchinkin, N. M. "Uniqueness of classes of positive quadratic and highest known kissing number in seven dimensions.". Appears in: $E_7$ root lattice
A. Vezzani, “Spontaneous magnetization of the Ising model on the Sierpinski carpet fractal, a rigorous result”, Journal of Physics A: Mathematical and General 36, 1593 (2003) arXiv:cond-mat/0212497 DOI. Appears in: Fractal surface code, Self-correcting quantum code
J. I. de Vicente and M. Huber, “Multipartite entanglement detection from correlation tensors”, Physical Review A 84, (2011) arXiv:1106.5756 DOI. Appears in: Tensor-network code
Victor V. Albert and Michel H. Devoret, private communication, 2016. Appears in: Bosonic $q$-ary expansion
G. Vidal and R. Tarrach, “Robustness of entanglement”, Physical Review A 59, 141 (1999) arXiv:quant-ph/9806094 DOI. Appears in: Qubit stabilizer code
J. Vidal, S. Dusuel, and K. P. Schmidt, “Low-energy effective theory of the toric code model in a parallel magnetic field”, Physical Review B 79, (2009) arXiv:0807.0487 DOI. Appears in: Kitaev surface code
M. Viderman, “Linear-time decoding of regular expander codes”, ACM Transactions on Computation Theory 5, 1 (2013) DOI. Appears in: Expander code, Hypergraph product (HGP) code
R. Vidhya Lavanya and M. Madheswaran, “Wimax (IEEE 802.16 m) system based on space time block code and discrete multiwavelet transform and implementation in FPGA”, Telecommunication Systems 56, 327 (2013) DOI. Appears in: Spacetime block code (STBC)
S. Vijay, J. Haah, and L. Fu, “A new kind of topological quantum order: A dimensional hierarchy of quasiparticles built from stationary excitations”, Physical Review B 92, (2015) arXiv:1505.02576 DOI. Appears in: Checkerboard model code, Majorana checkerboard code
S. Vijay, T. H. Hsieh, and L. Fu, “Majorana Fermion Surface Code for Universal Quantum Computation”, Physical Review X 5, (2015) arXiv:1504.01724 DOI. Appears in: Majorana surface code
S. Vijay, J. Haah, and L. Fu, “Fracton topological order, generalized lattice gauge theory, and duality”, Physical Review B 94, (2016) arXiv:1603.04442 DOI. Appears in: Chamon model code, X-cube model code
S. Vijay and L. Fu, “Quantum Error Correction for Complex and Majorana Fermion Qubits”, (2017) arXiv:1703.00459. Appears in: Cyclic linear binary code, Linear binary code, Dual linear code, $[[6,1,3]]_{f}$ Vijay-Fu Majorana code, Majorana stabilizer code, Reed-Muller (RM) code
L. Viola, E. Knill, and S. Lloyd, “Dynamical Decoupling of Open Quantum Systems”, Physical Review Letters 82, 2417 (1999) arXiv:quant-ph/9809071 DOI. Appears in: $[[2m,2m-2,2]]$ error-detecting code
J. Viszlai, J. D. Chadwick, S. Joshi, G. S. Ravi, Y. Li, and F. T. Chong, “Predictive Window Decoding for Fault-Tolerant Quantum Programs”, (2024) arXiv:2412.05115. Appears in: Kitaev surface code
J. Viszlai, W. Yang, S. F. Lin, J. Liu, N. Nottingham, J. M. Baker, and F. T. Chong, “Matching Generalized-Bicycle Codes to Neutral Atoms for Low-Overhead Fault-Tolerance”, (2024) arXiv:2311.16980. Appears in: Generalized bicycle (GB) code
A. J. VITERBI, “Error Bounds for Convolutional Codes and an Asymptotically Optimum Decoding Algorithm”, The Foundations of the Digital Wireless World 41 (2009) DOI. Appears in: $[24, 12, 8]$ Extended Golay code, $[23, 12, 7]$ Golay code
A. Viterbi, “Error bounds for convolutional codes and an asymptotically optimum decoding algorithm”, IEEE Transactions on Information Theory 13, 260 (1967) DOI. Appears in: Convolutional code
E. Viterbo and J. Bouros, “A universal lattice code decoder for fading channels”, IEEE Transactions on Information Theory 45, 1639 (1999) DOI. Appears in: Linear STC
S. Vittal, A. Javadi-Abhari, A. W. Cross, L. S. Bishop, and M. Qureshi, “Flag Proxy Networks: Tackling the Architectural, Scheduling, and Decoding Obstacles of Quantum LDPC codes”, (2024) arXiv:2409.14283. Appears in: Hyperbolic color code, Qubit stabilizer code, 2D hyperbolic surface code
S. Vladut, “On the decoding of algebraic-geometric codes over F/sub q/ for q&lt;or=16”, IEEE Transactions on Information Theory 36, 1461 (1990) DOI. Appears in: Evaluation AG code
S. G. Vlăduţ, V. G. Drinfeld, “Number of points of an algebraic curve”, Funktsional. Anal. i Prilozhen., 17:1 (1983), 68–69; Funct. Anal. Appl., 17:1 (1983), 53–54. Appears in: Algebraic-geometry (AG) code
S. G. Vléduts and Yu. I. Manin, “Linear codes and modular curves”, Journal of Soviet Mathematics 30, 2611 (1985) DOI. Appears in: Polynomial evaluation code, Generalized RM (GRM) code
Von Neumann, John, and Arthur Walter Burks. "Theory of self-reproducing automata." (1966).. Appears in: Repetition code
P. O. Vontobel and R. M. Tanner, “Construction of codes based on finite generalized quadrangles for iterative decoding”, Proceedings. 2001 IEEE International Symposium on Information Theory (IEEE Cat. No.01CH37252) DOI. Appears in: Algebraic LDPC code
L. Voss, S. J. Xian, T. Haug, and K. Bharti, “Multivariate Bicycle Codes”, (2024) arXiv:2406.19151. Appears in: Bivariate bicycle (BB) code
Vries, L.B. and Odaka, K., 1982, June. CIRC-the error-correcting code for the compact disc digital audio system. In Audio Engineering Society Conference: 1st International Conference: Digital Audio. Audio Engineering Society.. Appears in: Cross-interleaved RS (CIRS) code
B. Vucetic and J. Yuan, Turbo Codes (Springer US, 2000) DOI. Appears in: Turbo code
C. Vuillot, H. Asasi, Y. Wang, L. P. Pryadko, and B. M. Terhal, “Quantum error correction with the toric Gottesman-Kitaev-Preskill code”, Physical Review A 99, (2019) arXiv:1810.00047 DOI. Appears in: Analog stabilizer code, Analog surface code, Asymmetric quantum code, Oscillator-into-oscillator GKP code, GKP-surface code, Gottesman-Kitaev-Preskill (GKP) code, Toric code
C. Vuillot, L. Lao, B. Criger, C. García Almudéver, K. Bertels, and B. M. Terhal, “Code deformation and lattice surgery are gauge fixing”, New Journal of Physics 21, 033028 (2019) arXiv:1810.10037 DOI. Appears in: Subsystem modular-qudit stabilizer code
C. Vuillot, “Planar Floquet Codes”, (2021) arXiv:2110.05348. Appears in: Honeycomb Floquet code, Hyperbolic Floquet code
C. Vuillot and N. P. Breuckmann, “Quantum Pin Codes”, IEEE Transactions on Information Theory 68, 5955 (2022) arXiv:1906.11394 DOI. Appears in: 2D color code, Color code, Hyperbolic color code, Quantum divisible code, $k$-orthogonal code, Quantum pin code, Quantum Reed-Muller code, Generalized homological-product qubit CSS code, $[[8,2,2]]$ hyperbolic color code, Subsystem color code
C. Vuillot, A. Ciani, and B. M. Terhal, “Homological Quantum Rotor Codes: Logical Qubits from Torsion”, Communications in Mathematical Physics 405, (2024) arXiv:2303.13723 DOI. Appears in: Kitaev current-mirror qubit code, Homological rotor code, Zero-pi qubit code
M. N. Vyalyi, “Hardness of approximating the weight enumerator of a binary linear code”, (2003) arXiv:cs/0304044. Appears in: Linear binary code
M. Waegell and P. K. Aravind, “Critical noncolorings of the 600-cell proving the Bell–Kochen–Specker theorem”, Journal of Physics A: Mathematical and Theoretical 43, 105304 (2010) arXiv:0911.2289 DOI. Appears in: 120-cell code, 24-cell code, 600-cell code
M. Waegell and P. K. Aravind, “Parity Proofs of the Kochen–Specker Theorem Based on the 120-Cell”, Foundations of Physics 44, 1085 (2014) arXiv:1309.7530 DOI. Appears in: 120-cell code, 24-cell code, 600-cell code
M. Waegell and P. K. Aravind, “Golay codes and quantum contextuality”, Physical Review A 106, (2022) arXiv:2206.04209 DOI. Appears in: $[23, 12, 7]$ Golay code, Ternary Golay code
T. Wagner, H. Kampermann, D. Bruß, and M. Kliesch, “Pauli channels can be estimated from syndrome measurements in quantum error correction”, Quantum 6, 809 (2022) arXiv:2107.14252 DOI. Appears in: Quantum data-syndrome (QDS) code, Qubit stabilizer code, Qubit code
T. Wagner, H. Kampermann, D. Bruß, and M. Kliesch, “Learning Logical Pauli Noise in Quantum Error Correction”, Physical Review Letters 130, (2023) arXiv:2209.09267 DOI. Appears in: Quantum data-syndrome (QDS) code, Qubit stabilizer code, Subsystem qubit stabilizer code
Wagner, M. Unitary transformations in solid state physics. Netherlands.. Appears in: Bosonic code
G. Waldherr et al., “Quantum error correction in a solid-state hybrid spin register”, Nature 506, 204 (2014) arXiv:1309.6424 DOI. Appears in: Quantum repetition code
K. Walker and Z. Wang, “(3+1)-TQFTs and Topological Insulators”, (2011) arXiv:1104.2632. Appears in: 3D fermionic surface code, Walker-Wang model code
T. A. Walker and S. L. Braunstein, “Five-wave-packet linear optics quantum-error-correcting code”, Physical Review A 81, (2010) DOI. Appears in: Analog stabilizer code, $[[5,1,3]]_{\mathbb{R}}$ Braunstein five-mode code
B. W. Walshe, L. J. Mensen, B. Q. Baragiola, and N. C. Menicucci, “Robust fault tolerance for continuous-variable cluster states with excess antisqueezing”, Physical Review A 100, (2019) arXiv:1903.02162 DOI. Appears in: GKP CV-cluster-state code
B. W. Walshe, B. Q. Baragiola, R. N. Alexander, and N. C. Menicucci, “Continuous-variable gate teleportation and bosonic-code error correction”, Physical Review A 102, (2020) arXiv:2008.12791 DOI. Appears in: GKP CV-cluster-state code, Square-lattice GKP code
B. W. Walshe et al., “Linear-optical quantum computation with arbitrary error-correcting codes”, (2024) arXiv:2408.04126. Appears in: Concatenated GKP code
R. Walter Ogburn and J. Preskill, “Topological Quantum Computation”, Lecture Notes in Computer Science 341 (1999) DOI. Appears in: Quantum-double code
P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing”, Nature 434, 169 (2005) arXiv:quant-ph/0503126 DOI. Appears in: Cluster-state code
K. H. Wan, M. Webber, A. G. Fowler, and W. K. Hensinger, “An iterative transversal CNOT decoder”, (2024) arXiv:2407.20976. Appears in: Rotated surface code
K. H. Wan and Z. Zhong, “Pauli web of the $|Y\rangle$ state surface code injection”, (2025) arXiv:2501.15566. Appears in: Rotated surface code
K. H. Wan and Z. Zhong, “Pauli webs spun by transversal $|Y\rangle$ state initialisation”, (2025) arXiv:2502.00957. Appears in: Rotated surface code, Kitaev surface code
