The Error Correction Zoo

Victor V. Albert; Philippe Faist

References

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D. Aharonov and L. Eldar, “Quantum Locally Testable Codes”, (2013) arXiv:1310.5664. 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
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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 and Y. Touati, “Quantum Circuit Depth Lower Bounds For Homological Codes”, (2018) arXiv:1810.03912. Appears in: Kitaev surface 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
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C. T. Aitchison et al., “Boundaries and defects in the cubic code”, Physical Review B 109, (2024) arXiv:2308.00138 DOI. Appears in: Haah cubic code (CC)
C. Akers et al., “The black hole interior from non-isometric codes and complexity”, (2022) arXiv:2207.06536. Appears in: Holographic tensor-network code
G. Alagic et al., “Quantum Fully Homomorphic Encryption with Verification”, Advances in Cryptology – ASIACRYPT 2017 438 (2017) arXiv:1708.09156 DOI. Appears in: Qubit CSS code
A. Alahmadi et al., “On the lifted Melas code”, Cryptography and Communications 8, 7 (2015) DOI. Appears in: Melas code, Quaternary linear code over $\mathbb{Z}_4$
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)
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. Al-Bassam and B. Bose, “On balanced codes”, IEEE Transactions on Information Theory 36, 406 (1990) DOI. Appears in: Balanced code
G. Alber et al., “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
G. Alber et al., “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
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, 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 et al., “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 et al., “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 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 et al., “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, 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, “Lindbladians with multiple steady states: theory and applications”, (2018) arXiv:1802.00010. Appears in: Frustration-free Hamiltonian 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, Homological rotor code, Qudit cubic code, Rotor code
V. V. Albert, private communication, 2024.. Appears in: Hexacode, Spherical design
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
C. D. Albuquerque, R. Palazzo Jr., and E. B. Silva, “New classes of TQC associated with self-dual, quasi self-dual and denser tessellations”, Quantum Information and Computation 10, 956 (2010) DOI. Appears in: 2D hyperbolic surface code
C. D. Albuquerque, 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
Aleksander Kubica, private communication, 2019. Appears in: Majorana stabilizer code, Five-qubit perfect code
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
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)
M. G. Algaba et al., “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 et al., “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 et al., “On thermal stability of topological qubit in Kitaev’s 4D model”, (2008) arXiv:0811.0033. Appears in: Loop toric code, Self-correcting quantum code
R. Alicki, M. Fannes, and M. Horodecki, “On thermalization in Kitaev’s 2D model”, Journal of Physics A: Mathematical and Theoretical 42, 065303 (2009) arXiv:0810.4584 DOI. Appears in: Self-correcting quantum code
R. Alicki, 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
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 et al., “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, 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 stabilizer code, Qubit 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 and J. Preskill, “Fibonacci scheme for fault-tolerant quantum computation”, Physical Review A 79, (2009) arXiv:0809.5063 DOI. Appears in: Qubit stabilizer 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 et al., “Testing Reed–Muller Codes”, IEEE Transactions on Information Theory 51, 4032 (2005) DOI. Appears in: Binary linear LTC, Reed-Muller (RM) 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
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
Y. Altug and A. B. Wagner, “Moderate Deviations in Channel Coding”, (2012) arXiv:1208.1924. Appears in: Error-correcting code (ECC)
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, “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, “A Class of Quantum LDPC Codes Constructed From Finite Geometries”, IEEE GLOBECOM 2008 - 2008 IEEE Global Telecommunications Conference (2008) arXiv:0712.4115 DOI. Appears in: Finite-geometry LDPC (FG-LDPC) code, Finite-geometry (FG) QLDPC 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. 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, “On Quantum and Classical BCH Codes”, IEEE Transactions on Information Theory 53, 1183 (2007) DOI. Appears in: Galois-qudit BCH 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
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, “Remarkable Degenerate Quantum Stabilizer Codes Derived from Duadic Codes”, (2006) arXiv:quant-ph/0601117. Appears in: Quantum duadic code
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 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, “A Note on Quantum Hamming Bound”, (2007) arXiv:0711.4603. Appears in: Perfect quantum 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
W. Dür and H.-J. Briegel, “Entanglement Purification for Quantum Computation”, Physical Review Letters 90, (2003) arXiv:quant-ph/0210069 DOI. Appears in: Qubit CSS code
U. L. Andersen et al., “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
T. I. Andersen et al., “Non-Abelian braiding of graph vertices in a superconducting processor”, (2023) arXiv:2210.10255. Appears in: XZZX surface code
C. K. Andersen et al., “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
S. Anders et al., “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
