Quantum Error Correction and Orthogonal Geometry

Mixed-state entanglement and quantum error correction

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Scheme for reducing decoherence in quantum computer memory

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Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels

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Error Correcting Codes in Quantum Theory

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Good quantum error-correcting codes exist

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The Subgroup Structure of the Finite Classical Groups

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Multiple-particle interference and quantum error correction

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Class of quantum error-correcting codes saturating the quantum Hamming bound

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Perfect Quantum Error Correcting Code

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Z 4 -Kerdock Codes, Orthogonal Spreads, and Extremal Euclidean Line-Sets

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Grassmannian connection between three- and four-qubit observables, Mermin’s contextuality and black holes

Lévay, P., Planat, M. R. P., & Санига, М. (2013) · Journal of High Energy Physics · doi:10.1007/jhep09(2013)037 · Cited by 23

New families of asymmetric quantum BCH codes

Guardia, G. G. L. (2011) · Quantum Information and Computation · doi:10.26421/qic11.3-4-4 · Cited by 23

A New Class of Designs Which Protect against Quantum Jumps

Beth, T., Charnes, C., Grassl, M., Alber, G., Delgado, A., & Mussinger, M. (2003) · Designs Codes and Cryptography · doi:10.1023/a:1024188005329 · Cited by 23

Quanta and information

Kilin, S. Y. (2001) · Progress in optics · doi:10.1016/s0079-6638(01)80015-9 · Cited by 24

Generalized toric codes coupled to thermal baths

Viyuela, O., Rivas, A., & Martin-Delgado, M. A. (2012) · New Journal of Physics · doi:10.1088/1367-2630/14/3/033044 · Cited by 22

A Family of Asymptotically Good Quantum Codes Based on Code Concatenation

Li, Z., Xing, L., & Wang, X. (2009) · IEEE Transactions on Information Theory · doi:10.1109/tit.2009.2023715 · Cited by 22

Synthesis of Logical Clifford Operators via Symplectic Geometry

Rengaswamy, N., Calderbank, R., Pfister, H. D., & Kadhe, S. (2018) · IEEE International Symposium on Information Theory (ISIT) · doi:10.1109/isit.2018.8437652 · Cited by 22

Detecting entanglement can be more effective with inequivalent mutually unbiased bases

Hiesmayr, B. C., McNulty, D., Baek, S., Roy, S. S., Bae, J., & Chruściński, D. (2021) · New Journal of Physics · doi:10.1088/1367-2630/ac20ea · Cited by 22

Simple rate-1/3 convolutional and tail-biting quantum error-correcting codes

Forney, G. D., & Guha, S. (2005) · IEEE International Symposium on Information Theory (ISIT) · doi:10.1109/isit.2005.1523495 · Cited by 22

NOTES ON THE FIDELITY OF SYMPLECTIC QUANTUM ERROR-CORRECTING CODES

Hamada, M. (2003) · International Journal of Quantum Information · doi:10.1142/s0219749903000358 · Cited by 25

Quantum States far from the Energy Eigenstates of Any Local Hamiltonian

Haselgrove, H. L., Nielsen, M. A., & Osborne, T. J. (2003) · Physical Review Letters · doi:10.1103/physrevlett.91.210401 · Cited by 24

A brief introduction to multipartite entanglementPreprint

Bengtsson, I., & Życzkowski, K. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1612.07747 · Cited by 22

Narain CFTs from nonbinary stabilizer codes

Alam, Y. F., Kawabata, K., Nishioka, T., Okuda, T., & Yahagi, S. (2023) · Journal of High Energy Physics · doi:10.1007/jhep12(2023)127 · Cited by 21

Infinite number of solvable generalizations of XY-chain, with cluster state, and with central charge c=m/2

Minami, K. (2017) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2017.10.004 · Cited by 21

Near-Hashing-Bound Multiple-Rate Quantum Turbo Short-Block Codes

Chandra, D., Babar, Z., Ng, S. X., & Hanzo, L. (2019) · IEEE Access · doi:10.1109/access.2019.2911515 · Cited by 21

A synthesis framework for stitching surface code with superconducting quantum devices

Wu, A., Li, G., Zhang, H., Guerreschi, G. G., Ding, Y., & Xie, Y. (2022) · Proceedings - International Symposium on Computer Architecture/Proceedings · doi:10.1145/3470496.3527381 · Cited by 27

