The DOI matches its Crossref record; 15 of the 15 references it cites were found in a registry or an index.
Simple quantum error-correcting codes
Open accessAbstract
Methods of finding good quantum error-correcting codes are discussed, and many example codes are presented. The recipe ${\mathit{C}}_{2}^{\mathrm{\ensuremath{\perp}}}$\ensuremath{\subset}${\mathit{C}}_{1}$, where ${\mathit{C}}_{1}$ and ${\mathit{C}}_{2}$ are classical codes, is used to obtain codes for up to 16 information quantum bits (qubits) with correction of small numbers of errors. The results are tabulated. More efficient codes are obtained by allowing ${\mathit{C}}_{1}$ to have reduced distance, and introducing sign changes among the code words in a systematic manner. This systematic approach leads to single-error-correcting codes for 3, 4, and 5 information qubits with block lengths of 8, 10, and 11 qubits, respectively. \textcopyright{} 1996 The American Physical Society.
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“In 1D, these consist of parity checks along each row of an array of surface codes29.”
From Yoked surface codes (2025) · cites this paper as [29]
In the citing paper
“In particular, for 1D and square 2D codes, we obtain families of [[n, n − 2, 2]]29 and [[n2, n2 − 4n + 2, 4]] codes, respectively.”
From Yoked surface codes (2025) · cites this paper as [29]
Citations
Cites
The Theory of Error-Correcting Codes
(1977) · North-Holland mathematical library · doi:10.1016/s0924-6509(08)x7030-8 · Cited by 10,875
Mixed-state entanglement and quantum error correction
Bennett, C. H., DiVincenzo, D. P., Smolin, J. A., & Wootters, W. K. (1996) · Physical Review A · doi:10.1103/physreva.54.3824 · Cited by 5,272
Scheme for reducing decoherence in quantum computer memory
Shor, P. W. (1995) · Physical Review A · doi:10.1103/physreva.52.r2493 · Cited by 4,479
Error Correcting Codes in Quantum Theory
Steane, A. M. (1996) · Physical Review Letters · doi:10.1103/physrevlett.77.793 · Cited by 2,677
Self-citationGood quantum error-correcting codes exist
Calderbank, A. R., & Shor, P. W. (1996) · Physical Review A · doi:10.1103/physreva.54.1098 · Cited by 2,516
Multiple-particle interference and quantum error correction
(1996) · Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences · doi:10.1098/rspa.1996.0136 · Cited by 1,284
Self-citationClass of quantum error-correcting codes saturating the quantum Hamming bound
Gottesman, D. (1996) · Physical Review A · doi:10.1103/physreva.54.1862 · Cited by 1,227 · cited 1×
“However, whereas the pioneering works just mentioned established the possibility of efficient quantum error correction, and presented the simplest codes possible, they did not address the more pragmatic issue of identifying other specific useful codes.”
BackgroundSchumacher, B. (1995) · Physical Review A · doi:10.1103/physreva.51.2738 · Cited by 1,090
Perfect Quantum Error Correcting Code
Laflamme, R., Miquel, C., Paz, J. P., & Zurek, W. H. (1996) · Physical Review Letters · doi:10.1103/physrevlett.77.198 · Cited by 966
Quantum Error Correction and Orthogonal Geometry
Calderbank, A. R., Rains, E. M., Shor, P. W., & Sloane, N. J. A. (1997) · Physical Review Letters · doi:10.1103/physrevlett.78.405 · Cited by 811
Flagged first, then by citations
Cited by
Sorted by citations
Items 201–300 of 525
Quantum Codes Obtained From Constacyclic Codes Over a Family of Finite Rings Fp[u₁, u₂, …, us]
Dinh, H. Q., Bag, T., Pathak, S., Upadhyay, A. K., & Chinnakum, W. (2020) · IEEE Access · doi:10.1109/access.2020.3033326 · Cited by 13
Quantum Information Protection Scheme Based on Reinforcement Learning for Periodic Surface Codes
