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
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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
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E. Abbe, A. Shpilka, and M. Ye, “Reed-Muller Codes: Theory and Algorithms”, (2020) arXiv:2002.03317. Appears in: Reed-Muller (RM) code
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R. Acharya et al., “Quantum error correction below the surface code threshold”, (2024) arXiv:2408.13687. Appears in: Quantum repetition code, XZZX surface code
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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
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
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
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, 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
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, “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 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
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A. Ashikhmin and E. Knill, “Nonbinary Quantum Stabilizer Codes”, (2000) arXiv:quant-ph/0005008. Appears in: Quantum Goppa code, Quantum AG code
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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
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C. Bachoc, “Designs, groups and lattices”, (2007) arXiv:0712.1939. Appears in: Barnes-Wall (BW) lattice, $t$-design
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H. Bachor and T. C. Ralph, A Guide to Experiments in Quantum Optics (Wiley, 2019) DOI. Appears in: Two-component cat code
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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
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J. Baez and U. Schreiber, “Higher Gauge Theory: 2-Connections on 2-Bundles”, (2004) arXiv:hep-th/0412325. Appears in: Two-gauge theory code
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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
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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
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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)
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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)
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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
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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
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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
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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)
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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
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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
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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
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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
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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
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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
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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
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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)
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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: $[[8,3,2]]$ CSS 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, “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: 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
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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
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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
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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
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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
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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
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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: Hypergraph product (HGP) code, Plaquette Ising code, Repetition 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
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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
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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
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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
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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
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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
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
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
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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
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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
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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
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
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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
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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
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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
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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
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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, $[[8,3,2]]$ CSS 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
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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
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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
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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
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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
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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
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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
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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
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 (2024) arXiv:2309.02863 DOI. Appears in: Quantum repetition 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, $[[8,3,2]]$ CSS 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
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, 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
“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
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
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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
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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
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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, 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
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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
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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
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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
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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, J. T. Iosue, A. G. Burchards, and V. V. Albert, “Continuous-variable designs and design-based shadow tomography from random lattices”, (2024) arXiv:2412.17909. Appears in: Gottesman-Kitaev-Preskill (GKP) code, $t$-design
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
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
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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
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
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)
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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
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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
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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
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D. Gottesman, “The Heisenberg Representation of Quantum Computers”, (1998) arXiv:quant-ph/9807006. Appears in: Qubit code
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D. Gottesman, “An Introduction to Quantum Error Correction and Fault-Tolerant Quantum Computation”, (2009) arXiv:0904.2557. Appears in: Quantum error-correcting code (QECC)
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D. Gottesman, “Fault-Tolerant Quantum Computation with Constant Overhead”, (2014) arXiv:1310.2984. Appears in: Quantum LDPC (QLDPC) code
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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, “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
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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
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J. H. Griesmer, “A Bound for Error-Correcting Codes”, IBM Journal of Research and Development 4, 532 (1960) DOI. Appears in: Griesmer code
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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
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
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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
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
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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
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V. Guemard, “Lifts of quantum CSS codes”, (2024) arXiv:2404.16736. Appears in: Good QLDPC code, Quantum LDPC (QLDPC) code, Qubit CSS code, Lattice stabilizer code
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K. GUENDA, “QUANTUM DUADIC AND AFFINE-INVARIANT CODES”, International Journal of Quantum Information 07, 373 (2009) DOI. Appears in: Quantum duadic code
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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
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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
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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
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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: $[[8,3,2]]$ CSS 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
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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
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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
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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
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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
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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, $[[8,3,2]]$ CSS 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: $[2^r-1,2^r-r-1,3]$ Hamming code, Majorana color 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
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 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
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