Y. Wan, J. C. Wang, and H. He, “Twisted gauge theory model of topological phases in three dimensions”, Physical Review B 92, (2015) arXiv:1409.3216 DOI. Appears in: Dijkgraaf-Witten gauge theory code
Z. Wan, J. Wang, and Y. Zheng, “Quantum 4d Yang-Mills theory and time-reversal symmetric 5d higher-gauge topological field theory”, Physical Review D 100, (2019) arXiv:1904.00994 DOI. Appears in: Two-gauge theory code
A. Wang and Z. Zhang, “Repair Locality With Multiple Erasure Tolerance”, IEEE Transactions on Information Theory 60, 6979 (2014) arXiv:1306.4774 DOI. Appears in: Availability code
A. Wang and Z. Zhang, “Achieving Arbitrary Locality and Availability in Binary Codes”, (2015) arXiv:1501.04264. Appears in: Availability code
C. Wang, J. Harrington, and J. Preskill, “Confinement-Higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory”, Annals of Physics 303, 31 (2003) arXiv:quant-ph/0207088 DOI. Appears in: Kitaev surface code, Toric code
D. S. Wang, A. G. Fowler, C. D. Hill, and L. C. L. Hollenberg, “Graphical algorithms and threshold error rates for the 2d colour code”, (2009) arXiv:0907.1708. Appears in: Square-octagon (4.8.8) color code
D. S. Wang, A. G. Fowler, A. M. Stephens, and L. C. L. Hollenberg, “Threshold error rates for the toric and surface codes”, (2009) arXiv:0905.0531. Appears in: Kitaev surface code, Toric code
D. S. Wang, A. G. Fowler, and L. C. L. Hollenberg, “Surface code quantum computing with error rates over 1%”, Physical Review A 83, (2011) arXiv:1009.3686 DOI. Appears in: Kitaev surface code
D.-S. Wang, G. Zhu, C. Okay, and R. Laflamme, “Quasi-exact quantum computation”, Physical Review Research 2, (2020) arXiv:1910.00038 DOI. Appears in: Frustration-free Hamiltonian code, Spin code, Symmetry-protected topological (SPT) code, Valence-bond-solid (VBS) code
D.-S. Wang, Y.-J. Wang, N. Cao, B. Zeng, and R. Laflamme, “Theory of quasi-exact fault-tolerant quantum computing and valence-bond-solid codes”, New Journal of Physics 24, 023019 (2022) arXiv:2105.14777 DOI. Appears in: Approximate quantum error-correcting code (AQECC), Covariant block quantum code, Frustration-free Hamiltonian code, Spin code, Valence-bond-solid (VBS) code
D.-S. Wang, Y.-D. Liu, Y.-J. Wang, and S. Luo, “Quantum resource theory of coding for error correction”, Physical Review A 110, (2024) arXiv:2409.09416 DOI. Appears in: Quantum error-correcting code (QECC)
G. Wang, C. Ottaviani, H. Guo, and S. Pirandola, “Improving the lower bound to the secret-key capacity of the thermal amplifier channel”, The European Physical Journal D 73, (2019) arXiv:1807.05402 DOI. Appears in: Bosonic code
H.-C. Wang, “Two-Point Homogeneous Spaces”, The Annals of Mathematics 55, 177 (1952) DOI. Appears in: $t$-design
H. Wang, Y. Li, Y. Hu, and Y. Wan, “Gapped boundary theory of the twisted gauge theory model of three-dimensional topological orders”, Journal of High Energy Physics 2018, (2018) arXiv:1807.11083 DOI. Appears in: Dijkgraaf-Witten gauge theory code
H. Wang, P. Liu, K. Shao, D. Li, J. Gu, D. Z. Pan, Y. Ding, and S. Han, “Transformer-QEC: Quantum Error Correction Code Decoding with Transferable Transformers”, (2023) arXiv:2311.16082. Appears in: Kitaev surface code
J. C. Wang and X.-G. Wen, “Non-Abelian string and particle braiding in topological order: ModularSL(3,Z)representation and(3+1)-dimensional twisted gauge theory”, Physical Review B 91, (2015) arXiv:1404.7854 DOI. Appears in: Dijkgraaf-Witten gauge theory code
L. Wang and R. Renner, “One-Shot Classical-Quantum Capacity and Hypothesis Testing”, Physical Review Letters 108, (2012) arXiv:1007.5456 DOI. Appears in: Classical-quantum (c-q) code
L. Wang and S. Zhu, “On the Construction of Optimal Asymmetric Quantum Codes”, (2014) arXiv:1403.7755. Appears in: Asymmetric quantum code
L. Wang and Z. Wang, “In and around abelian anyon models ${}^{\text{*}}$”, Journal of Physics A: Mathematical and Theoretical 53, 505203 (2020) arXiv:2004.12048 DOI. Appears in: Abelian topological code
M. Wang and F. Mueller, “Coprime Bivariate Bicycle Codes”, (2024) arXiv:2408.10001. Appears in: Bivariate bicycle (BB) code
R. Wang and L. P. Pryadko, “Distance bounds for generalized bicycle codes”, (2022) arXiv:2203.17216. Appears in: Generalized bicycle (GB) code, Hypergraph product (HGP) code
R. Wang, H.-K. Lin, and L. P. Pryadko, “Abelian and non-abelian quantum two-block codes”, (2023) arXiv:2305.06890. Appears in: Two-block group-algebra (2BGA) codes
T. Wang, W. Shirley, and X. Chen, “Foliated fracton order in the Majorana checkerboard model”, Physical Review B 100, (2019) arXiv:1904.01111 DOI. Appears in: Fracton stabilizer code, Majorana checkerboard code, X-cube model code
X. Wang and P. Zanardi, “Simulation of many-body interactions by conditional geometric phases”, Physical Review A 65, (2002) arXiv:quant-ph/0111017 DOI. Appears in: PI qubit code
X. WANG, T. HIROSHIMA, A. TOMITA, and M. HAYASHI, “Quantum information with Gaussian states”, Physics Reports 448, 1 (2007) arXiv:0801.4604 DOI. Appears in: Bosonic code
X. Wang, K. Fang, and M. Tomamichel, “On Converse Bounds for Classical Communication Over Quantum Channels”, IEEE Transactions on Information Theory 65, 4609 (2019) arXiv:1709.05258 DOI. Appears in: Classical-quantum (c-q) code
Y.-J. Wang, Z.-Y. Xiao, Y. Zhang, X.-Y. Xiong, and S. Shi, “Construction of Multiple-Rate Quantum LDPC Codes Sharing One Scalable Stabilizer Circuit”, IEEE Transactions on Communications 71, 1071 (2023) DOI. Appears in: Dual linear code, Qubit CSS code
Y. Wang and X. Zhu, “A fast algorithm for the Fourier transform over finite fields and its VLSI implementation”, IEEE Journal on Selected Areas in Communications 6, 572 (1988) DOI. Appears in: Reed-Solomon (RS) code
Y. Wang, Z. Hu, B. C. Sanders, and S. Kais, “Qudits and High-Dimensional Quantum Computing”, Frontiers in Physics 8, (2020) arXiv:2008.00959 DOI. Appears in: Modular-qudit code
Y. Wang, Y. Xu, and Z.-W. Liu, “Encoded quantum gates by geometric rotation on tessellations”, (2024) arXiv:2410.18713. Appears in: Hyperbolic sphere packing, Gottesman-Kitaev-Preskill (GKP) code, Pauli group-representation QSC, Quantum spherical code (QSC), Qutrit-Pauli group-representation code
Y. Wang et al., “Fault-tolerant one-bit addition with the smallest interesting color code”, Science Advances 10, (2024) arXiv:2309.09893 DOI. Appears in: $[[8,3,2]]$ Smallest interesting color code
Y. Wang, Y. Wang, Y.-A. Chen, W. Zhang, T. Zhang, J. Hu, W. Chen, Y. Gu, and Z.-W. Liu, “Efficient fault-tolerant implementations of non-Clifford gates with reconfigurable atom arrays”, npj Quantum Information 10, (2024) arXiv:2312.09111 DOI. Appears in: 3D surface code, Hyperbolic surface code
Z. Wang, K. Sun, H. Fan, and V. Vedral, “Nested Quantum Error Correction Codes”, (2009) arXiv:0909.5103. Appears in: Concatenated quantum code
Z. Wang, S. Yu, H. Fan, and C. H. Oh, “Quantum error-correcting codes over mixed alphabets”, Physical Review A 88, (2013) arXiv:1205.4253 DOI. Appears in: $[[6,2,3]]_{q}$ code, True Galois-qudit stabilizer code
Z. Wang, T. Rajabzadeh, N. Lee, and A. H. Safavi-Naeini, “Automated discovery of autonomous quantum error correction schemes”, (2021) arXiv:2108.02766. Appears in: Numerically optimized bosonic code, Neural network quantum code
Z. Wang and H. Tang, “Artificial Intelligence for Quantum Error Correction: A Comprehensive Review”, (2024) arXiv:2412.20380. Appears in: Neural network quantum code
H. N. Ward, “Divisible codes”, Archiv der Mathematik 36, 485 (1981) DOI. Appears in: Divisible code
H. N. Ward, “Divisibility of Codes Meeting the Griesmer Bound”, Journal of Combinatorial Theory, Series A 83, 79 (1998) DOI. Appears in: Divisible code, Griesmer code
A. Warke, J. Nötzel, K. Takase, W. Asavanant, H. Nagayoshi, K. Fukui, S. Takeda, A. Furusawa, and P. van Loock, “Photonic Quantum Receiver Attaining the Helstrom Bound”, (2024) arXiv:2410.21800. Appears in: BPSK c-q code
W. Wasilewski and K. Banaszek, “Protecting an optical qubit against photon loss”, Physical Review A 75, (2007) arXiv:quant-ph/0702075 DOI. Appears in: Wasilewski-Banaszek code
H. Watanabe, M. Cheng, and Y. Fuji, “Ground state degeneracy on torus in a family of ZN toric code”, Journal of Mathematical Physics 64, (2023) arXiv:2211.00299 DOI. Appears in: Modular-qudit surface code
J. Watrous, The Theory of Quantum Information (Cambridge University Press, 2018) DOI. Appears in: Finite-dimensional quantum error-correcting code
F. H. E. Watson, E. T. Campbell, H. Anwar, and D. E. Browne, “Qudit color codes and gauge color codes in all spatial dimensions”, Physical Review A 92, (2015) arXiv:1503.08800 DOI. Appears in: $k$-orthogonal code, Modular-qudit color code, Modular-qudit subsystem color code, Modular-qudit code, Lattice stabilizer code, Lattice subsystem code
F. H. E. Watson, H. Anwar, and D. E. Browne, “Fast fault-tolerant decoder for qubit and qudit surface codes”, Physical Review A 92, (2015) arXiv:1411.3028 DOI. Appears in: Modular-qudit surface code, Kitaev surface code
G. L. Watson, “The Class-Number of a Positive Quadratic Form”, Proceedings of the London Mathematical Society s3-13, 549 (1963) DOI. Appears in: $E_8$ Gosset lattice, $E_7$ root lattice, $E_6$ root lattice
A. B. Watts, R. Kothari, L. Schaeffer, and A. Tal, “Exponential separation between shallow quantum circuits and unbounded fan-in shallow classical circuits”, Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing (2019) arXiv:1906.08890 DOI. Appears in: $[[2m,2m-2,2]]$ error-detecting code, Quantum repetition code
Z. Webb, “The Clifford group forms a unitary 3-design”, (2016) arXiv:1510.02769. Appears in: Qubit stabilizer code, $t$-design
M. A. Webster, B. J. Brown, and S. D. Bartlett, “The XP Stabiliser Formalism: a Generalisation of the Pauli Stabiliser Formalism with Arbitrary Phases”, Quantum 6, 815 (2022) arXiv:2203.00103 DOI. Appears in: Cluster-state code, $[[2^r-1,1,3]]$ simplex code, $[[2^D,D,2]]$ hypercube quantum code, Qubit CSS code, $[[15,1,3]]$ quantum Reed-Muller code, $[[8,3,2]]$ Smallest interesting color code, XP stabilizer code, XS stabilizer code
M. A. Webster, A. O. Quintavalle, and S. D. Bartlett, “Transversal diagonal logical operators for stabiliser codes”, New Journal of Physics 25, 103018 (2023) arXiv:2303.15615 DOI. Appears in: Qubit CSS code