Xue, Y.-J., Wang, H., Tian, Y., Wang, Y., Wang, Y., & Wang, S. (2022) · Quantum Engineering · doi:10.1155/2022/7643871 · Cited by 13
Continuous quantum error correction through local operations
Mascarenhas, E., Marques, B., Cunha, M. T., & Santos, M. F. (2010) · Physical Review A · doi:10.1103/physreva.82.032327 · Cited by 14
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
Aly, S. A., Klappenecker, A., & Sarvepalli, P. K. (2007) · IEEE International Symposium on Information Theory (ISIT) · doi:10.1109/isit.2007.4557530 · Cited by 13
An algorithm for minimization of quantum costPreprint
Banerjee, A., & Pathak, A. (2009) · arXiv (Cornell University) · doi:10.48550/arxiv.0910.2129 · Cited by 13
One-generator quasi-cyclic codes and their dual codes
Abdukhalikov, K., Bag, T., & Panario, D. (2023) · Discrete Mathematics · doi:10.1016/j.disc.2023.113369 · Cited by 12
Duality and free energy analyticity bounds for few-body Ising models with extensive homology rank
Jiang, Y., Dumer, I. I., Kovalev, A. A., & Pryadko, L. P. (2019) · Journal of Mathematical Physics · doi:10.1063/1.5039735 · Cited by 12
New stabilizer codes from the construction of dual-containing matrix-product codes
Cao, M., & Cui, J. (2020) · Finite Fields and Their Applications · doi:10.1016/j.ffa.2020.101643 · Cited by 12
Modifying Method of Constructing Quantum Codes From Highly Entangled States
Raissi, Z. (2020) · IEEE Access · doi:10.1109/access.2020.3043401 · Cited by 12
New Quantum and LCD Codes Over the Finite Field of Odd Characteristic
Ashraf, M., Khan, N., & Mohammad, G. (2021) · International Journal of Theoretical Physics · doi:10.1007/s10773-021-04849-2 · 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
Quantum MDS codes with new length and large minimum distance
Fang, W., Wen, J., & Fu, F. (2023) · Discrete Mathematics · doi:10.1016/j.disc.2023.113662 · 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
Two Classes of New Optimal Asymmetric Quantum Codes
Chen, X., Zhu, S., & Kai, X. (2018) · International Journal of Theoretical Physics · doi:10.1007/s10773-018-3708-4 · Cited by 12
Akshata Shenoy, H., & Srikanth, R. (2019) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/ab0046 · Cited by 12
Homological Product CodesPreprint
Bravyi, S. B., & Hastings, M. B. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1311.0885 · Cited by 12
Quantum subsystem codes, CFTs and their ℤ2-gaugings
Ando, K., Kawabata, K., & Nishioka, T. (2024) · Journal of High Energy Physics · doi:10.1007/jhep11(2024)125 · Cited by 13
Three families of self-orthogonal codes and their application in optimal quantum codes
Li, D., Heng, Z., & Li, C. (2023) · Discrete Mathematics · doi:10.1016/j.disc.2023.113626 · Cited by 11
New quantum codes from constacyclic codes over a general non-chain ring
Bhardwaj, S., Goyal, M., & Raka, M. (2023) · Discrete Mathematics Algorithms and Applications · doi:10.1142/s1793830923500726 · Cited by 11
Ab-initio tree-tensor-network digital twin for quantum computer benchmarking in 2D
Jaschke, D., Pagano, A., Weber, S., & Montangero, S. (2024) · Quantum Science and Technology · doi:10.1088/2058-9565/ad5585 · Cited by 14
Spin glass reflection of the decoding transition for quantum error correcting codes
Kovalev, A. A., & Pryadko, L. P. (2015) · Quantum Information and Computation · doi:10.26421/qic15.9-10-5 · Cited by 11
On the construction of optimal asymmetric quantum codes
Wang, L., & Zhu, S. (2014) · International Journal of Quantum Information · doi:10.1142/s0219749914500178 · Cited by 11
Density matrix simulation of quantum error correction codes for near-term quantum devices
Baek, C., Ostuka, T., Tarucha, S., & Choi, B.-S. (2019) · Quantum Science and Technology · doi:10.1088/2058-9565/ab5887 · Cited by 12