Lower bound for the quantum capacity of a discrete memoryless quantum channel

Matsumoto, R., & Uyematsu, T. (2002) · Journal of Mathematical Physics · doi:10.1063/1.1497999 · Cited by 21

On the distance of stabilizer quantum codes from J-affine variety codes

Galindo, C., Geil, O., Hernando, F., & Ruano, D. (2017) · Quantum Information Processing · doi:10.1007/s11128-017-1559-1 · Cited by 21

Quantum Codes from Generalized Reed-Solomon Codes and Matrix-Product CodesPreprint

Zhang, T., & Ge, G. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1508.00978 · Cited by 21

Constructing quantum error-correcting codes for p^m-state systems from classical error-correcting codesPreprint

Matsumoto, R., & Uyematsu, T. (1999) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/9911011 · Cited by 21

Bibliographic guide to the foundations of quantum mechanics and quantum informationPreprint

Cabello, A. (2000) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0012089 · Cited by 33

“Security of quantum key distribution protocols,”

Mafu, M., & Senekane, M. (2018) · Advanced Technologies of Quantum Key Distribution · doi:10.5772/intechopen.74234 · Cited by 20

Compilation of algorithm-specific graph states for quantum circuits

Vijayan, M. K., Paler, A., Gavriel, J., Myers, C. R., Rohde, P. P., & Devitt, S. J. (2024) · Quantum Science and Technology · doi:10.1088/2058-9565/ad1f39 · Cited by 20

Near-Term n to k Distillation Protocols Using Graph Codes

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Entanglement patterns in mutually unbiased basis sets

Lawrence, J. (2011) · Physical Review A · doi:10.1103/physreva.84.022338 · Cited by 21

Private algebras in quantum information and infinite-dimensional complementarity

Crann, J., Kribs, D. W., Levene, R. H., & Todorov, I. G. (2015) · Journal of Mathematical Physics · doi:10.1063/1.4935399 · Cited by 20

Exponential lower bound on the highest fidelity achievable by quantum error-correcting codes

Hamada, M. (2002) · Physical Review A · doi:10.1103/physreva.65.052305 · Cited by 23

Quantum complexity fluctuations from nuclear and hypernuclear forces

Robin, C., & A, M. J. S. (2025) · Physical Review C · doi:10.1103/r8rq-y9tb · Cited by 19

Quantum Coding Bounds and a Closed-Form Approximation of the Minimum Distance Versus Quantum Coding Rate

Chandra, D., Babar, Z., Nguyen, H. V., Alanis, D., Botsinis, P., Ng, S. X., & Hanzo, L. (2017) · IEEE Access · doi:10.1109/access.2017.2716367 · Cited by 19

Quantum Error Correction

Djordjević, I. B. (2021) · Elsevier eBooks · doi:10.1016/b978-0-12-821982-9.00013-7 · Cited by 19

Some Nonprimitive BCH Codes and Related Quantum Codes

Liu, Y., Li, R., Guo, G., & Wang, J. (2019) · IEEE Transactions on Information Theory · doi:10.1109/tit.2019.2932670 · Cited by 19

An Efficient Quantum Algorithm for the Hidden Subgroup Problem in Extraspecial Groups

Ivanyos, G., Sanselme, L., & Sántha, M. (2007) · Lecture notes in computer science · doi:10.1007/978-3-540-70918-3_50 · Cited by 19

A Simple Construction for the Barnes-Wall Lattices

Nebe, G., Rains, E. M., & Sloane, N. J. A. (2002) · Kluwer international series in engineering and computer science · doi:10.1007/978-1-4615-0895-3_19 · Cited by 19

Quantum Interleaver: Quantum Error Correction for Burst Error

Kawabata, S. (2000) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.69.3540 · Cited by 19

Channel-Adapted Quantum Error CorrectionPreprint

Fletcher, A. S. (2007) · arXiv (Cornell University) · doi:10.48550/arxiv.0706.3400 · Cited by 19

Lattice Quantum Codes and Exotic Topological Phases of Matter

Haah, J. (2013) · CaltechTHESIS (California Institute of Technology) · doi:10.48550/arxiv.1305.6973 · Cited by 19

State-injection schemes of quantum computation in Spekkens' toy theory

Catani, L., & Browne, D. E. (2018) · Physical Review A · doi:10.1103/physreva.98.052108 · Cited by 18

Quantum codes from a new construction of self-orthogonal algebraic geometry codes

