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Class of quantum error-correcting codes saturating the quantum Hamming bound
Open accessAbstract
I develop methods for analyzing quantum error-correcting codes, and use these methods to construct an infinite class of codes saturating the quantum Hamming bound. These codes encode k=n-j-2 quantum bits (qubits) in n=${2}^{\mathit{j}}$ qubits and correct t=1 error. \textcopyright{} 1996 The American Physical Society.
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“Without error corrections, the effect of noise will accumulate and ruin the entire computation[72, 17, 54, 52, 7], and hence the computation must be protected.”
From Fault-Tolerant Quantum Computation with Constant Error Rate (2008) · cites this paper as [52]
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Controlling Decoherence from Fluctuating Magnetic Field
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“The quantum Hamming bound states (see [20,22]) that: THEOREM 1.4 Quantum Hamming Bound Any pure (( n, K, d )) q stabilizer code satisfies While the quantum Singleton bound holds for all quantum codes, it is not known if the quantum Hamming bound is of equal applicability.”
BackgroundInfluentialA Unification of the Coding Theory and OAQEC Perspectives on Hybrid Codes
Majidy, S. (2023) · International Journal of Theoretical Physics · doi:10.1007/s10773-023-05439-0 · Cited by 7
“This bound is a seminal result in quantum error correction and loadstone for developing quantum error-correcting codes [11].”
BackgroundThe idiots guide to Quantum Error CorrectionPreprint
Devitt, S. J., Nemoto, K., & Munro, W. J. (2009) · arXiv (Cornell University) · Cited by 7
On Quantum and Classical Error Control Codes: Constructions and ApplicationsPreprint
Aly, S. A. (2008) · arXiv (Cornell University) · doi:10.48550/arxiv.0812.5104 · Cited by 7
Stability of topologically-protected quantum computing proposals as seen through spin glassesPreprint
Katzgraber, H. G., & Andrist, R. S. (2016) · Cited by 7
Metadata
- Authors
- Gottesman, D.
- Affiliations
- California Institute of Technology (US)
- Corresponding author
- Gottesman, Daniel
- ORCID
- Gottesman, Daniel
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 1996-09-01
- Volume
- 54
- Issue
- 3
- Pages
- 1862-1868
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2069711632
- Cited by
- 1,227
- References
- 3
- Citations by year
- 2026: 26 · 2025: 75 · 2024: 48 · 2023: 56 · 2022: 45 · 2021: 65 · 2020: 44 · 2019: 36 · 2018: 34 · 2017: 36 · 2016: 33 · 2015: 32 · 2014: 41 · 2013: 38 · 2012: 34
- FWCI
- 38.07
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Funders
- U.S. Department of Energy (FG0392ER40701)
- 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, code construction, single error correction, qubit encoding, code rate, quantum information
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