Gowdhaman, K., Mohan, C., Durairajan, C., & Gao, J. (2020) · Journal of Applied Mathematics and Computing · doi:10.1007/s12190-020-01407-7 · 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
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
Williamson, D. J., & Baspin, N. (2024) · Nature Communications · doi:10.1038/s41467-024-53881-3 · Cited by 22
Minimal distances for certain quantum product codes and tensor products of chain complexes
Zeng, W., & Pryadko, L. P. (2020) · Physical Review A · doi:10.1103/physreva.102.062402 · Cited by 10
Constacyclic codes over mixed alphabets and their applications in constructing new quantum codes
Dinh, H. Q., Pathak, S., Bag, T., Upadhyay, A. K., & Yamaka, W. (2021) · Quantum Information Processing · doi:10.1007/s11128-021-03083-3 · Cited by 10
Designing the Quantum Channels Induced by Diagonal Gates
Hu, J., Liang, Q., & Calderbank, R. (2022) · Quantum · doi:10.22331/q-2022-09-08-802 · Cited by 10
Local non–Calderbank-Shor-Steane quantum error-correcting code on a three-dimensional lattice
Kim, I. H. (2011) · Physical Review A · doi:10.1103/physreva.83.052308 · Cited by 10
Asymmetric Quantum Concatenated and Tensor Product Codes With Large Z-Distances
Fan, J., Li, J., Wang, J., Wei, Z., & Hsieh, M.-H. (2021) · IEEE Transactions on Communications · doi:10.1109/tcomm.2021.3064566 · Cited by 10
Cavallaro, G., Heras, D. B., Wu, Z., Maskey, M., López, S., Gawron, P., Coca, M., & Datcu, M. P. (2022) · IEEE Geoscience and Remote Sensing Magazine · doi:10.1109/mgrs.2022.3145478 · Cited by 10
Quantum codes from codes over Gaussian integers with respect to the Mannheim metric
Özen, M., & Güzeltepe, M. (2012) · Quantum Information and Computation · doi:10.26421/qic12.9-10-6 · Cited by 10
Quantum error-correcting codes: the unit design strategy
Hurley, B., Hurley, T., & Hurley, D. (2018) · International Journal of Information and Coding Theory · doi:10.1504/ijicot.2018.095018 · Cited by 10
Conditions for independent decoherence
Duan, L.-M., & Guo, G. (1998) · Quantum and Semiclassical Optics Journal of the European Optical Society Part B · doi:10.1088/1355-5111/10/4/004 · Cited by 10
Self-correction in Wegner's three-dimensional Ising lattice gauge theory
Poulin, D., Melko, R. G., & Hastings, M. B. (2019) · Physical review. B./Physical review. B · doi:10.1103/physrevb.99.094103 · Cited by 14
Kerdock Codes Determine Unitary 2-Designs
Can, T., Rengaswamy, N., Calderbank, R., & Pfister, H. D. (2020) · IEEE Transactions on Information Theory · doi:10.1109/tit.2020.3015683 · Cited by 10
Software Tools for Decoding Quantum Low-Density Parity-Check Codes
Berent, L., Burgholzer, L., & Wille, R. (2023) · Asia and South Pacific Design Automation Conference (ASP-DAC) · doi:10.1145/3566097.3567934 · Cited by 9
CSS-T Codes From Reed-Muller Codes
Bolkema, J., Andrade, E., Dexter, T., Eggers, H., Fisher, V. L., Szramowsky, L., & Manganiello, F. (2025) · IEEE Journal on Selected Areas in Information Theory · doi:10.1109/jsait.2025.3583217 · Cited by 9
Two-qubit gates for decoherence-free qubits using a ring exchange interaction
Antonio, B., & Bose, S. (2013) · Physical Review A · doi:10.1103/physreva.88.042306 · Cited by 9
Robustness of channel-adapted quantum error correction
Balló, G., & Gurin, P. (2009) · Physical Review A · doi:10.1103/physreva.80.012326 · Cited by 9
On a Problem Concerning the Quantum Hamming Bound for Impure Quantum Codes
Li, Z., & Xing, L. (2010) · IEEE Transactions on Information Theory · doi:10.1109/tit.2010.2054610 · Cited by 13
Some Families of Asymmetric Quantum MDS Codes Constructed from Constacyclic Codes
