Quantum Error Correction and Orthogonal Geometry
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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 a quantum algorithm on the QC_C is a graph state.
“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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- 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 › Computer Science › Artificial Intelligence › Coding theory and cryptography
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Keywords
- quantum error correction, quantum error-correcting codes, group theory, code construction, orthogonal geometry, code rate
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