M. Webster and D. Browne, “Engineering Quantum Error Correction Codes Using Evolutionary Algorithms”, (2024) arXiv:2409.13017. Appears in: Qubit stabilizer code
P. Webster, S. D. Bartlett, and D. Poulin, “Reducing the overhead for quantum computation when noise is biased”, Physical Review A 92, (2015) arXiv:1509.05032 DOI. Appears in: Asymmetric quantum code
P. Webster and S. D. Bartlett, “Locality-preserving logical operators in topological stabilizer codes”, Physical Review A 97, (2018) arXiv:1709.00020 DOI. Appears in: Homological code
P. Webster and S. D. Bartlett, “Fault-tolerant quantum gates with defects in topological stabilizer codes”, Physical Review A 102, (2020) arXiv:1906.01045 DOI. Appears in: 3D bosonization code, 3D fermionic surface code, Kitaev chain code
Webster, Mark. The XP Stabilizer Formalism. Dissertation, University of Sydney, 2023.. Appears in: Cluster-state code, Qubit CSS code, Qubit stabilizer code, XP stabilizer code
C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information”, Reviews of Modern Physics 84, 621 (2012) arXiv:1110.3234 DOI. Appears in: Bosonic code
F. J. Wegner, “Duality in Generalized Ising Models and Phase Transitions without Local Order Parameters”, Journal of Mathematical Physics 12, 2259 (1971) DOI. Appears in: Clifford-deformed surface code (CDSC), Abelian quantum-double stabilizer code, Kitaev surface code
F. J. Wegner, “Duality in generalized Ising models”, (2014) arXiv:1411.5815. Appears in: Kitaev surface code
T.-C. Wei, I. Affleck, and R. Raussendorf, “Affleck-Kennedy-Lieb-Tasaki State on a Honeycomb Lattice is a Universal Quantum Computational Resource”, Physical Review Letters 106, (2011) arXiv:1102.5064 DOI. Appears in: Cluster-state code, Symmetry-protected topological (SPT) code, Lattice stabilizer code
T.-C. Wei, I. Affleck, and R. Raussendorf, “Two-dimensional Affleck-Kennedy-Lieb-Tasaki state on the honeycomb lattice is a universal resource for quantum computation”, Physical Review A 86, (2012) arXiv:1009.2840 DOI. Appears in: Cluster-state code, Symmetry-protected topological (SPT) code, Lattice stabilizer code
T.-C. Wei, P. Haghnegahdar, and R. Raussendorf, “Hybrid valence-bond states for universal quantum computation”, Physical Review A 90, (2014) arXiv:1310.5100 DOI. Appears in: Cluster-state code, Symmetry-protected topological (SPT) code, Lattice stabilizer code
D. J. Weigand and B. M. Terhal, “Generating grid states from Schrödinger-cat states without postselection”, Physical Review A 97, (2018) arXiv:1709.08580 DOI. Appears in: Square-lattice GKP code
Y. S. Weinstein, “Fidelity of an encoded [7,1,3] logical zero”, Physical Review A 84, (2011) arXiv:1101.1950 DOI. Appears in: $[[7,1,3]]$ Steane code
Y. S. Weinstein and S. D. Buchbinder, “Use of Shor states for the [7,1,3] quantum error-correcting code”, Physical Review A 86, (2012) arXiv:1111.3930 DOI. Appears in: $[[7,1,3]]$ Steane code
Y. S. Weinstein, “Non-fault-tolerantTgates for the [7,1,3] quantum error-correction code”, Physical Review A 87, (2013) arXiv:1303.4291 DOI. Appears in: $[[7,1,3]]$ Steane code
D. K. Weiss, A. C. Y. Li, D. G. Ferguson, and J. Koch, “Spectrum and coherence properties of the current-mirror qubit”, Physical Review B 100, (2019) arXiv:1908.04615 DOI. Appears in: Kitaev current-mirror qubit code
O. Weissl and E. Egorov, “Equivariant Machine Learning Decoder for 3D Toric Codes”, (2024) arXiv:2409.04300. Appears in: 3D surface code
E. J. Weldon Jr., “Difference-Set Cyclic Codes”, Bell System Technical Journal 45, 1045 (1966) DOI. Appears in: Difference-set cyclic (DSC) code
E. J. Weldon, “Justesen’s construction--The low-rate case (Corresp.)”, IEEE Transactions on Information Theory 19, 711 (1973) DOI. Appears in: Justesen code, Bose–Chaudhuri–Hocquenghem (BCH) code
E. Weldon, “New generalizations of the Reed-Muller codes--II: Nonprimitive codes”, IEEE Transactions on Information Theory 14, 199 (1968) DOI. Appears in: Generalized RM (GRM) code
Wells, Richard B. Applied coding and information theory for engineers. Prentice-Hall, Inc., 1998.. Appears in: Cyclic redundancy check (CRC) code
X.-G. Wen, “Quantum Orders in an Exact Soluble Model”, Physical Review Letters 90, (2003) arXiv:quant-ph/0205004 DOI. Appears in: Abelian quantum-double stabilizer code, XZZX surface code
X.-G. Wen, “Topological Order: From Long-Range Entangled Quantum Matter to a Unified Origin of Light and Electrons”, ISRN Condensed Matter Physics 2013, 1 (2013) arXiv:1210.1281 DOI. Appears in: Approximate quantum error-correcting code (AQECC)
X.-G. Wen, “Colloquium : Zoo of quantum-topological phases of matter”, Reviews of Modern Physics 89, (2017) arXiv:1610.03911 DOI. Appears in: Hamiltonian-based code, Topological code
R. F. Werner and A. S. Holevo, “Counterexample to an additivity conjecture for output purity of quantum channels”, Journal of Mathematical Physics 43, 4353 (2002) arXiv:quant-ph/0203003 DOI. Appears in: Qubit code
A. Westfeld, “F5—A Steganographic Algorithm”, Lecture Notes in Computer Science 289 (2001) DOI. Appears in: $[2^r-1,2^r-r-1,3]$ Hamming code
J. van de Wetering and M. Amy, “Optimising quantum circuits is generally hard”, (2024) arXiv:2310.05958. Appears in: Qubit code
O. C. Wetherbee, S. Roy, B. Royer, and V. Fatemi, “A Mathematical Structure for Amplitude-Mixing Error-Transparent Gates for Binomial Codes”, (2024) arXiv:2412.08870. Appears in: Binomial code
Weyl, Hermann. The theory of groups and quantum mechanics. Courier Corporation, 1950.. Appears in: Modular-qudit code
N. Wiberg, H. Loeliger, and R. Kotter, “Codes and iterative decoding on general graphs”, European Transactions on Telecommunications 6, 513 (1995) DOI. Appears in: Tanner code
S. B. Wicker and V. K. Bhargava, “Reed-Solomon Codes and Their Applications”, (1999) DOI. Appears in: Cross-interleaved RS (CIRS) code, Maximum distance separable (MDS) code, Reed-Solomon (RS) code
E. Wigner, “On the Quantum Correction For Thermodynamic Equilibrium”, Physical Review 40, 749 (1932) DOI. Appears in: Bosonic code
F. Wilczek, “Quantum Mechanics of Fractional-Spin Particles”, Physical Review Letters 49, 957 (1982) DOI. Appears in: Topological code
M. M. Wilde, H. Krovi, and T. A. Brun, “Entanglement-assisted quantum error correction with linear optics”, Physical Review A 76, (2007) arXiv:0705.4314 DOI. Appears in: EA analog stabilizer code
M. M. Wilde, “Quantum Coding with Entanglement”, (2008) arXiv:0806.4214. Appears in: EA quantum convolutional code, EA qubit code
M. M. Wilde and T. A. Brun, “Optimal entanglement formulas for entanglement-assisted quantum coding”, Physical Review A 77, (2008) arXiv:0804.1404 DOI. Appears in: EA qubit stabilizer code, Quantum convolutional code
M. M. Wilde and T. A. Brun, “Unified quantum convolutional coding”, 2008 IEEE International Symposium on Information Theory (2008) arXiv:0801.0821 DOI. Appears in: Hybrid convolutional code
M. M. Wilde and D. B. Uskov, “Linear-optical hyperentanglement-assisted quantum error-correcting code”, Physical Review A 79, (2009) arXiv:0807.4906 DOI. Appears in: EA qubit stabilizer code, Hybrid qudit-oscillator code
M. M. Wilde and T. A. Brun, “Extra shared entanglement reduces memory demand in quantum convolutional coding”, Physical Review A 79, (2009) arXiv:0812.4449 DOI. Appears in: EA quantum convolutional code
M. M. Wilde, “Quantum-shift-register circuits”, Physical Review A 79, (2009) arXiv:0903.3894 DOI. Appears in: Quantum convolutional code
M. M. Wilde, “Logical operators of quantum codes”, Physical Review A 79, (2009) arXiv:0903.5256 DOI. Appears in: Qubit stabilizer code
M. M. Wilde and M.-H. Hsieh, “Entanglement generation with a quantum channel and a shared state”, 2010 IEEE International Symposium on Information Theory (2010) arXiv:0904.1175 DOI. Appears in: Entanglement-assisted (EA) QECC
M. M. Wilde and T. A. Brun, “Entanglement-assisted quantum convolutional coding”, Physical Review A 81, (2010) arXiv:0712.2223 DOI. Appears in: EA quantum convolutional code
M. M. Wilde and T. A. Brun, “Quantum convolutional coding with shared entanglement: general structure”, Quantum Information Processing 9, 509 (2010) arXiv:0807.3803 DOI. Appears in: EA quantum convolutional code
M. M. Wilde and M.-H. Hsieh, “Entanglement boosts quantum turbo codes”, 2011 IEEE International Symposium on Information Theory Proceedings (2011) DOI. Appears in: EA quantum turbo code
M. M. Wilde, M. Houshmand, and S. Hosseini-Khayat, “Examples of minimal-memory, non-catastrophic quantum convolutional encoders”, 2011 IEEE International Symposium on Information Theory Proceedings 450 (2011) arXiv:1011.5535 DOI. Appears in: Quantum convolutional code
M. M. Wilde and J. M. Renes, “Quantum polar codes for arbitrary channels”, 2012 IEEE International Symposium on Information Theory Proceedings (2012) arXiv:1201.2906 DOI. Appears in: Quantum polar code
M. M. Wilde and S. Guha, “Polar Codes for Classical-Quantum Channels”, IEEE Transactions on Information Theory 59, 1175 (2013) arXiv:1109.2591 DOI. Appears in: Polar c-q code
M. M. Wilde, Quantum Information Theory (Cambridge University Press, 2013) DOI. Appears in: Finite-dimensional quantum error-correcting code, Qubit stabilizer code
M. M. Wilde and S. Guha, “Polar Codes for Degradable Quantum Channels”, IEEE Transactions on Information Theory 59, 4718 (2013) arXiv:1109.5346 DOI. Appears in: Quantum polar code
M. M. Wilde, M.-H. Hsieh, and Z. Babar, “Entanglement-Assisted Quantum Turbo Codes”, IEEE Transactions on Information Theory 60, 1203 (2014) arXiv:1010.1256 DOI. Appears in: EA quantum turbo code, Maximal-entanglement EA Galois-qudit stabilizer code, Quantum turbo code
M. M. Wilde, M. Tomamichel, and M. Berta, “Converse Bounds for Private Communication Over Quantum Channels”, IEEE Transactions on Information Theory 63, 1792 (2017) arXiv:1602.08898 DOI. Appears in: Bosonic code
M. Wilde, “Quantum convolutional codes”, Quantum Error Correction 231 (2013) DOI. Appears in: Quantum convolutional code
M. Will, T. A. Cochran, E. Rosenberg, B. Jobst, N. M. Eassa, P. Roushan, M. Knap, A. Gammon-Smith, and F. Pollmann, “Probing Non-Equilibrium Topological Order on a Quantum Processor”, (2025) arXiv:2501.18461. Appears in: Kitaev honeycomb code