Huang, Y., Chen, J., Feng, C., & Chen, R. (2017) · International Journal of Theoretical Physics · doi:10.1007/s10773-017-3578-1 · Cited by 9
Bag, T., Ashraf, M., Mohammad, G., & Upadhyay, A. K. (2019) · Quantum Information Processing · doi:10.1007/s11128-019-2384-5 · Cited by 9
Application of Constacyclic Codes Over the Semi Local Ring $${F_{{p^m}}} + v{F_{{p^m}}}$$
Bag, T., Dertli, A., Çengellenmiş, Y., & Upadhyay, A. K. (2020) · Indian Journal of Pure and Applied Mathematics · doi:10.1007/s13226-020-0399-3 · Cited by 9
Quantum Error Correction: Classic Group Theory Meets a Quantum Challenge
Pollatsek, H. (2001) · American Mathematical Monthly · doi:10.1080/00029890.2001.11919827 · Cited by 9
Quantum Reed-Muller CodesPreprint
Zhang, L., & Fuss, I. (1997) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/9703045 · Cited by 9
Asymmetric and Symmetric Subsystem BCH Codes and BeyondPreprint
Aly, S. A. (2008) · arXiv (Cornell University) · doi:10.48550/arxiv.0803.0764 · Cited by 9
Quantum stabilizer codes and beyondPreprint
Sarvepalli, P. K. (2008) · arXiv (Cornell University) · doi:10.48550/arxiv.0810.2574 · Cited by 9
Entanglement-assisted quantum error-correcting codes using matrix-product codes
Cao, M., Wei, F., & Luo, G. (2025) · Designs Codes and Cryptography · doi:10.1007/s10623-025-01685-x · Cited by 8
Campbell, C., Chen, H., Luk, W., & Fan, H. (2025) · ACM/IEEE Design Automation Conference (DAC) · doi:10.1109/dac63849.2025.11133316 · Cited by 8
On the linear codes over the ring Rp
Dertli, A., Çengellenmiş, Y., & Eren, Ş. (2016) · Discrete Mathematics Algorithms and Applications · doi:10.1142/s1793830916500361 · Cited by 8
Abelian and Non-Abelian Quantum Two-Block Codes
Wang, R., Lin, H.-K., & Pryadko, L. P. (2023) · International Symposium on Turbo Codes and Iterative Information Processing · doi:10.1109/istc57237.2023.10273492 · Cited by 8
Image Transmission Over Quantum Communication Systems With Three‐Qubit Error Correction
Jayasinghe, U., Samarathunga, P., Fernando, T., Ganearachchi, Y., & Fernando, A. (2025) · Electronics Letters · doi:10.1049/ell2.70205 · Cited by 8
Climbing the diagonal Clifford hierarchy
Hu, J., Liang, Q., & Calderbank, R. (2025) · Academia quantum. · doi:10.20935/acadquant7957 · Cited by 20
Additive semisimple multivariable codes over $${\mathbb{F}_4}$$
Martı́nez-Moro, E., Nicolás, A. P., & Rúa, I. F. (2012) · Designs Codes and Cryptography · doi:10.1007/s10623-012-9641-2 · Cited by 8
Quantum Codes from Constacyclic Codes over the Ring Fq[u1,u2]/〈 u 1 2 -u1, u 2 2 -u2,u1u2-u2u1〉
Al‐Kenani, A. N., Ashraf, M., & Mohammad, G. (2020) · Mathematics · doi:10.3390/math8050781 · Cited by 8
Quantum synchronizable codes from finite rings
Liu, H., & Liu, X. (2021) · Quantum Information Processing · doi:10.1007/s11128-021-03058-4 · Cited by 8
On the generalization of the construction of quantum codes from Hermitian self-orthogonal codes
Galindo, C., & Hernando, F. (2022) · Designs Codes and Cryptography · doi:10.1007/s10623-022-01018-2 · Cited by 8
Quantitative Treatment of Decoherence
Fedichkin, L. E., & Vladimir Privman, A. (2009) · Topics in applied physics · doi:10.1007/978-3-540-79365-6_8 · Cited by 8
Quantum Event-Error Detection Codes
Guo, Y., & Zeng, G. (2005) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.74.2949 · Cited by 8
Fault-tolerant simulation of Lattice Gauge Theories with gauge covariant codes
Spagnoli, L., Roggero, A., & Wiebe, N. (2026) · Quantum · doi:10.22331/q-2026-01-16-1968 · Cited by 28
Distribution of Bell-inequality violation versus multiparty-quantum-correlation measures
Sharma, K., Das, T., Sen, A., & Sen, U. (2016) · Physical Review A · doi:10.1103/physreva.93.062344 · Cited by 7