J. T. Anderson, G. Duclos-Cianci, and D. Poulin, “Fault-Tolerant Conversion between the Steane and Reed-Muller Quantum Codes”, Physical Review Letters 113, (2014) arXiv:1403.2734 DOI. Appears in: Quantum Reed-Muller code, $[[15,1,3]]$ quantum Reed-Muller code, $[[7,1,3]]$ Steane code
J. T. Anderson, “Homological Stabilizer Codes”, (2011) arXiv:1107.3502. Appears in: 2D color code, Rotated surface code, Kitaev surface code
J. T. Anderson and T. Jochym-O’Connor, “Classification of transversal gates in qubit stabilizer codes”, (2014) arXiv:1409.8320. Appears in: Qubit stabilizer code
J. T. Anderson, “On Groups in the Qubit Clifford Hierarchy”, Quantum 8, 1370 (2024) arXiv:2212.05398 DOI. Appears in: Qubit code
J. B. Anderson and A. Svensson, Coded Modulation Systems (Springer US, 2002) DOI. Appears in: Modulation scheme
E. Andrade et al., “CSS-T Codes from Reed Muller Codes for Quantum Fault Tolerance”, (2023) arXiv:2305.06423. Appears in: CSS-T code, Quantum Reed-Muller code
Andreev, N. N. Location of points on a sphere with minimal energy. (Russian) Tr. Mat. Inst. Steklova 219 (1997), Teor. Priblizh. Garmon. Anal., 27–31; translation in Proc. Steklov Inst. Math. 1997, no. 4(219), 20–24. Appears in: $\Lambda_{24}$ Leech lattice-shell code, Spherical sharp configuration
Andreev, Nikolay N. "An extremal property of the icosahedron." East J. Approx 2.4 (1996): 459-462.. Appears in: Icosahedron code, Spherical sharp configuration
Andrew Landahl, private communication, 2023. Appears in: Kitaev surface code
Andries E. Brouwer, Bounds on linear codes, in: Vera S. Pless and W. Cary Huffman (Eds.), Handbook of Coding Theory, pp. 295-461, Elsevier, 1998.. Appears in: Linear binary code, $q$-ary code
R. S. Andrist et al., “Optimal error correction in topological subsystem codes”, Physical Review A 85, (2012) arXiv:1204.1838 DOI. Appears in: 2D subsystem color code
I. Andriyanova, D. Maurice, and J.-P. Tillich, “New constructions of CSS codes obtained by moving to higher alphabets”, (2012) arXiv:1202.3338. Appears in: Galois-qudit surface code
B. Anker and M. Marvian, “Flag Gadgets based on Classical Codes”, (2024) arXiv:2212.10738. Appears in: Qubit stabilizer code
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
F. Annexstein and M. Baumslag, “A unified approach to off-line permutation routing on parallel networks”, Proceedings of the second annual ACM symposium on Parallel algorithms and architectures - SPAA ’90 (1990) DOI. Appears in: Hierarchical code
A. Anshu, N. P. Breuckmann, and C. Nirkhe, “NLTS Hamiltonians from Good Quantum Codes”, Proceedings of the 55th Annual ACM Symposium on Theory of Computing (2023) arXiv:2206.13228 DOI. Appears in: Quantum Tanner code
G. Anthony, H. Gregg, and M. Tshilidzi, “Image Classification Using SVMs: One-against-One Vs One-against-All”, (2007) arXiv:0711.2914. Appears in: Error-correcting output code (ECOC), One-hot code
Anthony Leverrier, Mapping the toric code to the rotated toric code, 2022.. Appears in: Quantum Tanner code, Rotated surface code, Kitaev surface code
A. V. Antipov, E. O. Kiktenko, and A. K. Fedorov, “Realizing a class of stabilizer quantum error correction codes using a single ancilla and circular connectivity”, Physical Review A 107, (2023) arXiv:2207.13356 DOI. Appears in: Five-qubit perfect code
S. Antonini et al., “Holographic measurement and bulk teleportation”, Journal of High Energy Physics 2022, (2022) arXiv:2209.12903 DOI. Appears in: Pastawski-Yoshida-Harlow-Preskill (HaPPY) code
Anvin, H. Peter. "The mathematics of RAID-6." (2007).. Appears in: Array code, Reed-Solomon (RS) code
H. Anwar et al., “Fast decoders for qudit topological codes”, New Journal of Physics 16, 063038 (2014) arXiv:1311.4895 DOI. Appears in: Modular-qudit surface code
Anxiao Jiang et al., “Rank Modulation for Flash Memories”, IEEE Transactions on Information Theory 55, 2659 (2009) DOI. Appears in: Gray code, Rank-modulation code
Anxiao Jiang, M. Schwartz, and J. Bruck, “Error-correcting codes for rank modulation”, 2008 IEEE International Symposium on Information Theory (2008) DOI. Appears in: Rank-modulation code
T. Aoki et al., “Quantum error correction beyond qubits”, (2008) arXiv:0811.3734. Appears in: $[[9,1,3]]_{\mathbb{R}}$ Lloyd-Slotine code
H. Apel and N. Baspin, “Simulating LDPC code Hamiltonians on 2D lattices”, (2023) arXiv:2308.13277. Appears in: Hamiltonian-based code, Quantum LDPC (QLDPC) code
H. Apel et al., “Security of quantum position-verification limits Hamiltonian simulation via holography”, Journal of High Energy Physics 2024, (2024) arXiv:2401.09058 DOI. Appears in: Holographic tensor-network code
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R. C. Ball, “Fermions without Fermion Fields”, Physical Review Letters 95, (2005) arXiv:cond-mat/0409485 DOI. Appears in: Ball-Verstraete-Cirac (BVC) code
S. Ball, “Grassl–Rötteler cyclic and consta-cyclic MDS codes are generalised Reed–Solomon codes”, Designs, Codes and Cryptography 91, 1685 (2022) DOI. Appears in: Generalized RS (GRS) code, Quantum maximum-distance-separable (MDS) code
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S. Ball, “On sets of vectors of a finite vector space in which every subset of basis size is a basis”, Journal of the European Mathematical Society 733 (2012) DOI. Appears in: Extended GRS code, Maximum distance separable (MDS) code, Narrow-sense RS code, Reed-Solomon (RS) code
P. Ball, “Real-Time Error Correction for Quantum Computing”, Physics 14, (2021) DOI. Appears in: $[[7,1,3]]$ Steane 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, Finite Geometry and Combinatorial Applications (Cambridge University Press, 2015) DOI. Appears in: Hirschfeld 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
B. Balsam and A. Kirillov Jr, “Kitaev’s Lattice Model and Turaev-Viro TQFTs”, (2012) arXiv:1206.2308. Appears in: Hopf-algebra quantum-double code, String-net code
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N. Bao and N. Cheng, “Eigenstate thermalization hypothesis and approximate quantum error correction”, Journal of High Energy Physics 2019, (2019) arXiv:1906.03669 DOI. Appears in: Eigenstate thermalization hypothesis (ETH) code
