The DOI matches its Crossref record; 12 of the 12 references it cites were found in a registry or an index.
Quantum Error Correction and Orthogonal Geometry
Open accessAbstract
A group theoretic framework is introduced that simplifies the description of known quantum error-correcting codes and greatly facilitates the construction of new examples. Codes are given which map 3 qubits to 8 qubits correcting 1 error, 4 to 10 qubits correcting 1 error, 1 to 13 qubits correcting 2 errors, and 1 to 29 qubits correcting 5 errors.
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“The required algorithm-specific non-universal quantum resource to run the remainder of the quantum algorithm on the QC C is then a graph state [9].”
From Measurement-based quantum computation on cluster states (2003) · cites this paper as [9]
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Citations
Cites
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
Self-citationPurification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
Bennett, C. H., Brassard, G., Popescu, S., Schumacher, B., Smolin, J. A., & Wootters, W. K. (1996) · Physical Review Letters · doi:10.1103/physrevlett.76.722 · Cited by 2,961
Error Correcting Codes in Quantum Theory
Steane, A. M. (1996) · Physical Review Letters · doi:10.1103/physrevlett.77.793 · Cited by 2,677
Good 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
Self-citationThe Subgroup Structure of the Finite Classical Groups
Kleidman, P. B., & Liebeck, M. W. (1990) · Cambridge University Press eBooks · doi:10.1017/cbo9780511629235 · Cited by 1,347
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
Class 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
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
Z 4 -Kerdock Codes, Orthogonal Spreads, and Extremal Euclidean Line-Sets
Calderbank, A. R., Cameron, P. J., Kantor, W., & Seidel, J. J. (1997) · Proceedings of the London Mathematical Society · doi:10.1112/s0024611597000403 · Cited by 313
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Fault-tolerant quantum computation by anyons
Kitaev, A. Y. (2003) · Annals of Physics · doi:10.1016/s0003-4916(02)00018-0 · Cited by 7,238
A scheme for efficient quantum computation with linear optics
Knill, E., Laflamme, R., & Milburn, G. J. (2001) · Nature · doi:10.1038/35051009 · Cited by 5,880
Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
Shor, P. W. (1999) · SIAM Review · doi:10.1137/s0036144598347011 · Cited by 3,904
Self-citationQuantum information with continuous variables
Braunstein, S. L., & van Loock, P. (2005) · Reviews of Modern Physics · doi:10.1103/revmodphys.77.513 · Cited by 3,858
Gottesman, D., & Chuang, I. L. (1999) · Nature · doi:10.1038/46503 · Cited by 1,860
Metadata
- Authors
- Calderbank, A. R., Rains, E. M., Shor, P. W., & Sloane, N. J. A.
- Affiliations
- AT&T (United States) (US)
- Institute For Defense Analyses (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1997-01-20
- Volume
- 78
- Issue
- 3
- Pages
- 405-408
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2091331782
- Cited by
- 811
- References
- 12
- Citations by year
- 2026: 21 · 2025: 44 · 2024: 32 · 2023: 36 · 2022: 34 · 2021: 47 · 2020: 32 · 2019: 26 · 2018: 30 · 2017: 22 · 2016: 18 · 2015: 20 · 2014: 18 · 2013: 28 · 2012: 21
- FWCI
- 40.69
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CaltechAUTHORS (California Institute of Technology) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- 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 correction, quantum error-correcting codes, group theory, code construction, orthogonal geometry, code rate
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