W. Willems, "Codes in Group Algebras." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI. Appears in: $[24, 12, 8]$ Extended Golay code, Generalized RM (GRM) code, Group-algebra code, Hermitian code, Klein-quartic code, Cyclic linear $q$-ary code, Reed-Muller (RM) code, Reed-Solomon (RS) code, $[48,24,12]$ self-dual code, Suzuki-curve code
N. Willenborg, M. Borello, A.-L. Horlemann, and H. Islam, “Dihedral Quantum Codes”, (2024) arXiv:2310.15092. Appears in: Two-block CSS code
D. J. Williamson and Z. Wang, “Hamiltonian models for topological phases of matter in three spatial dimensions”, Annals of Physics 377, 311 (2017) arXiv:1606.07144 DOI. Appears in: $G$-enriched Walker-Wang model code, Walker-Wang model code, Two-gauge theory code
D. J. Williamson, C. Delcamp, F. Verstraete, and N. Schuch, “On the stability of topological order in tensor network states”, Physical Review B 104, (2021) arXiv:2012.15346 DOI. Appears in: 3D surface code, Hamiltonian-based code
D. J. Williamson and N. Baspin, “Layer Codes”, (2024) arXiv:2309.16503. Appears in: Fracton stabilizer code, Layer code
D. J. Williamson and T. J. Yoder, “Low-overhead fault-tolerant quantum computation by gauging logical operators”, (2024) arXiv:2410.02213. Appears in: Qubit stabilizer code
A. Wills, T.-C. Lin, and M.-H. Hsieh, “General Distance Balancing for Quantum Locally Testable Codes”, (2023) arXiv:2305.00689. Appears in: Distance-balanced code, Hemicubic code, Hypersphere product code, Quantum locally testable code (QLTC)
A. Wills, T.-C. Lin, and M.-H. Hsieh, “Tradeoff Constructions for Quantum Locally Testable Codes”, (2024) arXiv:2309.05541. Appears in: Distance-balanced code, Dinur-Lin-Vidick (DLV) code, Hemicubic code, Quantum locally testable code (QLTC)
A. Wills, M.-H. Hsieh, and H. Yamasaki, “Constant-Overhead Magic State Distillation”, (2024) arXiv:2408.07764. Appears in: Quantum AG code, Triorthogonal code
R. A. Wilson, “Vector stabilizers and subgroups of Leech lattice groups”, Journal of Algebra 127, 387 (1989) DOI. Appears in: $\Lambda_{24}$ Leech lattice-shell code, Spherical sharp configuration, Spherical design
R. A. Wilson, On lexicographic codes of minimal distance 4, Atti Sem. Mat. Fis. Univ. Modena 33 (1984). Appears in: Hexacode, Lexicographic code
T. Windeatt and R. Ghaderi, “Coding and decoding strategies for multi-class learning problems”, Information Fusion 4, 11 (2003) DOI. Appears in: Error-correcting output code (ECOC)
T. Windeatt, “Boosted ECOC ensembles for face recognition”, International Conference on Visual Information Engineering (VIE 2003). Ideas, Applications, Experience (2003) DOI. Appears in: Error-correcting output code (ECOC)
M. S. Winnel, J. J. Guanzon, N. Hosseinidehaj, and T. C. Ralph, “Achieving the ultimate end-to-end rates of lossy quantum communication networks”, npj Quantum Information 8, (2022) arXiv:2203.13924 DOI. Appears in: Constant-excitation (CE) code
A. Winter, private communication (2019).. Appears in: Quantum maximum-distance-separable (MDS) code
“Wireless Communications & Networking”, (2007) DOI. Appears in: Modulation scheme
E. Witt, “Über Steinersche Systeme”, Collected Papers - Gesammelte Abhandlungen 288 (1998) DOI. Appears in: Combinatorial design
E. Witten, “Quantum field theory and the Jones polynomial”, Communications in Mathematical Physics 121, 351 (1989) DOI. Appears in: Topological code
C. Wittmann, M. Takeoka, K. N. Cassemiro, M. Sasaki, G. Leuchs, and U. L. Andersen, “Demonstration of Near-Optimal Discrimination of Optical Coherent States”, Physical Review Letters 101, (2008) arXiv:0809.4953 DOI. Appears in: BPSK c-q code
C. Wittmann, U. L. Andersen, and G. Leuchs, “Discrimination of optical coherent states using a photon number resolving detector”, Journal of Modern Optics 57, 213 (2010) arXiv:0905.2496 DOI. Appears in: PSK c-q code
S. Wolanski and B. Barber, “Ambiguity Clustering: an accurate and efficient decoder for qLDPC codes”, (2025) arXiv:2406.14527. Appears in: $[[144,12,12]]$ gross code, Quantum LDPC (QLDPC) code
J. Wolf, “Efficient maximum likelihood decoding of linear block codes using a trellis”, IEEE Transactions on Information Theory 24, 76 (1978) DOI. Appears in: Linear $q$-ary code
J. Wolf, “Redundancy, the Discrete Fourier Transform, and Impulse Noise Cancellation”, IEEE Transactions on Communications 31, 458 (1983) DOI. Appears in: Analog RS code, Real-number block code
M. M. Wolf, D. Pérez-García, and G. Giedke, “Quantum Capacities of Bosonic Channels”, Physical Review Letters 98, (2007) arXiv:quant-ph/0606132 DOI. Appears in: Amplitude-damping (AD) code, Bosonic code
M. M. Wolf, “Not-So-Normal Mode Decomposition”, Physical Review Letters 100, (2008) arXiv:0707.0604 DOI. Appears in: Bosonic code
R. A. Wolf, “Quantum Error Correction for Kids”, (2024) arXiv:2405.06795. Appears in: Qubit stabilizer code
L. H. Wolff, P. Belzig, M. Christandl, B. Durhuus, and M. Tomamichel, “Fundamental Limit on the Power of Entanglement Assistance in Quantum Communication”, Physical Review Letters 134, (2025) arXiv:2408.17290 DOI. Appears in: EA qubit code
Wolf, Jack Keil. "An introduction to tensor product codes and applications to digital storage systems." 2006 IEEE Information Theory Workshop-ITW 2006 Chengdu. IEEE, 2006.. Appears in: Tensor-product code
J. Wolfmann, “Codes projectifs a deux ou trois poids associfs aux hyperquadriques d’une geometrie finie”, Discrete Mathematics 13, 185 (1975) DOI. Appears in: Quadric code
M. Wolinsky and H. J. Carmichael, “Quantum noise in the parametric oscillator: From squeezed states to coherent-state superpositions”, Physical Review Letters 60, 1836 (1988) DOI. Appears in: Cat code, Two-component cat code
M. P. Woods and Á. M. Alhambra, “Continuous groups of transversal gates for quantum error correcting codes from finite clock reference frames”, Quantum 4, 245 (2020) arXiv:1902.07725 DOI. Appears in: $U(d)$-covariant approximate erasure code
W. K. Wootters and W. H. Zurek, “A single quantum cannot be cloned”, Nature 299, 802 (1982) DOI. Appears in: Error-correcting code (ECC), Quantum error-correcting code (QECC)
J. R. Wootton, “Quantum memories and error correction”, Journal of Modern Optics 59, 1717 (2012) arXiv:1210.3207 DOI. Appears in: Self-correcting quantum code
J. R. Wootton, “A family of stabilizer codes for $D({{\mathbb{Z}}_{2}})$ anyons and Majorana modes”, Journal of Physics A: Mathematical and Theoretical 48, 215302 (2015) arXiv:1501.07779 DOI. Appears in: Matching code
J. R. Wootton, “Demonstrating non-Abelian braiding of surface code defects in a five qubit experiment”, Quantum Science and Technology 2, 015006 (2017) arXiv:1609.07774 DOI. Appears in: Matching code
J. R. Wootton and D. Loss, “Repetition code of 15 qubits”, Physical Review A 97, (2018) arXiv:1709.00990 DOI. Appears in: Quantum repetition code
J. R. Wootton, “Benchmarking near-term devices with quantum error correction”, Quantum Science and Technology 5, 044004 (2020) arXiv:2004.11037 DOI. Appears in: Quantum repetition code
J. R. Wootton, “Hexagonal matching codes with two-body measurements”, Journal of Physics A: Mathematical and Theoretical 55, 295302 (2022) arXiv:2109.13308 DOI. Appears in: XYZ$^2$ hexagonal stabilizer code
J. Wootton, “A Simple Decoder for Topological Codes”, Entropy 17, 1946 (2015) arXiv:1310.2393 DOI. Appears in: Kitaev surface code
Wootton, James R., “Quantum error correction: From the blackboard to the cloud”, University of Basel (2023) arXiv:2210.13154 DOI. Appears in: Floquet color code, Honeycomb Floquet code
A. Wu, G. Li, H. Zhang, G. G. Guerreschi, Y. Ding, and Y. Xie, “Mapping Surface Code to Superconducting Quantum Processors”, (2021) arXiv:2111.13729. Appears in: Kitaev surface code
C. Wu, Y. Wang, C. Guo, Y. Ouyang, G. Wang, and X.-L. Feng, “Initializing a permutation-invariant quantum error-correction code”, Physical Review A 99, (2019) DOI. Appears in: Permutation-invariant (PI) code
D. H. Wu and V. V. Albert, “Approximating the two-mode two-photon Rabi model”, Physics Letters A 422, 127779 (2022) arXiv:2012.06994 DOI. Appears in: Bosonic $q$-ary expansion
J. Wu, A. J. Brady, and Q. Zhuang, “Optimal encoding of oscillators into more oscillators”, Quantum 7, 1082 (2023) arXiv:2212.11970 DOI. Appears in: $D_4$ hyper-diamond GKP code, Oscillator-into-oscillator GKP code, Hexagonal GKP code, Bosonic code
R.-B. Wu, T.-J. Tarn, and C.-W. Li, “Smooth controllability of infinite-dimensional quantum-mechanical systems”, Physical Review A 73, (2006) arXiv:quant-ph/0505063 DOI. Appears in: Bosonic code
Y. Wu and S. Verdu, “The impact of constellation cardinality on Gaussian channel capacity”, 2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton) 620 (2010) DOI. Appears in: Binary PSK (BPSK) code, Coherent-state constellation code, Modulation scheme, Sphere packing
Y. Wu, S. Kolkowitz, S. Puri, and J. D. Thompson, “Erasure conversion for fault-tolerant quantum computing in alkaline earth Rydberg atom arrays”, Nature Communications 13, (2022) arXiv:2201.03540 DOI. Appears in: XZZX surface code
Y. Wu and L. Zhong, “Fusion Blossom: Fast MWPM Decoders for QEC”, (2023) arXiv:2305.08307. Appears in: Kitaev surface code
Z. Wu, S. Cheng, and B. Zeng, “A ZX-Calculus Approach for the Construction of Graph Codes”, (2024) arXiv:2304.08363. Appears in: Cluster-state code, Pastawski-Yoshida-Harlow-Preskill (HaPPY) code
A. Wunsche, “Displaced Fock states and their connection to quasiprobabilities”, Quantum Optics: Journal of the European Optical Society Part B 3, 359 (1991) DOI. Appears in: Two-component cat code
N. Wyderka and O. Gühne, “Characterizing quantum states via sector lengths”, Journal of Physics A: Mathematical and Theoretical 53, 345302 (2020) arXiv:1905.06928 DOI. Appears in: Cluster-state code
A. D. Wyner, “Capabilities of Bounded Discrepancy Decoding”, Bell System Technical Journal 44, 1061 (1965) DOI. Appears in: Spherical code
J.-L. Xia, “Quotient Space Quantum Codes”, (2024) arXiv:2311.07265. Appears in: Union stabilizer (USt) code
