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Quantum Error Correction and Orthogonal Geometry

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Calderbank, A. R., Rains, E. M., Shor, P. W., Sloane, N. J. A.·1997·Physical Review Letters

DOI 10.1103/physrevlett.78.405

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Abstract

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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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)
ORCID: Calderbank, A. R.
Shor, P. W.
Sloane, N. J. A.
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
DOI: 10.1103/physrevlett.78.405
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
Licence: link.aps.org/licenses/aps-default-license (vor)
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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Quantum Error Correction and Orthogonal Geometry

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