Hernando, F., McGuire, G., Monserrat, F., & Moyano‐Fernández, J. J. (2020) · Quantum Information Processing · doi:10.1007/s11128-020-2616-8 · Cited by 18

Between Shor and Steane: A Unifying Construction for Measuring Error Syndromes

Huang, S., & Brown, K. R. (2021) · Physical Review Letters · doi:10.1103/physrevlett.127.090505 · Cited by 18

Decoding holographic codes with an integer optimization decoder

Harris, R. J., Coupe, E., McMahon, N. A., Brennen, G. K., & Stace, T. M. (2020) · Physical Review A · doi:10.1103/physreva.102.062417 · Cited by 23

Relating Measurement Patterns to Circuits via Pauli Flow

Simmons, W. (2021) · Electronic Proceedings in Theoretical Computer Science · doi:10.4204/eptcs.343.4 · Cited by 18

Quantum Convolutional Error Correction Codes

Chau, H. F. (1999) · Lecture notes in computer science · doi:10.1007/3-540-49208-9_28 · Cited by 18

Non-additive quantum codes from Goethals and Preparata codes

Grassl, M., & Rötteler, M. (2008) · IEEE Information Theory Workshop (ITW) · doi:10.1109/itw.2008.4578694 · Cited by 18

A complete graphical calculus for Spekkens ’ toy bit theoryPreprint

Duman, A. N., & Backens, M. (2016) · Cited by 18

New constructions of entanglement-assisted quantum MDS codes from negacyclic codes

Li, R., Guo, G., Song, H., & Liu, Y. (2019) · International Journal of Quantum Information · doi:10.1142/s0219749919500229 · Cited by 17

Several Families of Self-Orthogonal Codes and Their Applications in Optimal Quantum Codes and LCD Codes

Wang, X., & Heng, Z. (2023) · IEEE Transactions on Information Theory · doi:10.1109/tit.2023.3332332 · Cited by 16

Homological Invariants of Pauli Stabilizer Codes

Ruba, B., & Yang, B. (2024) · Communications in Mathematical Physics · doi:10.1007/s00220-024-04991-y · Cited by 16

Improved Constructions of Nested Code Pairs

Galindo, C., Geil, O., Hernando, F., & Ruano, D. (2017) · IEEE Transactions on Information Theory · doi:10.1109/tit.2017.2755682 · Cited by 16

Constructions of quantum MDS codes

Liu, H., & Liu, X. (2021) · Quantum Information Processing · doi:10.1007/s11128-020-02949-2 · Cited by 16

Magic three-qubit Veldkamp line: A finite geometric underpinning for form theories of gravity and black hole entropy

Lévay, P., Holweck, F., & Санига, М. (2017) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.96.026018 · Cited by 16

Two families of BCH codes and new quantum codes

Song, H., Li, R., Wang, J., & Liu, Y. (2018) · Quantum Information Processing · doi:10.1007/s11128-018-2042-3 · Cited by 16

Quantum error avoiding codes verses quantum error correcting codes

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Scheme for fault-tolerant holonomic computation on stabilizer codes

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Theory of multiwave mixing and decoherence control in a qubit array system

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A Nonperturbative Proposal for Nonabelian Tensor Gauge Theory and Dynamical Quantum Yang-Baxter MapsPreprint

Rey, S.-J., & Sugino, F. (2010) · arXiv (Cornell University) · doi:10.48550/arxiv.1002.4636 · Cited by 16

Qubit-Oscillator Concatenated Codes: Decoding Formalism and Code Comparison

Xu, Y., Wang, Y., Kuo, E.-J., & Albert, V. V. (2023) · PRX Quantum · doi:10.1103/prxquantum.4.020342 · Cited by 22

A Survey of Quantum Error Correction

Matsumoto, R., & Hagiwara, M. (2021) · IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences · doi:10.1587/transfun.2021eai0001 · Cited by 17

Error Correction for Continuous Quantum Variables

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Space-time Reed-Muller codes for noncoherent MIMO transmission

Ashikhmin, A., & Calderbank, A. R. (2005) · IEEE International Symposium on Information Theory (ISIT) · doi:10.1109/isit.2005.1523686 · Cited by 15

Limits to Error Correction in Quantum Chaos

Silvestrov, P. G., Schomerus, H., & Beenakker, C. W. J. (2001) · Physical Review Letters · doi:10.1103/physrevlett.86.5192 · Cited by 19