L. Xiang, Z. B. Kaykac Egilmez, R. G. Maunder, and L. Hanzo, “CRC-Aided Logarithmic Stack Decoding of Polar Codes for Ultra Reliable Low Latency Communication in 3GPP New Radio”, IEEE Access 7, 28559 (2019) DOI. Appears in: Cyclic redundancy check (CRC) code, Polar code
Z. Xiang, “Explicit spherical designs”, Algebraic Combinatorics 5, 347 (2022) DOI. Appears in: Spherical design
Xiao Han, Kai Niu, and Zhiqiang He, “Implementation of IEEE 802.11n LDPC codes based on general purpose processors”, 2013 15th IEEE International Conference on Communication Technology (2013) DOI. Appears in: Quasi-cyclic LDPC (QC-LDPC) code
Y. Xie, J. Yuan, and Y. Fujiwara, “Quantum Synchronizable Codes From Quadratic Residue Codes and Their Supercodes”, (2014) arXiv:1403.6192. Appears in: Binary quadratic-residue (QR) code, Quantum synchronizable code
C. Xu and J. E. Moore, “Strong-Weak Coupling Self-Duality in the Two-Dimensional Quantum Phase Transition ofp+ipSuperconducting Arrays”, Physical Review Letters 93, (2004) arXiv:cond-mat/0312587 DOI. Appears in: Plaquette Ising code
J.-S. Xu, K. Sun, Y.-J. Han, C.-F. Li, J. K. Pachos, and G.-C. Guo, “Simulating the exchange of Majorana zero modes with a photonic system”, Nature Communications 7, (2016) arXiv:1411.7751 DOI. Appears in: Kitaev chain code
Q. Xu, G. Zheng, Y.-X. Wang, P. Zoller, A. A. Clerk, and L. Jiang, “Autonomous quantum error correction and fault-tolerant quantum computation with squeezed cat qubits”, (2022) arXiv:2210.13406. Appears in: Squeezed cat code, Two-component cat code
Q. Xu, N. Mannucci, A. Seif, A. Kubica, S. T. Flammia, and L. Jiang, “Tailored XZZX codes for biased noise”, (2022) arXiv:2203.16486. Appears in: Asymmetric quantum code, Twisted XZZX toric code
Q. Xu, A. Seif, H. Yan, N. Mannucci, B. O. Sane, R. Van Meter, A. N. Cleland, and L. Jiang, “Distributed Quantum Error Correction for Chip-Level Catastrophic Errors”, Physical Review Letters 129, (2022) arXiv:2203.16488 DOI. Appears in: Concatenated qubit code
Q. Xu, P. Zeng, D. Xu, and L. Jiang, “Fault-Tolerant Operation of Bosonic Qubits with Discrete-Variable Ancillae”, (2023) arXiv:2310.20578. Appears in: Cat code
Q. Xu, J. P. B. Ataides, C. A. Pattison, N. Raveendran, D. Bluvstein, J. Wurtz, B. Vasic, M. D. Lukin, L. Jiang, and H. Zhou, “Constant-Overhead Fault-Tolerant Quantum Computation with Reconfigurable Atom Arrays”, (2023) arXiv:2308.08648. Appears in: Abelian LP code, Distance-balanced code, Bivariate bicycle (BB) code, Quantum LDPC (QLDPC) code, Single-shot code
Q. Xu, H. Zhou, G. Zheng, D. Bluvstein, J. P. B. Ataides, M. D. Lukin, and L. Jiang, “Fast and Parallelizable Logical Computation with Homological Product Codes”, (2024) arXiv:2407.18490. Appears in: Homological product code
S. Xu et al., “Digital Simulation of Projective Non-Abelian Anyons with 68 Superconducting Qubits”, Chinese Physics Letters 40, 060301 (2023) arXiv:2211.09802 DOI. Appears in: Twist-defect surface code
S. Xu et al., “Non-Abelian braiding of Fibonacci anyons with a superconducting processor”, Nature Physics (2024) arXiv:2404.00091 DOI. Appears in: Fibonacci string-net code
X. Xu, N. de Beaudrap, J. O’Gorman, and S. C. Benjamin, “An integrity measure to benchmark quantum error correcting memories”, New Journal of Physics 20, 023009 (2018) arXiv:1707.09951 DOI. Appears in: Approximate quantum error-correcting code (AQECC)
X. Xu, Q. Zhao, X. Yuan, and S. C. Benjamin, “High-Threshold Code for Modular Hardware With Asymmetric Noise”, Physical Review Applied 12, (2019) arXiv:1812.01505 DOI. Appears in: Kitaev surface code
Y. Xu et al., “Demonstration of Controlled-Phase Gates between Two Error-Correctable Photonic Qubits”, Physical Review Letters 124, (2020) arXiv:1810.04690 DOI. Appears in: Binomial code
Y. Xu, Y. Wang, E.-J. Kuo, and V. V. Albert, “Qubit-Oscillator Concatenated Codes: Decoding Formalism and Code Comparison”, PRX Quantum 4, (2023) arXiv:2209.04573 DOI. Appears in: Oscillator-into-oscillator GKP code, Concatenated GKP code
Y. Xu, Y. Wang, and V. V. Albert, “Multimode rotation-symmetric bosonic codes from homological rotor codes”, Physical Review A 110, (2024) arXiv:2311.07679 DOI. Appears in: Oscillator-into-oscillator GKP code, Homological number-phase code, Homological rotor code, Number-phase code, Bosonic code, Concatenated quantum code, Modular-qudit GKP code, Rotor code, Rotor GKP code
Y. Xu, Y. Wang, C. Vuillot, and V. V. Albert, “Letting the tiger out of its cage: bosonic coding without concatenation”, (2024) arXiv:2411.09668. Appears in: $\chi^{(2)}$ code, Coherent-state constellation code, Coherent-state repetition code, Generalized homological-product CSS code, Homological number-phase code, Pair-cat code, Tiger code, Tiger surface code, Two-mode binomial code
Xue-Bin Liang, “Orthogonal designs with maximal rates”, IEEE Transactions on Information Theory 49, 2468 (2003) DOI. Appears in: Orthogonal Spacetime Block Code (OSTBC)
S. A. Yadavalli and I. Marvian, “Noisy Quantum Trees: Infinite Protection Without Correction”, (2024) arXiv:2306.14294. Appears in: Tensor-network code, Quantum parity code (QPC)
T. Yaghoobian and I. F. Blake, “Hermitian codes as generalized Reed-Solomon codes”, Designs, Codes and Cryptography 2, 5 (1992) DOI. Appears in: Generalized RS (GRS) code, Hermitian code
A. Yahya, O. Sidek, M. F. M. Salleh, and F. Ghani, “A new Quasi-Cyclic low density parity check codes”, 2009 IEEE Symposium on Industrial Electronics & Applications (2009) DOI. Appears in: Quasi-cyclic LDPC (QC-LDPC) code
T. Yamada, “CCSDS Telemetry/Tele-command Standards Restructured as Communications Protocols”, SpaceOps 2002 Conference (2002) DOI. Appears in: Turbo code
F. Yamaguchi, K. Nemoto, and W. J. Munro, “Quantum error correction via robust probe modes”, Physical Review A 73, (2006) arXiv:quant-ph/0511098 DOI. Appears in: Qubit stabilizer code, Two-component cat code
T. Yamakawa and M. Zhandry, “Verifiable Quantum Advantage without Structure”, Journal of the ACM 71, 1 (2024) arXiv:2204.02063 DOI. Appears in: Folded RS (FRS) code
K. Yamamoto, S. Duffield, Y. Kikuchi, and D. Muñoz Ramo, “Demonstrating Bayesian quantum phase estimation with quantum error detection”, Physical Review Research 6, (2024) arXiv:2306.16608 DOI. Appears in: $[[6,4,2]]$ error-detecting code
N. Yamamoto, S. Hara, and K. Tsumura, “Suboptimal quantum-error-correcting procedure based on semidefinite programming”, Physical Review A 71, (2005) arXiv:quant-ph/0606105 DOI. Appears in: Approximate quantum error-correcting code (AQECC)
H. Yamasaki and M. Koashi, “Time-Efficient Constant-Space-Overhead Fault-Tolerant Quantum Computation”, Nature Physics 20, 247 (2024) arXiv:2207.08826 DOI. Appears in: $[[2^r-1, 2^r-2r-1, 3]]$ quantum Hamming code, Concatenated qubit code, Qubit code, $[[4,2,2]]$ Four-qubit code, $[[6,2,2]]$ $C_6$ code
Yan Jia, San Ling, and Chaoping Xing, “On Self-Dual Cyclic Codes Over Finite Fields”, IEEE Transactions on Information Theory 57, 2243 (2011) DOI. Appears in: Cyclic linear $q$-ary code, Self-dual linear code
K. Yang and P. V. Kumar, “On the true minimum distance of Hermitian codes”, Lecture Notes in Mathematics 99 (1992) DOI. Appears in: Hermitian code
M. Yang and W. E. Ryan, “Lowering the error-rate floors of moderate-length high-rate irregular ldpc codes”, IEEE International Symposium on Information Theory, 2003. Proceedings. (2003) DOI. Appears in: Extended IRA (eIRA) code
M. Yang, W. E. Ryan, and Y. Li, “Design of Efficiently Encodable Moderate-Length High-Rate Irregular LDPC Codes”, IEEE Transactions on Communications 52, 564 (2004) DOI. Appears in: Extended IRA (eIRA) code
S. Yang and R. Calderbank, “Spatially-Coupled QDLPC Codes”, (2023) arXiv:2305.00137. Appears in: Generalized bicycle (GB) code, Hypergraph product (HGP) code, Quantum spatially coupled (SC-QLDPC) code, XYZ product code
Y. Yang, Y. Mo, J. M. Renes, G. Chiribella, and M. P. Woods, “Optimal universal quantum error correction via bounded reference frames”, Physical Review Research 4, (2022) arXiv:2007.09154 DOI. Appears in: $U(d)$-covariant approximate erasure code
M. Yang, Y. Li, andW.E. Ryan, Design of efficiently-encodable moderate-length high-rate irregular LDPC codes, Proc. 40th Annual Allerton Conference on Communication, Control, and Computing, Champaign, IL., pp. 1415–1424, October 2002.. Appears in: Extended IRA (eIRA) code
H. Yao, W. A. Laban, C. Häger, A. G. i Amat, and H. D. Pfister, “Belief Propagation Decoding of Quantum LDPC Codes with Guided Decimation”, (2024) arXiv:2312.10950. Appears in: Quantum LDPC (QLDPC) code
H. Yao, M. Gökduman, and H. D. Pfister, “Cluster Decomposition for Improved Erasure Decoding of Quantum LDPC Codes”, (2024) arXiv:2412.08817. Appears in: Hypergraph product (HGP) code, Quantum LDPC (QLDPC) code
X.-C. Yao et al., “Experimental demonstration of topological error correction”, Nature 482, 489 (2012) arXiv:1202.5459 DOI. Appears in: Cluster-state code
J. Yard, P. Hayden, and I. Devetak, “Capacity theorems for quantum multiple-access channels: classical-quantum and quantum-quantum capacity regions”, IEEE Transactions on Information Theory 54, 3091 (2008) arXiv:quant-ph/0501045 DOI. Appears in: Entanglement-assisted (EA) hybrid QECC
S. M. H. T. Yazdi, Y. Yuan, J. Ma, H. Zhao, and O. Milenkovic, “A Rewritable, Random-Access DNA-Based Storage System”, (2015) arXiv:1505.02199. Appears in: DNA storage code
S. M. H. T. Yazdi, H. M. Kiah, E. R. Garcia, J. Ma, H. Zhao, and O. Milenkovic, “DNA-Based Storage: Trends and Methods”, (2015) arXiv:1507.01611. Appears in: DNA storage code
S. M. H. T. Yazdi, R. Gabrys, and O. Milenkovic, “Portable and Error-Free DNA-Based Data Storage”, Scientific Reports 7, (2017) DOI. Appears in: DNA storage code
M. Ye and A. Barg, “Explicit constructions of high-rate MDS array codes with optimal repair bandwidth”, (2016) arXiv:1604.00454. Appears in: Ye-Barg code
M. Ye and A. Barg, “Explicit constructions of MDS array codes and RS codes with optimal repair bandwidth”, 2016 IEEE International Symposium on Information Theory (ISIT) (2016) DOI. Appears in: Diagonal code
M. Ye and A. Barg, “Explicit constructions of optimal-access MDS codes with nearly optimal sub-packetization”, (2017) arXiv:1605.08630. Appears in: Locally recoverable code (LRC), Regenerating code (RGC), Ye-Barg code
