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.
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“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]
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“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
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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
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