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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]
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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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