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N. Bao and J. Naskar, “Code properties of the holographic Sierpinski triangle”, Physical Review D 106, (2022) arXiv:2203.01379 DOI. Appears in: Approximate operator-algebra QECC, Holographic code
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A. Barg, “At the Dawn of the Theory of Codes”, The Mathematical Intelligencer 15, 20 (1993) DOI. Appears in: Covering code, Ternary Golay code
A. Barg et al., “A Hypergraph Approach to the Identifying Parent Property: The Case of Multiple Parents”, SIAM Journal on Discrete Mathematics 14, 423 (2001) DOI. Appears in: Identifiable parent property (IPP) code
A. Barg et al., “On the size of maximal binary codes with 2, 3, and 4 distances”, (2022) arXiv:2210.07496. Appears in: Two-weight code
A. Barg and G. D. Forney, “Random codes: minimum distances and error exponents”, IEEE Transactions on Information Theory 48, 2568 (2002) DOI. Appears in: Random code
A. Barg, J. Justesen, and C. Thommesen, “Concatenated codes with fixed inner code and random outer code”, IEEE Transactions on Information Theory 47, 361 (2001) DOI. Appears in: Concatenated code
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A. Barg and A. Mazumdar, “Codes in permutations and error correction for rank modulation”, 2010 IEEE International Symposium on Information Theory (2010) DOI. Appears in: Rank-modulation code
A. Barg and P. Purkayastha, “Bounds on ordered codes and orthogonal arrays”, (2009) arXiv:cs/0702033. Appears in: $t$-design
A. Barg, I. Tamo, and S. Vladut, “Locally recoverable codes on algebraic curves”, (2015) arXiv:1501.04904. Appears in: Tamo-Barg-Vladut code
A. Barg, I. Tamo, and S. Vladut, “Locally recoverable codes on algebraic curves”, 2015 IEEE International Symposium on Information Theory (ISIT) (2015) arXiv:1603.08876 DOI. Appears in: Locally recoverable code (LRC), Tamo-Barg-Vladut code
A. Barg and G. Zemor, “Concatenated Codes: Serial and Parallel”, IEEE Transactions on Information Theory 51, 1625 (2005) DOI. Appears in: Concatenated code, Parallel concatenated code, Regular binary Tanner code, Tanner code, Tensor-product code
A. Barg and S. Zhou, “A quantum decoding algorithm for the simplex code”, in Proceedings of the 36th Annual Allerton Conference on Communication, Control and Computing, Monticello, IL, 23–25 September 1998 (UIUC 1998) 359–365. Appears in: $[2^m-1,m,2^{m-1}]$ simplex code
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M. Barkeshli et al., “Higher-group symmetry in finite gauge theory and stabilizer codes”, SciPost Physics 16, (2024) arXiv:2211.11764 DOI. Appears in: 3D surface code, Lattice stabilizer code
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M. Barkeshli et al., “Symmetry fractionalization, defects, and gauging of topological phases”, Physical Review B 100, (2019) arXiv:1410.4540 DOI. Appears in: $G$-enriched Walker-Wang model code
M. Barkeshli, P.-S. Hsin, and R. Kobayashi, “Higher-group symmetry of (3+1)D fermionic $\mathbb{Z}_2$ gauge theory: Logical CCZ, CS, and T gates from higher symmetry”, SciPost Physics 16, (2024) arXiv:2311.05674 DOI. Appears in: 3D fermionic surface code
M. Barkeshli, C.-M. Jian, and X.-L. Qi, “Theory of defects in Abelian topological states”, Physical Review B 88, (2013) arXiv:1305.7203 DOI. Appears in: Abelian topological code
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E. S. Barnes and G. E. Wall, “Some extreme forms defined in terms of Abelian groups”, Journal of the Australian Mathematical Society 1, 47 (1959) DOI. Appears in: Barnes-Wall (BW) lattice code, $BW_{32}$ Barnes-Wall lattice code, $\Lambda_{16}$ Barnes-Wall lattice code
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H. Bombin, “An Introduction to Topological Quantum Codes”, (2013) arXiv:1311.0277. Appears in: Color 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, “Dimensional Jump in Quantum Error Correction”, (2016) arXiv:1412.5079. Appears in: 2D color code, 3D color code
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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, “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, “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 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
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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
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S. L. Braunstein, “Error Correction for Continuous Quantum Variables”, Physical Review Letters 80, 4084 (1998) arXiv:quant-ph/9711049 DOI. Appears in: $[[5,1,3]]_{\mathbb{R}}$ Braunstein five-mode code, $[[9,1,3]]_{\mathbb{R}}$ Lloyd-Slotine code, Oscillator-into-oscillator code
S. L. Braunstein, “Quantum error correction for communication with linear optics”, Nature 394, 47 (1998) DOI. Appears in: $[[5,1,3]]_{\mathbb{R}}$ Braunstein five-mode code
S. L. Braunstein and P. van Loock, “Quantum information with continuous variables”, Reviews of Modern Physics 77, 513 (2005) arXiv:quant-ph/0410100 DOI. Appears in: Bosonic code
S. 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 et al., “Adaptive constant-depth circuits for manipulating non-abelian anyons”, (2022) arXiv:2205.01933. Appears in: Quantum-double code
S. Bravyi et al., “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 et al., “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
S. Bravyi et al., “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 et al., “Obstacles to Variational Quantum Optimization from Symmetry Protection”, Physical Review Letters 125, (2020) arXiv:1910.08980 DOI. Appears in: Quantum repetition code
S. Bravyi et al., “Quantum advantage with noisy shallow circuits”, Nature Physics 16, 1040 (2020) arXiv:1904.01502 DOI. Appears in: Kitaev surface code