Y. Ye et al., “Logical Magic State Preparation with Fidelity Beyond the Distillation Threshold on a Superconducting Quantum Processor”, (2023) arXiv:2305.15972. Appears in: $[[9,1,3]]$ Surface-17 code
J. S. Yedidia, W. T. Freeman, and Y. Weiss, Generalized belief propagation, in NIPS, Vol. 13 (2000) pp. 689–695.. Appears in: Qubit stabilizer code, Kitaev surface code
S. Yekhanin, Locally Decodable Codes and Private Information Retrieval Schemes (Springer Berlin Heidelberg, 2010) DOI. Appears in: Locally decodable code (LDC), Private information retrieval (PIR) code
S. Yekhanin, “Locally Decodable Codes”, Foundations and Trends® in Theoretical Computer Science 6, 139 (2012) DOI. Appears in: Generalized RM (GRM) code, Hadamard code, Locally decodable code (LDC), $q$-ary linear LCC
W.-T. Yen and L.-Y. Hsu, “Optimal Nonadditive Quantum Error-Detecting Code”, (2009) arXiv:0901.1353. Appears in: Small-distance block quantum code
D. N. YETTER, “TQFT’S FROM HOMOTOPY 2-TYPES”, Journal of Knot Theory and Its Ramifications 02, 113 (1993) DOI. Appears in: Two-gauge theory code
O. W. Yeung and K. M. Chugg, “An Iterative Algorithm and Low Complexity Hardware Architecture for Fast Acquisition of Long PN Codes in UWB Systems”, Journal of VLSI signal processing systems for signal, image and video technology 43, 25 (2006) DOI. Appears in: Gold code
J. Yi, W. Ye, D. Gottesman, and Z.-W. Liu, “Complexity and order in approximate quantum error-correcting codes”, Nature Physics (2024) arXiv:2310.04710 DOI. Appears in: Approximate quantum error-correcting code (AQECC), Conformal-field theory (CFT) code, Circuit-to-Hamiltonian approximate code, Eigenstate thermalization hypothesis (ETH) code, Random quantum code, Topological code
Z. Yi, Z. Liang, K. Zhong, Y. Wu, Z. Fang, and X. Wang, “Improved belief propagation decoding algorithm based on decoupling representation of Pauli operators for quantum LDPC codes”, (2023) arXiv:2305.17505. Appears in: Quantum LDPC (QLDPC) code, Qubit stabilizer code
Yicong Zhou, K. Panetta, S. Agaian, and C. L. P. Chen, “(n, k, p)-Gray code for image systems”, IEEE Transactions on Cybernetics 43, 515 (2013) DOI. Appears in: Gray code
C. Yin and A. Lucas, “Low-density parity-check codes as stable phases of quantum matter”, (2024) arXiv:2411.01002. Appears in: Commuting-projector Hamiltonian code, Hamiltonian-based code, Quantum LDPC (QLDPC) code, Topological code
K. Yin, X. Fang, J. Ruan, H. Zhang, D. Tullsen, A. Sornborger, C. Liu, A. Li, T. Humble, and Y. Ding, “SymBreak: Mitigating Quantum Degeneracy Issues in QLDPC Code Decoders by Breaking Symmetry”, (2024) arXiv:2412.02885. Appears in: Quantum LDPC (QLDPC) code
K. Yin, X. Fang, Y. Shi, T. Humble, A. Li, and Y. Ding, “Surf-Deformer: Mitigating Dynamic Defects on Surface Code via Adaptive Deformation”, (2024) arXiv:2405.06941. Appears in: Kitaev surface code
T. J. Yoder, R. Takagi, and I. L. Chuang, “Universal Fault-Tolerant Gates on Concatenated Stabilizer Codes”, Physical Review X 6, (2016) arXiv:1603.03948 DOI. Appears in: Qubit stabilizer code, Five-qubit perfect code, $[[7,1,3]]$ Steane code
T. J. Yoder and I. H. Kim, “The surface code with a twist”, Quantum 1, 2 (2017) arXiv:1612.04795 DOI. Appears in: $[[7,1,3]]$ Steane code, Triangular surface code, $[[7,1,3]]$ twist-defect surface code, Twist-defect surface code
T. J. Yoder, “Universal fault-tolerant quantum computation with Bacon-Shor codes”, (2017) arXiv:1705.01686. Appears in: 3D Bacon-Shor code, Bacon-Shor code
T. J. Yoder, “Optimal quantum subsystem codes in two dimensions”, Physical Review A 99, (2019) arXiv:1901.06319 DOI. Appears in: Bravyi-Bacon-Shor (BBS) code
Yoder, Theodore., DSpace@MIT Practical Fault-Tolerant Quantum Computation (2018). Appears in: Bacon-Shor code, Qubit stabilizer code
Yoder, Theodore J. "A generalization of the stabilizer formalism for simulating arbitrary quantum circuits." See https://www. scottaaronson. com/showcase2/report/ted-yoder. pdf (2012).. Appears in: Qubit stabilizer code
S. Yokoyama, R. Ukai, S. C. Armstrong, C. Sornphiphatphong, T. Kaji, S. Suzuki, J. Yoshikawa, H. Yonezawa, N. C. Menicucci, and A. Furusawa, “Ultra-large-scale continuous-variable cluster states multiplexed in the time domain”, Nature Photonics 7, 982 (2013) arXiv:1306.3366 DOI. Appears in: Analog-cluster-state code
H. Yonezawa, T. Aoki, and A. Furusawa, “Demonstration of a quantum teleportation network for continuous variables”, Nature 431, 430 (2004) DOI. Appears in: Analog repetition code
Yongyi Mao and A. H. Banihashemi, “Decoding low-density parity-check codes with probabilistic schedule”, 2001 IEEE Pacific Rim Conference on Communications, Computers and Signal Processing (IEEE Cat. No.01CH37233) DOI. Appears in: Tanner code
N. Yoran and B. Reznik, “Deterministic Linear Optics Quantum Computation with Single Photon Qubits”, Physical Review Letters 91, (2003) arXiv:quant-ph/0303008 DOI. Appears in: Cluster-state code, Dual-rail quantum code
B. Yoshida, “Feasibility of self-correcting quantum memory and thermal stability of topological order”, Annals of Physics 326, 2566 (2011) arXiv:1103.1885 DOI. Appears in: 3D lattice stabilizer code, Self-correcting quantum code
B. Yoshida, “Classification of quantum phases and topology of logical operators in an exactly solved model of quantum codes”, Annals of Physics 326, 15 (2011) arXiv:1007.4601 DOI. Appears in: 2D color code, 3D color code, 3D surface code, Color code, Homological code, Concatenated qubit code, Kitaev surface code
B. Yoshida, “Exotic topological order in fractal spin liquids”, Physical Review B 88, (2013) arXiv:1302.6248 DOI. Appears in: Classical fractal liquid code, Fibonacci fractal spin-liquid code, Fibonacci code, Type-II fractal spin-liquid code, Fracton stabilizer code, Sierpinsky fractal spin-liquid (SFSL) code
B. Yoshida, “Information storage capacity of discrete spin systems”, Annals of Physics 338, 134 (2013) arXiv:1111.3275 DOI. Appears in: Classical fractal liquid code
B. Yoshida, “Topological phases with generalized global symmetries”, Physical Review B 93, (2016) arXiv:1508.03468 DOI. Appears in: Abelian quantum-double stabilizer code, Dihedral $G=D_m$ quantum-double code, Kitaev surface code, Abelian TQD stabilizer code
B. Yoshida and A. Kitaev, “Efficient decoding for the Hayden-Preskill protocol”, (2017) arXiv:1710.03363. Appears in: Approximate quantum error-correcting code (AQECC)
B. Yoshida, “Gapped boundaries, group cohomology and fault-tolerant logical gates”, Annals of Physics 377, 387 (2017) arXiv:1509.03626 DOI. Appears in: 3D surface code
B. Yoshida, “Soft mode and interior operator in the Hayden-Preskill thought experiment”, Physical Review D 100, (2019) DOI. Appears in: Monitored random-circuit code
B. Yoshida, “Decoding the Entanglement Structure of Monitored Quantum Circuits”, (2021) arXiv:2109.08691. Appears in: Error-correcting code (ECC), Quantum error-correcting code (QECC)
M. Yoshida, G. Kimura, T. Miyadera, H. Imai, and J. Cheng, “Solution to the mean king’s problem using quantum error-correcting codes”, Physical Review A 91, (2015) arXiv:1507.07072 DOI. Appears in: Finite-dimensional quantum error-correcting code
M. Yoshida, T. Kuriyama, and J. Cheng, “Solutions to the mean king’s problem: Higher-dimensional quantum error-correcting codes”, International Journal of Quantum Information 14, 1650048 (2016) arXiv:1701.01828 DOI. Appears in: $[[2m,2m-2,2]]$ error-detecting code
S. Yoshida, S. Tamiya, and H. Yamasaki, “Concatenate codes, save qubits”, (2024) arXiv:2402.09606. Appears in: $[[2^r-1, 2^r-2r-1, 3]]$ quantum Hamming code, Concatenated qubit code, Qubit code, $[[4,2,2]]$ Four-qubit code, $[[6,2,2]]$ $C_6$ code
J. Yoshikawa, S. Yokoyama, T. Kaji, C. Sornphiphatphong, Y. Shiozawa, K. Makino, and A. Furusawa, “Invited Article: Generation of one-million-mode continuous-variable cluster state by unlimited time-domain multiplexing”, APL Photonics 1, (2016) arXiv:1606.06688 DOI. Appears in: Analog-cluster-state code
Y. You, T. Devakul, F. J. Burnell, and S. L. Sondhi, “Subsystem symmetry protected topological order”, Physical Review B 98, (2018) arXiv:1803.02369 DOI. Appears in: Cluster-state code, Symmetry-protected topological (SPT) code, Square-lattice cluster-state code, Lattice stabilizer code
J. Yu, S. R. Muleady, Y.-X. Wang, N. Schine, A. V. Gorshkov, and A. M. Childs, “Efficient preparation of Dicke states”, (2024) arXiv:2411.03428. Appears in: PI qubit code
S. Yu, Q. Chen, and C. H. Oh, “Graphical Quantum Error-Correcting Codes”, (2007) arXiv:0709.1780. Appears in: $[[7,1,3]]$ bare code, $((7,2))$ QETC, $((10,24,3))$ qubit code, $((5,6,2))$ qubit code, Smolin-Smith-Wehner (SSW) code, $[[8, 3, 3]]$ Eight-qubit Gottesman code, $[[7,1,3]]$ Steane code, $[[7,1,3]]$ twist-defect surface code
S. Yu, Q. Chen, C. H. Lai, and C. H. Oh, “Nonadditive Quantum Error-Correcting Code”, Physical Review Letters 101, (2008) arXiv:0704.2122 DOI. Appears in: $((9,12,3))$ qubit code
S. Yu, Q. Chen, and C. H. Oh, “Two infinite families of nonadditive quantum error-correcting codes”, (2009) arXiv:0901.1935. Appears in: $((10,24,3))$ qubit code, $((9,12,3))$ qubit code, Small-distance block quantum code
S. Yu, J. Bierbrauer, Y. Dong, Q. Chen, and C. H. Oh, “All the stabilizer codes of distance 3”, (2011) arXiv:0901.1968. Appears in: Small-distance qubit stabilizer code
M. Yuan, Q. Xu, and L. Jiang, “Construction of bias-preserving operations for pair-cat codes”, Physical Review A 106, (2022) arXiv:2208.06913 DOI. Appears in: Pair-cat code
R. Yuan, M. Zhao, S. Han, and J. Cheng, “Optimally Displaced Threshold Detection for Discriminating Binary Coherent States Using Imperfect Devices”, (2020) arXiv:2007.11109. Appears in: BPSK c-q code
V. A. Yudin, “Minimum potential energy of a point system of charges”, Diskr. Mat., 4:2 (1992), 115–121; Discrete Math. Appl., 3:1 (1993), 75–81. Appears in: Universally optimal spherical code
H. P. Yuen and M. Ozawa, “Ultimate information carrying limit of quantum systems”, Physical Review Letters 70, 363 (1993) DOI. Appears in: Bosonic c-q code