Quantum codes from $$\mathbb {Z}_2\mathbb {Z}_2[u]/\langle u^4 \rangle $$-cyclic codes
Biswas, S., & Bhaintwal, M. (2022) · Designs Codes and Cryptography · doi:10.1007/s10623-021-00978-1 · Cited by 7
Jayasinghe, U., Pollwaththage, N., Ganearachchi, Y., Samarathunga, P., Fernando, T., & Fernando, A. (2025) · International Conference on Consumer Electronics · doi:10.1109/icce63647.2025.10930032 · Cited by 7
Measure of decoherence in quantum error correction for solid-state quantum computing
Melnikov, A. A., & Fedichkin, L. E. (2013) · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · doi:10.1117/12.2016639 · Cited by 7
New construction of binary and nonbinary quantum stabilizer codes based on symmetric matrices
Nguyen, D. M., & Kim, S. (2019) · International Journal of Modern Physics B · doi:10.1142/s0217979219502746 · Cited by 7
Rating the performance of noisy teleportation using fluctuations in fidelity
Roy, S., & Ghosal, A. (2020) · Physical Review A · doi:10.1103/physreva.102.012428 · Cited by 7
Simple proof of security of the multiparty prepare and measure QKD
Nilesh, K. (2022) · Quantum Information Processing · doi:10.1007/s11128-022-03691-7 · Cited by 7
Quantum mean estimation for lattice field theory
Gustafson, E., Lamm, H., & Unmuth-Yockey, J. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.107.114511 · Cited by 7
Constructions of new Quantum Burst-correcting Codes
Qian, J., & Zhang, L. (2014) · International Journal of Theoretical Physics · doi:10.1007/s10773-014-2287-2 · Cited by 7
Deterministic distributed dense coding with stabilizer states
Wang, G., & Ying, M. (2008) · Physical Review A · doi:10.1103/physreva.77.032306 · Cited by 7
Perfect coding for dephased quantum state transfer
Kay, A. (2018) · Physical Review A · doi:10.1103/physreva.97.032317 · Cited by 7
Euclidean and hyperbolic asymmetric topological quantum codes
de Albuquerque, C. D., Guardia, G. G. L., Palazzo, R., Queiroz, C. R. D. O. Q., & Vieira, V. L. (2022) · Quantum Information Processing · doi:10.1007/s11128-022-03488-8 · Cited by 7
Combating errors in quantum communication: an integrated approach
Bala, R., Asthana, S., & Ravishankar, V. (2023) · Scientific Reports · doi:10.1038/s41598-023-30178-x · Cited by 7
On the Codes over a Semilocal Finite Ring
Dertli, A., Çengellenmiş, Y., & Eren, Ş. (2015) · International Journal of Advanced Computer Science and Applications · doi:10.14569/ijacsa.2015.061038 · Cited by 7
Automated discovery of logical gates for quantum error correction (with Supplementary (153 pages))
Chen, H., Vasmer, M., Breuckmann, N. P., & Grant, E. (2022) · Quantum Information and Computation · doi:10.26421/qic22.11-12-3 · Cited by 7
Noise tolerance of the BB84 protocol with random privacy amplification
Watanabe, S., Matsumoto, R., & Uyematsu, R. (2005) · IEEE International Symposium on Information Theory (ISIT) · doi:10.1109/isit.2005.1523492 · Cited by 7
Sarvepalli, P. K., Klappenecker, A., & Aly, S. A. (2007) · Chapman & Hall/CRC applied mathematics and nonlinear science series · doi:10.1201/9781584889007.ch10 · Cited by 7
A Unification of the Coding Theory and OAQEC Perspectives on Hybrid Codes
Majidy, S. (2023) · International Journal of Theoretical Physics · doi:10.1007/s10773-023-05439-0 · Cited by 7
The idiots guide to Quantum Error CorrectionPreprint
Devitt, S. J., Nemoto, K., & Munro, W. J. (2009) · arXiv (Cornell University) · Cited by 7
On Quantum and Classical Error Control Codes: Constructions and ApplicationsPreprint
Aly, S. A. (2008) · arXiv (Cornell University) · doi:10.48550/arxiv.0812.5104 · Cited by 7
Families of LDPC Codes Derived from Nonprimitive BCH Codes and Cyclotomic CosetsPreprint