S. Bravyi et al., “Subsystem surface codes with three-qubit check operators”, (2013) arXiv:1207.1443. Appears in: Subsystem surface 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 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 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 M. B. Hastings, “Homological Product Codes”, (2013) arXiv:1311.0885. Appears in: Homological product code, Qubit 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, 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, Topological 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 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, “Lagrangian representation for fermionic linear optics”, (2004) arXiv:quant-ph/0404180. Appears in: Fermion 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 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 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 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, 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: Homological code, Newman-Moore code, Linear $q$-ary code, Lattice stabilizer 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, Subsystem hypergraph product (SHP) code, Lattice stabilizer code, Lattice subsystem 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, 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 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, “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 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. 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. B. Bravyi and A. Yu. Kitaev, “Quantum codes on a lattice with boundary”, (1998) arXiv:quant-ph/9811052. Appears in: Kitaev surface code
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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
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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
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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 (2007) DOI. Appears in: Entanglement-assisted (EA) subsystem QECC
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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
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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
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A. R. Calderbank, “The art of signaling: fifty years of coding theory”, IEEE Transactions on Information Theory 44, 2561 (1998) DOI. Appears in: Sphere packing, Error-correcting code (ECC), Golay code
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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
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Y.-A. Chen, “Exact bosonization in arbitrary dimensions”, Physical Review Research 2, (2020) arXiv:1911.00017 DOI. Appears in: Bosonization code
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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
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
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
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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 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
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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
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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 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 et al., “The sphere packing problem in dimension $24$”, Annals of Mathematics 185, (2017) arXiv:1603.06518 DOI. Appears in: $E_8$ Gosset lattice code, $\Lambda_{24}$ Leech lattice code
H. Cohn et al., “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 et al., “Universal optimality of the $E_8$ and Leech lattices and interpolation formulas”, (2022) arXiv:1902.05438. Appears in: $E_8$ Gosset lattice code, $\Lambda_{24}$ Leech lattice code, Universally optimal sphere packing
H. Cohn. "Kissing numbers." https://cohn.mit.edu/kissing-numbers. Appears in: Lattice-based code
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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 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 code, $E_7$ lattice-shell code, $E_6$ lattice-shell code, $3_{21}$ polytope code, Hessian polyhedron code, Icosahedron code, $\Lambda_{24}$ Leech lattice code, $\Lambda_{24}$ 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, “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
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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, “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, Sphere Packings, Lattices and Groups (Springer New York, 1999) DOI. Appears in: Sphere packing, Anticode, Antipode lattice code, 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 code, Divisible code, $[2^r,2^r-r-1,4]$ Extended Hamming code, Extended GRS code, Golay code, Linear code over $G$, $[2^r-1,2^r-r-1,3]$ Hamming code, $3_{21}$ polytope code, Hexacode, $A_2$ hexagonal lattice code, Julin-Golay code, $\Lambda_{24}$ Leech lattice code, $\Lambda_{24}$ 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 code, Self-dual linear code, Unimodular lattice code, Spherical code, Spherical design, Ternary Golay code, Tetracode, Witting polytope code
J. H. Conway and N. J. A. Sloane, “The antipode construction for sphere packings”, Inventiones Mathematicae 123, 309 (1996) DOI. Appears in: Antipode lattice 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, “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 code
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A. Couvreur et al., “Distinguisher-Based Attacks on Public-Key Cryptosystems Using Reed-Solomon Codes”, (2014) arXiv:1307.6458. Appears in: Generalized RS (GRS) code
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A. Cross et al., “Linear-Size Ancilla Systems for Logical Measurements in QLDPC Codes”, (2024) arXiv:2407.18393. Appears in: $[[144,12,12]]$ gross code
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David J. C. MacKay. Information Theory, Inference and Learning Algorithms. Cambridge university press, 2003.. Appears in: Low-density parity-check (LDPC) code, Repeat-accumulate (RA) code