H. Yuen, R. Kennedy, and M. Lax, “Optimum testing of multiple hypotheses in quantum detection theory”, IEEE Transactions on Information Theory 21, 125 (1975) DOI. Appears in: Coherent-state c-q code
V. Yu. Krachkovskii, "Decoding of codes on algebraic curves," (in Russian), Conference Odessa, 1988.. Appears in: Plane-curve code
Yunfeng Lin, Ben Liang, and Baochun Li, “Priority Random Linear Codes in Distributed Storage Systems”, IEEE Transactions on Parallel and Distributed Systems 20, 1653 (2009) DOI. Appears in: Random code
B. Yurke and D. Stoler, “Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion”, Physical Review Letters 57, 13 (1986) DOI. Appears in: Two-component cat code
M. Yu. Rosenbloom, M. A. Tsfasman, “Codes for the m-Metric”, Probl. Peredachi Inf., 33:1 (1997), 55–63; Problems Inform. Transmission, 33:1 (1997), 45–52. Appears in: Multiplicity code, Niederreiter-Rosenbloom-Tsfasman (NRT) code, RS NRT code
“Z2-systolic freedom and quantum codes”, Mathematics of Quantum Computation 303 (2002) DOI. Appears in: Freedman-Meyer-Luo code, Homological code
A. Zabalo, M. J. Gullans, J. H. Wilson, S. Gopalakrishnan, D. A. Huse, and J. H. Pixley, “Critical properties of the measurement-induced transition in random quantum circuits”, Physical Review B 101, (2020) arXiv:1911.00008 DOI. Appears in: Monitored random-circuit code
C. Zachos, “Hamiltonian Flows, SU(∞), SO(∞), USp(∞), and Strings”, Differential Geometric Methods in Theoretical Physics 423 (1990) DOI. Appears in: Modular-qudit code
P. Zador, “Asymptotic quantization error of continuous signals and the quantization dimension”, IEEE Transactions on Information Theory 28, 139 (1982) DOI. Appears in: Lattice-based code
P. L. Zador, Development and evaluation of procedures for quantiZing multivariate distributions, Ph.D. Dissertation, Stanford Univ., 1963. Appears in: Lattice-based code
J. Zak, “Finite Translations in Solid-State Physics”, Physical Review Letters 19, 1385 (1967) DOI. Appears in: Square-lattice GKP code
P. Zanardi and M. Rasetti, “Noiseless Quantum Codes”, Physical Review Letters 79, 3306 (1997) arXiv:quant-ph/9705044 DOI. Appears in: Constant-excitation (CE) code
P. Zanardi and M. Rasetti, “Holonomic quantum computation”, Physics Letters A 264, 94 (1999) arXiv:quant-ph/9904011 DOI. Appears in: Honeycomb Floquet code, Qubit stabilizer code, Kitaev surface code
P. Zanardi, C. Zalka, and L. Faoro, “Entangling power of quantum evolutions”, Physical Review A 62, (2000) arXiv:quant-ph/0005031 DOI. Appears in: Perfect-tensor code
M. H. Zarei, “Strong-weak coupling duality between two perturbed quantum many-body systems: Calderbank-Shor-Steane codes and Ising-like systems”, Physical Review B 96, (2017) arXiv:1710.02646 DOI. Appears in: Qubit CSS code, Abelian topological code, Lattice stabilizer code
M. H. Zarei, “General scheme for preparation of different topological states on cluster states”, Physical Review A 95, (2017) arXiv:1705.05602 DOI. Appears in: Cluster-state code
Zauner, G. (1999). Grundzüge einer nichtkommutativen Designtheorie. Ph. D. dissertation, PhD thesis.. Appears in: $t$-design
K. Zeger, A. Vardy, and E. Agrell, “Upper bounds for constant-weight codes”, IEEE Transactions on Information Theory 46, 2373 (2000) DOI. Appears in: Constant-weight code
G. Zemor, “On expander codes”, IEEE Transactions on Information Theory 47, 835 (2001) DOI. Appears in: Regular binary Tanner code
G. Zémor, “On Cayley Graphs, Surface Codes, and the Limits of Homological Coding for Quantum Error Correction”, Lecture Notes in Computer Science 259 (2009) DOI. Appears in: Cycle LDPC code, Generalized homological-product code, Homological code, Cycle code, Margulis LDPC code, Quantum-inspired classical block code
R. Zen, J. Olle, L. Colmenarez, M. Puviani, M. Müller, and F. Marquardt, “Quantum Circuit Discovery for Fault-Tolerant Logical State Preparation with Reinforcement Learning”, (2024) arXiv:2402.17761. Appears in: Qubit CSS code, $[[9,1,3]]$ Shor code, $[[15,1,3]]$ quantum Reed-Muller code, Five-qubit perfect code, $[[7,1,3]]$ Steane code, $[[9,1,3]]$ Surface-17 code
B. Zeng, A. Cross, and I. L. Chuang, “Transversality versus Universality for Additive Quantum Codes”, (2007) arXiv:0706.1382. Appears in: Qubit stabilizer code, $[[7,1,3]]$ Steane code
B. Zeng, H. Chung, A. W. Cross, and I. L. Chuang, “Local unitary versus local Clifford equivalence of stabilizer and graph states”, Physical Review A 75, (2007) arXiv:quant-ph/0611214 DOI. Appears in: $[[2^r-1,1,3]]$ simplex code
B. Zeng, X. Chen, and I. L. Chuang, “Semi-Clifford operations, structure ofCkhierarchy, and gate complexity for fault-tolerant quantum computation”, Physical Review A 77, (2008) arXiv:0712.2084 DOI. Appears in: Qubit stabilizer code
B. Zeng and D.-L. Zhou, “Topological and Error-Correcting Properties for Symmetry-Protected Topological Order”, (2014) arXiv:1407.3413. Appears in: Binary code, Hamiltonian-based code, Symmetry-protected topological (SPT) code
B. Zeng and X.-G. Wen, “Gapped quantum liquids and topological order, stochastic local transformations and emergence of unitarity”, Physical Review B 91, (2015) arXiv:1406.5090 DOI. Appears in: Topological code
B. Zeng, X. Chen, D.-L. Zhou, and X.-G. Wen, “Quantum Information Meets Quantum Matter -- From Quantum Entanglement to Topological Phase in Many-Body Systems”, (2018) arXiv:1508.02595. Appears in: Hamiltonian-based code, Topological code
W. Zeng, A. Ashikhmin, M. Woolls, and L. P. Pryadko, “Quantum convolutional data-syndrome codes”, 2019 IEEE 20th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC) (2019) arXiv:1902.07395 DOI. Appears in: Quantum data-syndrome (QDS) code, Quantum convolutional code
W. Zeng and L. P. Pryadko, “Higher-Dimensional Quantum Hypergraph-Product Codes with Finite Rates”, Physical Review Letters 122, (2019) arXiv:1810.01519 DOI. Appears in: Hypergraph product (HGP) code
W. Zeng and L. P. Pryadko, “Minimal distances for certain quantum product codes and tensor products of chain complexes”, Physical Review A 102, (2020) arXiv:2007.12152 DOI. Appears in: Homological product code, Hypergraph product (HGP) code, Concatenated qubit code, Subsystem homological product code, Subsystem hypergraph product (SHP) code
Y. Zeng, Z.-Y. Zhou, E. Rinaldi, C. Gneiting, and F. Nori, “Approximate Autonomous Quantum Error Correction with Reinforcement Learning”, Physical Review Letters 131, (2023) arXiv:2212.11651 DOI. Appears in: Numerically optimized bosonic code, Neural network quantum code
Y. Zeng, W. Qin, Y.-H. Chen, C. Gneiting, and F. Nori, “Neural Network-Based Design of Approximate Gottesman-Kitaev-Preskill Code”, (2024) arXiv:2411.01265. Appears in: Gottesman-Kitaev-Preskill (GKP) code, Numerically optimized bosonic code
Zeng, Bei. Quantum operations and codes beyond the Stabilizer-Clifford framework. Diss. Massachusetts Institute of Technology, 2009.. Appears in: Codeword stabilized (CWS) code
L.-H. Zetterberg, “Cyclic codes from irreducible polynomials for correction of multiple errors”, IEEE Transactions on Information Theory 8, 13 (1962) DOI. Appears in: Zetterberg code
L.-H. Zetterberg, “A class of codes for polyphase signals on a bandlimited Gaussian channel”, IEEE Transactions on Information Theory 11, 385 (1965) DOI. Appears in: Polyphase code
L.-H. Zetterberg, “Detection of a class of coded and phase-modulated signals”, IEEE Transactions on Information Theory 12, 153 (1966) DOI. Appears in: Polyphase code
A. Zhang, Z.-L. Wu, C.-H. Li, and K.-T. Fang, “On Hadamard-Type Output Coding in Multiclass Learning”, Intelligent Data Engineering and Automated Learning 397 (2003) DOI. Appears in: Error-correcting output code (ECOC), Hadamard code
D. Zhang, K. Ho-Van, and T. Le-Ngoc, “Impulse noise detection techniques for retransmission to reduce delay in DSL systems”, 2012 IEEE International Conference on Communications (ICC) 3160 (2012) DOI. Appears in: Reed-Solomon (RS) code
D. Zhang and T. Cubitt, “Quantum Error Transmutation”, (2023) arXiv:2310.10278. Appears in: Ball-Verstraete-Cirac (BVC) code, Derby-Klassen (DK) code, Subsystem QECC, Quantum error-transmuting code (QETC), $((7,2))$ QETC
G. Zhang and Y. Li, “Time-efficient logical operations on quantum LDPC codes”, (2024) arXiv:2408.01339. Appears in: Qubit stabilizer code
H. Zhang, E. Yaakobi, and N. Silberstein, “Multiset Combinatorial Batch Codes”, (2017) arXiv:1701.02708. Appears in: Locally decodable code (LDC), Private information retrieval (PIR) code
J. Zhang and S. L. Braunstein, “Continuous-variable Gaussian analog of cluster states”, Physical Review A 73, (2006) DOI. Appears in: Analog-cluster-state code
J. Zhang, C. Xie, K. Peng, and P. van Loock, “Anyon statistics with continuous variables”, Physical Review A 78, (2008) arXiv:0711.0820 DOI. Appears in: Analog surface code
J. Zhang, D. Gangloff, O. Moussa, and R. Laflamme, “Experimental quantum error correction with high fidelity”, Physical Review A 84, (2011) arXiv:1109.4821 DOI. Appears in: Quantum repetition code
J. Zhang, M. Grassl, B. Zeng, and R. Laflamme, “Experimental implementation of a codeword-stabilized quantum code”, Physical Review A 85, (2012) arXiv:1111.5445 DOI. Appears in: Smolin-Smith-Wehner (SSW) code
J. Zhang, R. Laflamme, and D. Suter, “Experimental Implementation of Encoded Logical Qubit Operations in a Perfect Quantum Error Correcting Code”, Physical Review Letters 109, (2012) arXiv:1208.4797 DOI. Appears in: Five-qubit perfect code
J. Zhang, S. J. Devitt, J. Q. You, and F. Nori, “Holonomic surface codes for fault-tolerant quantum computation”, Physical Review A 97, (2018) arXiv:1708.02360 DOI. Appears in: Kitaev surface code
J. Zhang, J. Zhao, Y.-C. Wu, and G.-P. Guo, “Quantum error correction with the color-Gottesman-Kitaev-Preskill code”, Physical Review A 104, (2021) arXiv:2112.14447 DOI. Appears in: Square-octagon (4.8.8) color code, Concatenated GKP code
J. Zhang, Y.-C. Wu, and G.-P. Guo, “Concatenation of the Gottesman-Kitaev-Preskill code with the XZZX surface code”, Physical Review A 107, (2023) arXiv:2207.04383 DOI. Appears in: GKP-surface code, XZZX surface code
L. Zhang and I. Fuss, “Quantum Reed-Muller Codes”, (1997) arXiv:quant-ph/9703045. Appears in: Quantum Reed-Muller code