Aly, S. A. (2008) · arXiv (Cornell University) · doi:10.48550/arxiv.0802.4079 · Cited by 7
Quantum Information and Convex Optimization
Reimpell, M. (2007) · Digitale Bibliothek Braunschweig (Verbundzentrale Göttingen (VZG)) · doi:10.24355/dbbs.084-200803130100-3 · Cited by 7
Transversal Clifford and T -Gate Codes of Short Length and High Distance
Jain, S. P., & Albert, V. V. (2025) · IEEE Journal on Selected Areas in Information Theory · doi:10.1109/jsait.2025.3570832 · Cited by 8
Berthusen, N., Tan, S., Huang, E., & Gottesman, D. (2025) · PRX Quantum · doi:10.1103/ps3r-wf84 · Cited by 6
Hulls of Projective Reed–Muller Codes over the Projective Plane
Ruano, D., & San–José, R. (2024) · SIAM Journal on Applied Algebra and Geometry · doi:10.1137/23m1626153 · Cited by 6
Quantum codes from skew cyclic codes over mixed alphabets
Prakash, O., Patel, S., & Islam, H. (2025) · Computational and Applied Mathematics · doi:10.1007/s40314-025-03349-x · Cited by 6
Bergamaschi, T. (2024) · Lecture notes in computer science · doi:10.1007/978-3-031-58734-4_14 · Cited by 6
Asymmetric quantum codes detecting a single amplitude error
Ezerman, M. F., & Grassl, M. (2013) · IEEE International Symposium on Information Theory (ISIT) · doi:10.1109/isit.2013.6620361 · Cited by 6
How efficient is transport of quantum cargo through multiple highways?
Roy, S., Das, T., Das, D., Sen(De), A., & Sen, U. (2020) · Annals of Physics · doi:10.1016/j.aop.2020.168281 · Cited by 6
Matsumoto, R. (2020) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2020.2978454 · Cited by 6
Quasi-cyclic constructions of asymmetric quantum error-correcting codes
Lv, J., Li, R., & Yao, Y. (2021) · Cryptography and Communications · doi:10.1007/s12095-021-00489-9 · Cited by 6
Zero-error quantum hypothesis testing in finite time with quantum error correction
Chen, Y., & Yuan, H. (2019) · Physical Review A · doi:10.1103/physreva.100.022336 · Cited by 6
Polynomial procedure of avoiding multiqubit errors arising due to qubit-qubit interactionPreprint
Fedichkin, L. E. (2000) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0011005 · Cited by 6
A Quantum Frequency-Domain Framework for Image Transmission with Three-Qubit Error Correction
Jayasinghe, U., Fernando, T., & Fernando, A. (2025) · Algorithms · doi:10.3390/a18090574 · Cited by 5
New EAQEC codes from cyclic codes over $${\mathbb {Z}}_{4}+v{\mathbb {Z}}_{4}$$
Liu, H., & Liu, X. (2024) · Quantum Information Processing · doi:10.1007/s11128-024-04277-1 · Cited by 5
Error-correctable efficient quantum homomorphic encryption using Calderbank–Shor–Steane codes
Sohn, I., Kim, B., Bae, K., Song, W., & Lee, W. (2025) · Quantum Information Processing · doi:10.1007/s11128-025-04651-7 · Cited by 8
Metadata
- Authors
- Steane, A. M.
- Affiliations
- University of Oxford (GB)
- Corresponding author
- Steane, A. M.
- ORCID
- Steane, A. M.
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 1996-12-01
- Volume
- 54
- Issue
- 6
- Pages
- 4741-4751
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2063592138
- Cited by
- 522
- References
- 15
- Citations by year
- 2026: 28 · 2025: 50 · 2024: 34 · 2023: 37 · 2022: 37 · 2021: 21 · 2020: 37 · 2019: 20 · 2018: 17 · 2017: 12 · 2016: 15 · 2015: 17 · 2014: 14 · 2013: 14 · 2012: 11
- FWCI
- 16.25
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Royal Society
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Coding theory and cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Keywords
- quantum error-correcting codes, CSS construction, classical codes, qubits, single-error-correcting codes, code distance, systematic codes, block length, quantum information
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