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N. de Beaudrap and D. Horsman, “The ZX calculus is a language for surface code lattice surgery”, Quantum 4, 218 (2020) arXiv:1704.08670 DOI. Appears in: Kitaev surface code
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D. Gottesman, “Opportunities and Challenges in Fault-Tolerant Quantum Computation”, (2022) arXiv:2210.15844. Appears in: Spacetime circuit code, Subsystem spacetime circuit code
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D. Gottesman, “Theory of fault-tolerant quantum computation”, Physical Review A 57, 127 (1998) arXiv:quant-ph/9702029 DOI. Appears in: $[[2m,2m-2,2]]$ error-detecting code, Five-qubit perfect code, $[[6,4,2]]$ error-detecting code, Hermitian qubit code
D. Gottesman and L. L. Zhang, “Fibre bundle framework for unitary quantum fault tolerance”, (2017) arXiv:1309.7062. Appears in: Honeycomb Floquet code, Gottesman-Kitaev-Preskill (GKP) code, Five-qubit perfect code, Kitaev surface code
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D. Goyeneche and K. Życzkowski, “Genuinely multipartite entangled states and orthogonal arrays”, Physical Review A 90, (2014) arXiv:1404.3586 DOI. Appears in: Perfect-tensor code, Orthogonal array (OA)
K. Gracie and M.-H. Hamon, “Turbo and Turbo-Like Codes: Principles and Applications in Telecommunications”, Proceedings of the IEEE 95, 1228 (2007) DOI. Appears in: Turbo code
L. Grans-Samuelsson, D. Aasen, and P. Bonderson, “A fault-tolerant pairwise measurement-based code on eight qubits”, (2024) arXiv:2409.13681. Appears in: Hastings-Haah Floquet code, Five-qubit perfect code
L. Grans-Samuelsson et al., “Improved Pairwise Measurement-Based Surface Code”, Quantum 8, 1429 (2024) arXiv:2310.12981 DOI. Appears in: Honeycomb Floquet code, Kitaev surface code
R. N. Grass et al., “Robust Chemical Preservation of Digital Information on DNA in Silica with Error‐Correcting Codes”, Angewandte Chemie International Edition 54, 2552 (2015) DOI. Appears in: DNA storage code, Reed-Solomon (RS) code
M. Grassl 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 and T. Beth, “Quantum BCH Codes”, (1999) arXiv:quant-ph/9910060. Appears in: Qubit BCH 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, $[[2m,2m-2,2]]$ error-detecting code, Quantum maximum-distance-separable (MDS) code, Hermitian Galois-qudit code
M. Grassl, “Classical Information Theory and Classical Error Correction”, Lectures on Quantum Information 3 (2006) DOI. Appears in: Qubit stabilizer code
M. Grassl, “Classical Information Theory and Classical Error Correction”, Quantum Information 1 (2016) DOI. Appears in: Quantum error-correcting code (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 et al., “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 et al., “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, W. Geiselmann, and T. Beth, “Quantum Reed—Solomon Codes”, Applied Algebra, Algebraic Algorithms and Error-Correcting Codes 231 (1999) arXiv:quant-ph/9910059 DOI. Appears in: Prime-qudit RS 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, 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, A. Klappenecker, and M. Rotteler, “Graphs, quadratic forms, and quantum codes”, Proceedings IEEE International Symposium on Information Theory, arXiv:quant-ph/0703112 DOI. Appears in: Perfect-tensor code, 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, 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, “New quantum codes from CSS codes”, Quantum Information Processing 22, (2023) arXiv:2208.05353 DOI. Appears in: Galois-qudit CSS 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 and M. Rotteler, “Constructions of Quantum Convolutional Codes”, 2007 IEEE International Symposium on Information Theory (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, “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 and M. Rotteler, “Quantum block and convolutional codes from self-orthogonal product codes”, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005. (2005) arXiv:quant-ph/0703181 DOI. Appears in: Galois-qudit RS code, Quantum convolutional code, Quantum tensor-product 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 and M. Rotteler, “Quantum MDS codes over small fields”, 2015 IEEE International Symposium on Information Theory (ISIT) (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, “Searching for linear codes with large minimum distance”, Discovering Mathematics with Magma 287 DOI. Appears in: Block quantum code, Galois-qudit stabilizer code, Qubit stabilizer code, Modular-qudit stabilizer 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, 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, 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 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, “Variations on Encoding Circuits for Stabilizer Quantum Codes”, Lecture Notes in Computer Science 142 (2011) DOI. Appears in: $[[6,2,3]]_{q}$ 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
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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L. F. Gray, “Toom’s Stability Theorem in Continuous Time”, Perplexing Problems in Probability 331 (1999) DOI. Appears in: Quantum repetition code, Repetition code
D. M. Greenberger, M. A. Horne, and A. Zeilinger, “Going Beyond Bell’s Theorem”, (2007) arXiv:0712.0921. Appears in: Quantum repetition code
C. Greene, “Weight Enumeration and the Geometry of Linear Codes”, Studies in Applied Mathematics 55, 119 (1976) DOI. Appears in: Projective geometry code
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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 et al., “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
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 et al., “Quantum key distribution using gaussian-modulated coherent states”, Nature 421, 238 (2003) arXiv:quant-ph/0312016 DOI. Appears in: Coherent-state c-q 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