L. Zhang, Q. Huang, S. Lin, K. Abdel-Ghaffar, and I. F. Blake, “Quasi-Cyclic LDPC Codes: An Algebraic Construction, Rank Analysis, and Codes on Latin Squares”, IEEE Transactions on Communications 58, 3126 (2010) DOI. Appears in: Algebraic LDPC code
R. Zhang, L.-Z. Liu, Z.-D. Li, Y.-Y. Fei, X.-F. Yin, L. Li, N.-L. Liu, Y. Mao, Y.-A. Chen, and J.-W. Pan, “Loss-tolerant all-photonic quantum repeater with generalized Shor code”, Optica 9, 152 (2022) arXiv:2203.07979 DOI. Appears in: $[[9,1,3]]$ Shor code
W. Zhang, S. Chen, X. Bai, and D. Zhou, “A full layer parallel QC-LDPC decoder for WiMAX and Wi-Fi”, 2015 IEEE 11th International Conference on ASIC (ASICON) (2015) DOI. Appears in: Quasi-cyclic LDPC (QC-LDPC) code
Y. Zhang, “Quantum Fourier Transform Over Galois Rings”, (2009) arXiv:0904.2560. Appears in: Category-based quantum code, Galois-qudit code, Group-based quantum code
Y. Zhang, “Abstract Error Groups Via Jones Unitary Braid Group Representations at q=i”, (2009) arXiv:0902.0383. Appears in: Knill code
Y. Zhang, T. Grover, A. Turner, M. Oshikawa, and A. Vishwanath, “Quasiparticle statistics and braiding from ground-state entanglement”, Physical Review B 85, (2012) arXiv:1111.2342 DOI. Appears in: Topological code
Z. Zhang, D. Aasen, and S. Vijay, “The X-Cube Floquet Code”, (2022) arXiv:2211.05784. Appears in: X-cube Floquet code
G. Zhao, A. C. Doherty, and I. H. Kim, “On the energy barrier of hypergraph product codes”, (2024) arXiv:2407.20526. Appears in: Hypergraph product (HGP) code, Self-correcting quantum code
J. Zhao, Y.-C. Wu, and G.-P. Guo, “Quantum memory error correction computation based on Chamon model”, (2023) arXiv:2303.05267. Appears in: Chamon model code
Q. Zhao, Y. Zhou, and A. M. Childs, “Entanglement accelerates quantum simulation”, (2024) arXiv:2406.02379. Appears in: Perfect-tensor code
X. Zhao, X. Li, Q. Wang, and T. Yan, “Hermitian dual-containing constacyclic BCH codes and related quantum codes of length $\frac{q^{2m}-1}{q+1}$”, (2020) arXiv:2007.13309. Appears in: Galois-qudit BCH code
Y. Zhao et al., “Realization of an Error-Correcting Surface Code with Superconducting Qubits”, Physical Review Letters 129, (2022) arXiv:2112.13505 DOI. Appears in: $[[9,1,3]]$ Surface-17 code
Y. Zhao and Y. Wan, “Noninvertible Gauge Symmetry in (2+1)d Topological Orders: A String-Net Model Realization”, (2024) arXiv:2408.02664. Appears in: String-net code, Topological code
Y. Zhao and D. E. Liu, “Extracting error thresholds through the framework of approximate quantum error correction condition”, Physical Review Research 6, (2024) arXiv:2312.16991 DOI. Appears in: Approximate quantum error-correcting code (AQECC), Qubit stabilizer code
G. Zheng, W. He, G. Lee, K. Noh, and L. Jiang, “Performance and achievable rates of the Gottesman-Kitaev-Preskill code for pure-loss and amplification channels”, (2024) arXiv:2412.06715. Appears in: Amplitude-damping (AD) code, Gottesman-Kitaev-Preskill (GKP) code
G. Zheng, W. He, G. Lee, and L. Jiang, “Near-Optimal Performance of Quantum Error Correction Codes”, Physical Review Letters 132, (2024) arXiv:2401.02022 DOI. Appears in: Approximate quantum error-correcting code (AQECC)
H. Zheng, A. Dua, and L. Jiang, “Demonstrating non-Abelian statistics of Majorana fermions using twist defects”, Physical Review B 92, (2015) arXiv:1508.04166 DOI. Appears in: Abelian topological code, Twist-defect surface code
Y.-C. Zheng and T. A. Brun, “Fault-tolerant holonomic quantum computation in surface codes”, Physical Review A 91, (2015) arXiv:1411.4248 DOI. Appears in: Honeycomb Floquet code, Kitaev surface code
Zhenghan Wang. private communication, 2017.. Appears in: 2D color code, Three-fermion (3F) subsystem code
W. Zhong, O. Shtanko, and R. Movassagh, “Advantage of Quantum Neural Networks as Quantum Information Decoders”, (2024) arXiv:2401.06300. Appears in: 2D lattice stabilizer code, Lattice stabilizer code
D. L. Zhou, B. Zeng, Z. Xu, and C. P. Sun, “Quantum computation based ond-level cluster state”, Physical Review A 68, (2003) arXiv:quant-ph/0304054 DOI. Appears in: Modular-qudit cluster-state code
J. Zhou and C. Y. Suen, “Unconstrained numeral pair recognition using enhanced error correcting output coding: a holistic approach”, Eighth International Conference on Document Analysis and Recognition (ICDAR’05) (2005) DOI. Appears in: Error-correcting output code (ECOC)
J. Zhou, H. Peng, and C. Y. Suen, “Data-driven decomposition for multi-class classification”, Pattern Recognition 41, 67 (2008) DOI. Appears in: Error-correcting output code (ECOC)
J. Zhou, S. Chessa, E. Chitambar, and F. Leditzky, “On the distinguishability of geometrically uniform quantum states”, (2025) arXiv:2501.12376. Appears in: Coherent-state c-q code
J. Zhou et al., “Experimental demonstration of entanglement pumping with bosonic logical qubits”, (2025) arXiv:2501.04460. Appears in: Binomial code
S. Zhou, M. Zhang, J. Preskill, and L. Jiang, “Achieving the Heisenberg limit in quantum metrology using quantum error correction”, Nature Communications 9, (2018) arXiv:1706.02445 DOI. Appears in: Error-corrected sensing code
S. Zhou and L. Jiang, “Optimal approximate quantum error correction for quantum metrology”, Physical Review Research 2, (2020) arXiv:1910.08472 DOI. Appears in: Error-corrected sensing code
S. Zhou, Z.-W. Liu, and L. Jiang, “New perspectives on covariant quantum error correction”, Quantum 5, 521 (2021) arXiv:2005.11918 DOI. Appears in: Covariant block quantum code
S. Zhou and L. Jiang, “Asymptotic Theory of Quantum Channel Estimation”, PRX Quantum 2, (2021) arXiv:2003.10559 DOI. Appears in: Error-corrected sensing code
S. Zhou, “Limits of Noisy Quantum Metrology with Restricted Quantum Controls”, Physical Review Letters 133, (2024) arXiv:2402.18765 DOI. Appears in: Error-corrected sensing code
S. Zhou, A. G. Manes, and L. Jiang, “Achieving metrological limits using ancilla-free quantum error-correcting codes”, Physical Review A 109, (2024) arXiv:2303.00881 DOI. Appears in: Error-corrected sensing code
X. Zhou, D. W. Leung, and I. L. Chuang, “Methodology for quantum logic gate construction”, Physical Review A 62, (2000) arXiv:quant-ph/0002039 DOI. Appears in: Bacon-Shor code, Qubit stabilizer code
Z. Zhou, N. Li, C. Fan, and T. Helleseth, “Linear Codes with Two or Three Weights From Quadratic Bent Functions”, (2015) arXiv:1506.06830. Appears in: Two-weight code
C. Zhu, T. Lan, and X.-G. Wen, “Topological nonlinear σ -model, higher gauge theory, and a systematic construction of 3+1D topological orders for boson systems”, Physical Review B 100, (2019) arXiv:1808.09394 DOI. Appears in: Topological code
C. Zhu and Q. Liao, “Complete weight enumerators for several classes of two-weight and three-weight linear codes”, (2021) arXiv:2107.02447. Appears in: Two-weight code
G. Zhu, A. Lavasani, and M. Barkeshli, “Universal Logical Gates on Topologically Encoded Qubits via Constant-Depth Unitary Circuits”, Physical Review Letters 125, (2020) arXiv:1806.02358 DOI. Appears in: Fibonacci string-net code, String-net code
G. Zhu, A. Lavasani, and M. Barkeshli, “Instantaneous braids and Dehn twists in topologically ordered states”, Physical Review B 102, (2020) arXiv:1806.06078 DOI. Appears in: Fibonacci string-net code, String-net code, Kitaev surface code
G. Zhu, M. Hafezi, and M. Barkeshli, “Quantum origami: Transversal gates for quantum computation and measurement of topological order”, Physical Review Research 2, (2020) arXiv:1711.05752 DOI. Appears in: Fibonacci string-net code
G. Zhu, T. Jochym-O’Connor, and A. Dua, “Topological Order, Quantum Codes, and Quantum Computation on Fractal Geometries”, PRX Quantum 3, (2022) arXiv:2108.00018 DOI. Appears in: 3D surface code, Fractal surface code
G. Zhu, S. Sikander, E. Portnoy, A. W. Cross, and B. J. Brown, “Non-Clifford and parallelizable fault-tolerant logical gates on constant and almost-constant rate homological quantum LDPC codes via higher symmetries”, (2024) arXiv:2310.16982. Appears in: 3D color code, 3D surface code, Freedman-Meyer-Luo code, Homological code, Quantum rainbow code, Triorthogonal code, Quasi-hyperbolic color code, Qubit CSS code, Qubit stabilizer code, Symmetry-protected topological (SPT) code
H. Zhu, “Mutually unbiased bases as minimal Clifford covariant 2-designs”, Physical Review A 91, (2015) arXiv:1505.01123 DOI. Appears in: $t$-design
H. Zhu, “Multiqubit Clifford groups are unitary 3-designs”, Physical Review A 96, (2017) arXiv:1510.02619 DOI. Appears in: Qubit stabilizer code, $t$-design
S. Zhu, Z. Sun, and X. Kai, “A Class of Narrow-Sense BCH Codes”, IEEE Transactions on Information Theory 65, 4699 (2019) DOI. Appears in: Bose–Chaudhuri–Hocquenghem (BCH) code
Ziman, John M. Models of disorder: the theoretical physics of homogeneously disordered systems. Cambridge university press, 1979.. Appears in: Plaquette Ising code
V. A. Zinoviev, “Generalized Cascade Codes”, Probl. Peredachi Inf., 12:1 (1976). Appears in: Generalized concatenated code (GCC)
V. A. Zinoviev, “Generalized Cascade Codes”, Probl. Peredachi Inf., 12:1 (1976), 5–15; Problems Inform. Transmission, 12:1 (1976), 2–9. Appears in: Generalized concatenated code (GCC)
V.A. Zinoviev, S.N. Litsyn and S.L. Portnoi, Cascade codes in Euclidean space, Problems of Information Transmission, Vol. 25, No. 3, pp. 62-75, 1989.. Appears in: Polyphase code
R. Zucchini, “Calibrated hypergraph states: II calibrated hypergraph state construction and applications”, (2025) arXiv:2501.18968. Appears in: Category-based quantum code, Galois-qudit code, Group-based quantum code
V. Zyablov, S. Shavgulidze, and M. Bossert, “An Introduction to Generalized Concatenated Codes”, European Transactions on Telecommunications 10, 609 (1999) DOI. Appears in: Generalized concatenated code (GCC)
V. V. Zyablov, M. S. Pinsker, “Estimation of the error-correction complexity for Gallager low-density codes”, Probl. Peredachi Inf., 11:1 (1975), 23–36; Problems Inform. Transmission, 11:1 (1975), 18–28. Appears in: Gallager (GL) code
V. V. Zyablov, S. L. Portnoi, “Modulation/Coding System for a Gaussian Channel”, Probl. Peredachi Inf., 23:3 (1987), 18–26; Problems Inform. Transmission, 23:3 (1987), 187–193. Appears in: Polyphase code