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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, “The Heisenberg Representation of Quantum Computers”, (1998) arXiv:quant-ph/9807006. Appears in: Qubit code
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• 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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• 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
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• 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
• 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
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• 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: Amplitude-damping (AD) code, Approximate quantum error-correcting code (AQECC), Gottesman-Kitaev-Preskill (GKP) code, Bosonic code
• R. J. Harris et al., “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 et al., “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 et al., “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
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• 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: Golay code, Hexacode
• 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)
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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 17, 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 17, 1276 (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
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• Rudolf Schürer and Wolfgang Ch. Schmid. “Denniston Codes.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2015-09-03. https://mint.sbg.ac.at/desc_CDenniston.html. Appears in: Denniston code, Hyperoval code, Projective two-weight code
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• Rudolf Schürer and Wolfgang Ch. Schmid. “Kerdock Codes.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2015-09-03. https://mint.sbg.ac.at/desc_CKerdock.html. Appears in: Kerdock code
• Rudolf Schürer and Wolfgang Ch. Schmid. “Preparata Codes.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2015-09-03. https://mint.sbg.ac.at/desc_CPreparata.html. Appears in: Preparata code
• Rudolf Schürer and Wolfgang Ch. Schmid. “Reed–Solomon Code.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2015-09-03. https://mint.sbg.ac.at/desc_CReedSolomon.html. Appears in: Reed-Solomon (RS) code
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• A. Zhang et al., “On Hadamard-Type Output Coding in Multiclass Learning”, Intelligent Data Engineering and Automated Learning 397 (2003) DOI. Appears in: Error-correcting output code (ECOC), Hadamard code
• J. Zhang et al., “Quantum error correction with the color-Gottesman-Kitaev-Preskill code”, Physical Review A 104, (2021) arXiv:2112.14447 DOI. Appears in: Square-octagon (4.8.8) color code, Concatenated GKP code
• Y. Zhang et al., “Quasiparticle statistics and braiding from ground-state entanglement”, Physical Review B 85, (2012) arXiv:1111.2342 DOI. Appears in: Topological code
• L. Zhang and I. Fuss, “Quantum Reed-Muller Codes”, (1997) arXiv:quant-ph/9703045. Appears in: Quantum Reed-Muller code
• D. Zhang, K. Ho-Van, and T. Le-Ngoc, “Impulse noise detection techniques for retransmission to reduce delay in DSL systems”, 2012 IEEE International Conference on Communications (ICC) (2012) DOI. Appears in: Reed-Solomon (RS) code
• J. Zhang, R. Laflamme, and D. Suter, “Experimental Implementation of Encoded Logical Qubit Operations in a Perfect Quantum Error Correcting Code”, Physical Review Letters 109, (2012) arXiv:1208.4797 DOI. Appears in: Five-qubit perfect code
• G. Zhang and Y. Li, “Time-efficient logical operations on quantum LDPC codes”, (2024) arXiv:2408.01339. Appears in: Qubit stabilizer code
• J. Zhang, Y.-C. Wu, and G.-P. Guo, “Concatenation of the Gottesman-Kitaev-Preskill code with the XZZX surface code”, Physical Review A 107, (2023) arXiv:2207.04383 DOI. Appears in: GKP-surface code, XZZX surface code
• H. Zhang, E. Yaakobi, and N. Silberstein, “Multiset Combinatorial Batch Codes”, (2017) arXiv:1701.02708. Appears in: Locally decodable code (LDC), Private information retrieval (PIR) code
• G. Zhao, A. C. Doherty, and I. H. Kim, “On the energy barrier of hypergraph product codes”, (2024) arXiv:2407.20526. Appears in: Hypergraph product (HGP) code, Self-correcting quantum code
• X. Zhao et al., “Hermitian dual-containing constacyclic BCH codes and related quantum codes of length \(\frac{q^{2m}-1}{q+1}\)”, (2020) arXiv:2007.13309. Appears in: Galois-qudit BCH code
• Y. Zhao et al., “Realization of an Error-Correcting Surface Code with Superconducting Qubits”, Physical Review Letters 129, (2022) arXiv:2112.13505 DOI. Appears in: Surface-17 code
• Y. Zhao and D. E. Liu, “Extracting Error Thresholds through the Framework of Approximate Quantum Error Correction Condition”, (2023) arXiv:2312.16991. Appears in: Approximate quantum error-correcting code (AQECC), Qubit stabilizer code
• Y. Zhao and Y. Wan, “Noninvertible Gauge Symmetry in (2+1)d Topological Orders: A String-Net Model Realization”, (2024) arXiv:2408.02664. Appears in: String-net code, Topological code
• J. Zhao, Y.-C. Wu, and G.-P. Guo, “Quantum memory error correction computation based on Chamon model”, (2023) arXiv:2303.05267. Appears in: Chamon model code
• Y.-C. Zheng and T. A. Brun, “Fault-tolerant holonomic quantum computation in surface codes”, Physical Review A 91, (2015) arXiv:1411.4248 DOI. Appears in: Honeycomb Floquet code, Kitaev surface code
• H. Zheng, A. Dua, and L. Jiang, “Demonstrating non-Abelian statistics of Majorana fermions using twist defects”, Physical Review B 92, (2015) arXiv:1508.04166 DOI. Appears in: Abelian topological code, Twist-defect surface code
• G. Zheng et al., “Near-Optimal Performance of Quantum Error Correction Codes”, Physical Review Letters 132, (2024) arXiv:2401.02022 DOI. Appears in: Approximate quantum error-correcting code (AQECC)
• Zhenghan Wang. private communication, 2017.. Appears in: 2D color code, Three-fermion (3F) subsystem code
• W. Zhong, O. Shtanko, and R. Movassagh, “Advantage of Quantum Neural Networks as Quantum Information Decoders”, (2024) arXiv:2401.06300. Appears in: 2D lattice stabilizer code, Lattice stabilizer code
• S. Zhou et al., “Achieving the Heisenberg limit in quantum metrology using quantum error correction”, Nature Communications 9, (2018) arXiv:1706.02445 DOI. Appears in: Error-corrected sensing code
• Z. Zhou et al., “Linear Codes with Two or Three Weights From Quadratic Bent Functions”, (2015) arXiv:1506.06830. Appears in: Two-weight code
• D. L. Zhou et al., “Quantum computation based ond-level cluster state”, Physical Review A 68, (2003) arXiv:quant-ph/0304054 DOI. Appears in: Modular-qudit cluster-state code
• S. Zhou and L. Jiang, “Asymptotic Theory of Quantum Channel Estimation”, PRX Quantum 2, (2021) arXiv:2003.10559 DOI. Appears in: Error-corrected sensing code
• S. Zhou and L. Jiang, “Optimal approximate quantum error correction for quantum metrology”, Physical Review Research 2, (2020) arXiv:1910.08472 DOI. Appears in: Error-corrected sensing code
• X. Zhou, D. W. Leung, and I. L. Chuang, “Methodology for quantum logic gate construction”, Physical Review A 62, (2000) arXiv:quant-ph/0002039 DOI. Appears in: Bacon-Shor code, Qubit stabilizer code
• S. Zhou, “Limits of Noisy Quantum Metrology with Restricted Quantum Controls”, Physical Review Letters 133, (2024) arXiv:2402.18765 DOI. Appears in: Error-corrected sensing code
• S. Zhou, Z.-W. Liu, and L. Jiang, “New perspectives on covariant quantum error correction”, Quantum 5, 521 (2021) arXiv:2005.11918 DOI. Appears in: Covariant block quantum code
• S. Zhou, A. G. Manes, and L. Jiang, “Achieving metrological limits using ancilla-free quantum error-correcting codes”, Physical Review A 109, (2024) arXiv:2303.00881 DOI. Appears in: Error-corrected sensing code
• J. Zhou, H. Peng, and C. Y. Suen, “Data-driven decomposition for multi-class classification”, Pattern Recognition 41, 67 (2008) DOI. Appears in: Error-correcting output code (ECOC)
• J. Zhou and C. Y. Suen, “Unconstrained numeral pair recognition using enhanced error correcting output coding: a holistic approach”, Eighth International Conference on Document Analysis and Recognition (ICDAR’05) (2005) DOI. Appears in: Error-correcting output code (ECOC)
• G. Zhu et al., “Non-Clifford and parallelizable fault-tolerant logical gates on constant and almost-constant rate homological quantum LDPC codes via higher symmetries”, (2024) arXiv:2310.16982. Appears in: 3D color code, Freedman-Meyer-Luo code, Homological code, Quantum rainbow code, Triorthogonal code, Quasi-hyperbolic color code, Qubit stabilizer code, Symmetry-protected topological (SPT) code
• G. Zhu, M. Hafezi, and M. Barkeshli, “Quantum origami: Transversal gates for quantum computation and measurement of topological order”, Physical Review Research 2, (2020) arXiv:1711.05752 DOI. Appears in: Fibonacci string-net code
• G. Zhu, T. Jochym-O’Connor, and A. Dua, “Topological Order, Quantum Codes, and Quantum Computation on Fractal Geometries”, PRX Quantum 3, (2022) arXiv:2108.00018 DOI. Appears in: Fractal surface code
• C. Zhu, T. Lan, and X.-G. Wen, “Topological nonlinear σ -model, higher gauge theory, and a systematic construction of 3+1D topological orders for boson systems”, Physical Review B 100, (2019) arXiv:1808.09394 DOI. Appears in: Topological code
• G. Zhu, A. Lavasani, and M. Barkeshli, “Instantaneous braids and Dehn twists in topologically ordered states”, Physical Review B 102, (2020) arXiv:1806.06078 DOI. Appears in: Fibonacci string-net code, String-net code, Kitaev surface code
• G. Zhu, A. Lavasani, and M. Barkeshli, “Universal Logical Gates on Topologically Encoded Qubits via Constant-Depth Unitary Circuits”, Physical Review Letters 125, (2020) arXiv:1806.02358 DOI. Appears in: Fibonacci string-net code, String-net code
• C. Zhu and Q. Liao, “Complete weight enumerators for several classes of two-weight and three-weight linear codes”, (2021) arXiv:2107.02447. Appears in: Two-weight code
• H. Zhu, “Multiqubit Clifford groups are unitary 3-designs”, Physical Review A 96, (2017) arXiv:1510.02619 DOI. Appears in: Qubit stabilizer code, \(t\)-design
• H. Zhu, “Mutually unbiased bases as minimal Clifford covariant 2-designs”, Physical Review A 91, (2015) arXiv:1505.01123 DOI. Appears in: \(t\)-design
• S. Zhu, Z. Sun, and X. Kai, “A Class of Narrow-Sense BCH Codes”, IEEE Transactions on Information Theory 65, 4699 (2019) DOI. Appears in: Bose–Chaudhuri–Hocquenghem (BCH) code
• V. A. Zinoviev, “Generalized Cascade Codes”, Probl. Peredachi Inf., 12:1 (1976). Appears in: Generalized concatenated code (GCC)
• V. A. Zinoviev, “Generalized Cascade Codes”, Probl. Peredachi Inf., 12:1 (1976), 5–15; Problems Inform. Transmission, 12:1 (1976), 2–9. Appears in: Generalized concatenated code (GCC)
• V.A. Zinoviev, S.N. Litsyn and S.L. Portnoi, Cascade codes in Euclidean space, Problems of Information Transmission, Vol. 25, No. 3, pp. 62-75, 1989.. Appears in: Polyphase code
• V. V. Zyablov, M. S. Pinsker, “Estimation of the error-correction complexity for Gallager low-density codes”, Probl. Peredachi Inf., 11:1 (1975), 23–36; Problems Inform. Transmission, 11:1 (1975), 18–28. Appears in: Gallager (GL) code
• V. V. Zyablov, S. L. Portnoi, “Modulation/Coding System for a Gaussian Channel”, Probl. Peredachi Inf., 23:3 (1987), 18–26; Problems Inform. Transmission, 23:3 (1987), 187–193. Appears in: Polyphase code
• V. Zyablov, S. Shavgulidze, and M. Bossert, “An Introduction to Generalized Concatenated Codes”, European Transactions on Telecommunications 10, 609 (1999) DOI. Appears in: Generalized concatenated code (GCC)