D. Gross, “Hudson’s theorem for finite-dimensional quantum systems”, Journal of Mathematical Physics 47, (2006) arXiv:quant-ph/0602001 DOI. Appears in: Galois-qudit stabilizer code, Modular-qudit stabilizer code
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T. Guaita, L. Hackl, and T. Quella, “Representation theory of Gaussian unitary transformations for bosonic and fermionic systems”, (2024) arXiv:2409.11628. Appears in: Fermion code, Bosonic code
K. Guenda, S. Jitman, and T. A. Gulliver, “Constructions of Good Entanglement-Assisted Quantum Error Correcting Codes”, (2016) arXiv:1606.00134. Appears in: EA Galois-qudit stabilizer code, EA quantum LCD code, Galois-qudit GRS code, Maximal-entanglement EA Galois-qudit stabilizer code
K. GUENDA, “QUANTUM DUADIC AND AFFINE-INVARIANT CODES”, International Journal of Quantum Information 07, 373 (2009) DOI. Appears in: Quantum duadic code
K. Guenda, “Two Families of Quantum Codes Derived from Cyclic Codes”, (2007) arXiv:0711.2050. Appears in: Quantum duadic code
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M. Gu et al., “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 et al., “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. 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
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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
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, Quantum repetition code, Two-component cat code
J. Guillaud and M. Mirrahimi, “Repetition Cat Qubits for Fault-Tolerant Quantum Computation”, Physical Review X 9, (2019) arXiv:1904.09474 DOI. Appears in: Asymmetric quantum code, Concatenated cat code, Quantum repetition code, Two-component cat code
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M. J. Gullans et al., “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
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
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, “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, “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, “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, “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
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R. S. Gupta et al., “Encoding a magic state with beyond break-even fidelity”, Nature 625, 259 (2024) arXiv:2305.13581 DOI. Appears in: 2D color code, Heavy-hexagon code, $[[4,2,2]]$ Four-qubit code
P. Gupta, A. Morello, and B. C. Sanders, “Universal transversal gates”, (2024) arXiv:2410.07045. Appears in: Covariant block quantum code
R. M. Guralnick and P. H. Tiep, “Decompositions of Small Tensor Powers and Larsen’s Conjecture”, (2005) arXiv:math/0502080. Appears in: $t$-design, Twisted $1$-group code
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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 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, “Linear-Algebraic List Decoding of Folded Reed-Solomon Codes”, 2011 IEEE 26th Annual Conference on Computational Complexity (2011) arXiv:1106.0436 DOI. 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 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 A. Rudra, “Limits to List Decoding Reed–Solomon Codes”, IEEE Transactions on Information Theory 52, 3642 (2006) DOI. Appears in: Reed-Solomon (RS) code
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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 M. Sudan, “Improved decoding of Reed-Solomon and algebraic-geometric codes”, Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280) DOI. Appears in: Alternant code, Binary BCH code, Evaluation AG code, Generalized RS (GRS) code, Reed-Solomon (RS) code
V. Guruswami and M. Sudan, “Improved decoding of Reed-Solomon and algebraic-geometry codes”, IEEE Transactions on Information Theory 45, 1757 (1999) DOI. Appears in: Alternant code, Binary BCH code, Generalized RS (GRS) code
V. Guruswami and A. Vardy, “Maximum-likelihood decoding of Reed-Solomon Codes is NP-hard”, (2004) arXiv:cs/0405005. Appears in: Reed-Solomon (RS) code
V. Guruswami and C. Wang, “Optimal rate list decoding via derivative codes”, (2011) arXiv:1106.3951. Appears in: Multiplicity 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
E. J. Gustafson et al., “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
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A. Gyenis et al., “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
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, “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, “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, “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, “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, “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, “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 et al., “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, Doubled color code, Cycle code, Petersen cycle code, Qubit CSS code, Quantum Golay code, Qubit stabilizer code, $[[15,1,3]]$ quantum Reed-Muller 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 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 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, “Lattice quantum codes and exotic topological phases of matter”, (2013) arXiv:1305.6973. Appears in: Quantum convolutional 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, “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, “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, “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, 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
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L. Hackl and E. Bianchi, “Bosonic and fermionic Gaussian states from Kähler structures”, SciPost Physics Core 4, (2021) arXiv:2010.15518 DOI. Appears in: Fermion code, Bosonic code
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M. Hagiwara et al., “Spatially Coupled Quasi-Cyclic Quantum LDPC Codes”, (2011) arXiv:1102.3181. Appears in: Quasi-cyclic code, Quantum spatially coupled (SC-QLDPC) code