Packing Planes in Four Dimensions and Other MysteriesPreprint

Sloane, N. J. A. (2002) · arXiv (Cornell University) · doi:10.48550/arxiv.math/0208017 · Cited by 15

Completeness and the ZX-calculusPreprint

Backens, M. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1602.08954 · Cited by 15

A Construction of Quantum Stabilizer Codes Based on Syndrome Assignment by Classical Parity-Check Matrices

Lai, C., & Lu, C.-C. (2011) · IEEE Transactions on Information Theory · doi:10.1109/tit.2011.2165812 · Cited by 14

Mermin pentagrams arising from Veldkamp lines for three qubits

Lévay, P., & Szabó, Z. (2017) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/aa56aa · Cited by 16

Design of Quantum LDPC Codes From Quadratic Residue Sets

Xie, Y., Yuan, J., & Sun, Q. T. (2018) · IEEE Transactions on Communications · doi:10.1109/tcomm.2018.2827945 · Cited by 14

Analog Subspace Coding: A New Approach to Coding for Non-Coherent Wireless Networks

Soleymani, M., & Mahdavifar, H. (2021) · IEEE Transactions on Information Theory · doi:10.1109/tit.2021.3133071 · Cited by 14

Achieving Fault Tolerance on Capped Color Codes with Few Ancillas

Tansuwannont, T., & Leung, D. (2022) · PRX Quantum · doi:10.1103/prxquantum.3.030322 · Cited by 17

Quantum error-correcting codes over mixed alphabets

Wang, Z., Yu, S., Fan, H., & Oh, C. H. (2013) · Physical Review A · doi:10.1103/physreva.88.022328 · Cited by 14

Volume thresholds for quantum fault tolerance

Aggarwal, V., Calderbank, A. R., Gilbert, G. N., & Weinstein, Y. S. (2010) · Quantum Information Processing · doi:10.1007/s11128-010-0181-2 · Cited by 14

Qubit state guidance without feedback

Paternostro, M., & Kim, M. S. (2005) · New Journal of Physics · doi:10.1088/1367-2630/7/1/043 · Cited by 14

A low-rate bound on the reliability of a quantum discrete memoryless channel

Barg, A. (2002) · IEEE Transactions on Information Theory · doi:10.1109/tit.2002.805080 · Cited by 14

Quotient Codes and Their Reliability

Hamada, M. (2005) · IPSJ Digital Courier · doi:10.2197/ipsjdc.1.450 · Cited by 14

A Complete Graphical Calculus for Spekkens’ Toy Bit Theory

Backens, M., & Duman, A. N. (2015) · Foundations of Physics · doi:10.1007/s10701-015-9957-7 · Cited by 13

Attractor mechanism as a distillation procedure

Lévay, P., & Szalay, S. (2010) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.82.026002 · Cited by 13

Ternary self-orthogonal codes of dual distance three and ternary quantum codes of distance three

Chen, G., & Li, R. (2012) · Designs Codes and Cryptography · doi:10.1007/s10623-012-9620-7 · Cited by 13

Quantum coherence in mutually unbiased bases

Wang, Y.-K., Ge, L.-Z., & Tao, Y.-H. (2019) · Quantum Information Processing · doi:10.1007/s11128-019-2283-9 · Cited by 13

Construction and Performance of Quantum Burst Error Correction Codes for Correlated Errors

Fan, J., Hsieh, M.-H., Chen, H., Chen, H. H., & Li, Y. (2018) · IEEE International Symposium on Information Theory (ISIT) · doi:10.1109/isit.2018.8437493 · Cited by 13

WHAT IS QUANTUM COMPUTATION?

EKERT, A. K., Hayden, P. M., Inamori, H., & Oi, D. K. L. (2001) · International Journal of Modern Physics A · doi:10.1142/s0217751x0100492x · Cited by 13

Entanglement-assisted Coding TheoryPreprint

Hsieh, M.-H. (2008) · arXiv (Cornell University) · doi:10.25549/usctheses-m1390 · Cited by 16

Low-depth Clifford circuits approximately solve MaxCut

Muñoz-Arias, M. H., Kourtis, S., & Blais, A. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.023294 · Cited by 18

Binary Subspace Chirps

Pllaha, T., Tirkkonen, O., & Calderbank, A. R. (2022) · IEEE Transactions on Information Theory · doi:10.1109/tit.2022.3186872 · Cited by 12