M. Hagiwara and H. Imai, “Quantum Quasi-Cyclic LDPC Codes”, 2007 IEEE International Symposium on Information Theory (2007) arXiv:quant-ph/0701020 DOI. Appears in: Quasi-cyclic quantum code, Quasi-cyclic QLDPC code
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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 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, 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 (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 (2021) DOI. Appears in: Fiber-bundle code, Lifted-product (LP) 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
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, LR codes, private communication, 2014.. Appears in: Two-block group-algebra (2BGA) codes
M. B. Hastings, “On Quantum Weight Reduction”, (2023) arXiv:2102.10030. Appears in: Distance-balanced 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, “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, “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, “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, “Turning Gate Synthesis Errors into Incoherent Errors”, (2016) arXiv:1612.01011. Appears in: Qubit stabilizer code, Qubit 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 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
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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)
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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
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S. Heußen, D. F. Locher, and M. Müller, “Measurement-free fault-tolerant quantum error correction in near-term devices”, (2023) arXiv:2307.13296. Appears in: Qubit CSS code
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O. Higgott and N. P. Breuckmann, “Improved Single-Shot Decoding of Higher-Dimensional Hypergraph-Product Codes”, PRX Quantum 4, (2023) arXiv:2206.03122 DOI. Appears in: 3D surface code, Loop toric code, Homological code, Hypergraph product (HGP) code
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M.-H. Hsieh and M. M. Wilde, “Entanglement-Assisted Communication of Classical and Quantum Information”, IEEE Transactions on Information Theory 56, 4682 (2010) arXiv:0811.4227 DOI. Appears in: Entanglement-assisted (EA) hybrid quantum code
M.-H. Hsieh and M. M. Wilde, “Public and private communication with a quantum channel and a secret key”, Physical Review A 80, (2009) arXiv:0903.3920 DOI. Appears in: Entanglement-assisted (EA) hybrid quantum code
M.-H. Hsieh, W.-T. Yen, and L.-Y. Hsu, “High Performance Entanglement-Assisted Quantum LDPC Codes Need Little Entanglement”, IEEE Transactions on Information Theory 57, 1761 (2011) arXiv:0906.5532 DOI. Appears in: EA FG-QLDPC code, EA QC-QLDPC code
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P. S. Hsin, private communication, 2024.. Appears in: Dijkgraaf-Witten gauge theory code, Two-gauge theory code
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E. Huang et al., “Tailoring Three-Dimensional Topological Codes for Biased Noise”, PRX Quantum 4, (2023) arXiv:2211.02116 DOI. Appears in: 3D lattice stabilizer code, 3D surface code, Asymmetric quantum code, Clifford-deformed surface code (CDSC), Rotated surface code
S. Huang, T. Jochym-O’Connor, and T. J. Yoder, “Homomorphic Logical Measurements”, (2022) arXiv:2211.03625. Appears in: Qubit CSS code, Kitaev surface code
S. Huang and S. Puri, “Improved Noisy Syndrome Decoding of Quantum LDPC Codes with Sliding Window”, (2023) arXiv:2311.03307. Appears in: Quantum LDPC (QLDPC) code
C. Huang, H. Simitci, Y. Xu, A. Ogus, B. Calder, P. Gopalan, J. Li, and S. Yekhanin. Erasure coding in Windows Azure Storage. In Proc. USENIX Annual Technical Conference (ATC), pgs. 15-26, Boston, Massachusetts, June 2012.. Appears in: Locally recoverable code (LRC)
T.-H. Huang and Y.-L. Ueng, “A Binary BP Decoding Using Posterior Adjustment for Quantum LDPC Codes”, ICASSP 2024 - 2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (2024) DOI. Appears in: Quantum LDPC (QLDPC) code
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Huaxiong Wang, Chaoping Xing, and R. Safavi-Naini, “Linear authentication codes: bounds and constructions”, IEEE Transactions on Information Theory 49, 866 (2003) DOI. Appears in: Gabidulin code, Subspace code
M. HUBER, “CODING THEORY AND ALGEBRAIC COMBINATORICS”, Selected Topics in Information and Coding Theory 121 (2010) arXiv:0811.1254 DOI. Appears in: Combinatorial design, Golay code, Pless symmetry code, $q$-ary quadratic-residue (QR) code, Ternary Golay code
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F. Huber and M. Grassl, “Quantum Codes of Maximal Distance and Highly Entangled Subspaces”, Quantum 4, 284 (2020) arXiv:1907.07733 DOI. Appears in: Perfect-tensor code, Quantum maximum-distance-separable (MDS) code
J. Hu et al., “CSS Codes that are Oblivious to Coherent Noise”, 2021 IEEE International Symposium on Information Theory (ISIT) (2021) DOI. Appears in: Constant-excitation (CE) code, Qubit CSS code
D. Hu et al., “Graphical nonbinary quantum error-correcting codes”, Physical Review A 78, (2008) arXiv:0801.0831 DOI. Appears in: $((5,6,2))$ qubit code, Modular-qudit CWS code, Modular-qudit USt code, $((5+2r,3\times 2^{2r+1},2))$ Rains code, Small-distance block quantum code
J. Hu et al., “Mitigating Coherent Noise by Balancing Weight-2 Z-Stabilizers”, IEEE Transactions on Information Theory 68, 1795 (2022) arXiv:2011.00197 DOI. Appears in: Constant-excitation (CE) code, $[[10,1,4]]_{G}$ tenfold code, Qubit CSS code, Five-qubit perfect code
L. Hu et al., “Quantum error correction and universal gate set operation on a binomial bosonic logical qubit”, Nature Physics 15, 503 (2019) arXiv:1805.09072 DOI. Appears in: Binomial code
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W. C. Huffman, J.-L. Kim, and P. Solé, Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI. Appears in: Evaluation AG code, Frameproof (FP) code, Kerdock code, Preparata code, Universally optimal $q$-ary code