Optimization of variational-quantum-eigensolver measurement by partitioning Pauli operators using multiqubit Clifford gates on noisy intermediate-scale quantum hardware

Jena, A., Genin, S. N., & Mosca, M. (2022) · Physical Review A · doi:10.1103/physreva.106.042443 · Cited by 12

Universal Decoding of Quantum Stabilizer Codes via Classical Guesswork

Chandra, D., Egilmez, Z. B. K., Xiong, Y., Ng, S. X., Maunder, R. G., & Hanzo, L. (2023) · IEEE Access · doi:10.1109/access.2023.3247966 · Cited by 12

Classical and Quantum Evaluation Codes at the Trace Roots

Galindo, C., Hernando, F., & Ruano, D. (2018) · IEEE Transactions on Information Theory · doi:10.1109/tit.2018.2868442 · Cited by 12

Holographic codes on Bruhat–Tits buildings and Drinfeld symmetric spaces

Marcolli, M. (2020) · Pure and Applied Mathematics Quarterly · doi:10.4310/pamq.2020.v16.n1.a1 · Cited by 12

High-dimensional quantum channel estimation using classical light

Mabena, C. M., & Roux, F. S. (2017) · Physical Review A · doi:10.1103/physreva.96.053860 · Cited by 12

Quantum Relational DatabasesPreprint

Cockshott, P. W. (1997) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/9712025 · Cited by 12

Alternative Computational Models: A Comparison of Biomolecular and Quantum Computation

Reif, J. H. (1998) · Lecture notes in computer science · doi:10.1007/978-3-540-49382-2_10 · Cited by 12

Spatially-Coupled QLDPC Codes

Yang, S., & Calderbank, R. (2025) · Quantum · doi:10.22331/q-2025-04-07-1693 · Cited by 11

Real classical shadows

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Mutually unbiased bases in 3 and 4 dimensions semi-quantum key distribution protocol

Hajji, H., & Baz, M. E. (2021) · Physics Letters A · doi:10.1016/j.physleta.2021.127884 · Cited by 11

Quantum Topological Error Correction Codes are Capable of Improving the Performance of Clifford Gates

Chandra, D., Babar, Z., Nguyen, H. V., Alanis, D., Botsinis, P., Ng, S. X., & Hanzo, L. (2019) · IEEE Access · doi:10.1109/access.2019.2936795 · Cited by 11

Two Gilbert–Varshamov-type existential bounds for asymmetric quantum error-correcting codes

Matsumoto, R. (2017) · Quantum Information Processing · doi:10.1007/s11128-017-1748-y · Cited by 11

How to Correct Small Quantum Errors

Keyl, M., & Werner, R. F. (2002) · Cited by 11

Conjugate Codes and Applications to CryptographyPreprint

Hamada, M. (2006) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0610193 · Cited by 11

Homomorphic Logical Measurements

Huang, S., Jochym-O’Connor, T., & Yoder, T. J. (2023) · PRX Quantum · doi:10.1103/prxquantum.4.030301 · Cited by 10

Asymmetric Entanglement-Assisted Quantum MDS Codes Constructed from Constacyclic Codes

Chen, J., Fang, W., Zhou, S., Qiu, J. F., Zhang, C., Xu, Y., Zeng, B., & Chen, Y. (2023) · Entropy · doi:10.3390/e25121603 · Cited by 10

Applications of quantum coherence via skew information under mutually unbiased bases

Sheng, Y.-H., Zhang, J., Tao, Y.-H., & Fei, S.-M. (2021) · Quantum Information Processing · doi:10.1007/s11128-021-03017-z · Cited by 11

Evolving quantum circuits

TANDEITNIK, D. R., & Guerreiro, T. (2024) · Quantum Information Processing · doi:10.1007/s11128-024-04317-w · Cited by 13

Boundaries and defects in the cubic code

Aitchison, C. T., Bulmash, D., Dua, A., Doherty, A. C., & Williamson, D. J. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.109.205125 · Cited by 10

Fault-Tolerant Error Correction with Efficient Quantum Codes

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Error Correcting Codes, Correlation and Quantum Entanglement

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Versatility in quantum error correcting code of encodingone qubit in five qubits

Jiang, L.-Z. (2002) · Journal of China Institute of Metrology

An inducing construction of quantum codes from classical error correcting codes

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A new description of quantum error-correcting codes

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