W. C. Huffman and V. Pless, Fundamentals of Error-Correcting Codes (Cambridge University Press, 2003) DOI. Appears in: Binary BCH code, Binary duadic code, Binary quadratic-residue (QR) code, Cross-interleaved RS (CIRS) code, Dodecacode, Extended GRS code, Generalized RM (GRM) code, Generalized RS (GRS) code, Goppa code, $[2^r-1,2^r-r-1,3]$ Hamming code, Hexacode, Maximum distance separable (MDS) code, Primitive narrow-sense BCH code, Narrow-sense RS code, Nearly perfect code, Perfect code, Pless symmetry code, Bose–Chaudhuri–Hocquenghem (BCH) code, $q$-ary duadic code, $q$-ary Hamming code, $q$-ary quadratic-residue (QR) code, Reed-Muller (RM) code, Self-dual linear code, Self-dual additive code, Hermitian qubit code
B. L. Hughes, “Differential space-time modulation”, IEEE Transactions on Information Theory 46, 2567 (2000) DOI. Appears in: Spacetime block code (STBC), Multi-channel group-orbit code
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Hui Jin and R. J. McEliece, “Coding theorems for turbo code ensembles”, IEEE Transactions on Information Theory 48, 1451 (2002) DOI. Appears in: Turbo code
J. Hu, Q. Liang, and R. Calderbank, “Designing the Quantum Channels Induced by Diagonal Gates”, Quantum 6, 802 (2022) arXiv:2109.13481 DOI. Appears in: Quantum divisible code, Qubit CSS code
J. Hu, Q. Liang, and R. Calderbank, “Divisible Codes for Quantum Computation”, (2022) arXiv:2204.13176. Appears in: $[2^m,m+1,2^{m-1}]$ First-order RM code, Quantum divisible code, Concatenated qubit code, Qubit CSS code, Five-qubit perfect code, $[[7,1,3]]$ Steane code
N. Hussami, S. B. Korada, and R. Urbanke, “Performance of polar codes for channel and source coding”, 2009 IEEE International Symposium on Information Theory (2009) DOI. Appears in: Polar code
A. Hutter, J. R. Wootton, and D. Loss, “Efficient Markov chain Monte Carlo algorithm for the surface code”, Physical Review A 89, (2014) arXiv:1302.2669 DOI. Appears in: Kitaev surface code, Toric code
Y. Hu, Y. Wan, and Y.-S. Wu, “Twisted quantum double model of topological phases in two dimensions”, Physical Review B 87, (2013) arXiv:1211.3695 DOI. Appears in: Dijkgraaf-Witten gauge theory code, String-net code, Twisted quantum double (TQD) code, Abelian TQD stabilizer code
J. Huxford, D. X. Nguyen, and Y. B. Kim, “Twisted Lattice Gauge Theory: Membrane Operators, Three-loop Braiding and Topological Charge”, (2024) arXiv:2401.13042. Appears in: Dijkgraaf-Witten gauge theory code
J. Huxford and S. H. Simon, “Excitations in the higher-lattice gauge theory model for topological phases. III. The (3+1)-dimensional case”, Physical Review B 109, (2024) arXiv:2206.09941 DOI. Appears in: Two-gauge theory code
J. Huxford and S. H. Simon, “Excitations in the higher-lattice gauge theory model for topological phases. II. The (2+1) -dimensional case”, Physical Review B 108, (2023) arXiv:2204.05341 DOI. Appears in: Quantum-double code
J. Huxford and S. H. Simon, “Excitations in the higher-lattice gauge theory model for topological phases. I. Overview”, Physical Review B 108, (2023) arXiv:2202.08294 DOI. Appears in: Two-gauge theory code
C. Hu, S. Yang, and S. S.-T. Yau, “Weight enumerators for nonbinary asymmetric quantum codes and their applications”, Advances in Applied Mathematics 121, 102085 (2020) DOI. Appears in: Qubit code
Y. Hu and Y. Zou, “Petz map recovery for long-range entangled quantum many-body states”, (2024) arXiv:2408.00857. Appears in: Approximate quantum error-correcting code (AQECC), Topological code
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Ian Teixeira, private communication, 2024. Appears in: Five-qubit perfect code
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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
I. Ingemarsson, “Group Codes for the Gaussian Channel”, Lecture Notes in Control and Information Sciences 73 DOI. Appears in: Slepian group-orbit code
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International Organization for Standardization, Information Technology: Automatic Identification and Data Capture Techniques-QR Code 2005 Bar Code Symbology Specification, 2nd ed., IEC18004 (ISO, 2006).. Appears in: Reed-Solomon (RS) code
International Telecommunication Union-T, Recommendation V.21: 300 bits per second duplex modem standardized for use in the general switched telephone network, 1984. Appears in: Binary PSK (BPSK) code
International Telecommunication Union-T, Recommendation V.23: 600/1200-baud modem standardized for use in the general switched telephone network, 1988. Appears in: Binary PSK (BPSK) code
International Telecommunication Union-T, Recommendation V.24: List of definitions for interchange circuits between data terminal equipment (DTE) and data circuit-terminating equipment (DCE), 1988. Appears in: Quadrature PSK (QPSK) code
International Telecommunication Union-T, Recommendation V.27ter: 4800/2400 Bits Per Second Modem Standardized For Use in the General Switched Telephone Network, 1984. Appears in: Phase-shift keying (PSK) code
International Telecommunication Union-T, Recommendation V.29: 9600 Bits Per Second Modem Standardized For Use on Point-to-Point 4-Wire Leased Telephone-Tpe Circuits, 1993. Appears in: Quadrature-amplitude modulation (QAM) code
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J. T. Iosue et al., “Projective toric designs, difference sets, and quantum state designs”, (2023) arXiv:2311.13479. Appears in: $t$-design
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Z. Jia, “Generalized cluster states from Hopf algebras: non-invertible symmetry and Hopf tensor network representation”, (2024) arXiv:2405.09277. Appears in: Hopf-algebra cluster-state code
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Z. Jiang et al., “Majorana Loop Stabilizer Codes for Error Mitigation in Fermionic Quantum Simulations”, Physical Review Applied 12, (2019) arXiv:1812.08190 DOI. Appears in: Bravyi-Kitaev superfast (BKSF) code, Majorana loop stabilizer code (MLSC)
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L. Jiang et al., “Quantum repeater with encoding”, Physical Review A 79, (2009) arXiv:0809.3629 DOI. Appears in: