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Class of quantum error-correcting codes saturating the quantum Hamming bound
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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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A Family of Quantum Stabilizer Codes Based on the Weyl Commutation Relations over a Finite Field
Arvind, V., & Parthasarathy, K. R. (2003) · Hindustan Book Agency · doi:10.1007/978-93-86279-11-8_12 · Cited by 15
“A broad class of quantum error correcting codes known as stabilizer codes was introduced by Gottesman [4] and Calderbank et al [2] (also see [3, 13, 12]).”
BackgroundConjugate Codes and Applications to CryptographyPreprint
Hamada, M. (2006) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0610193 · Cited by 11
“The first code was soon extended to a class of algebraic QECCs called Calderbank-Shor-Steane (CSS) codes [2] and then to a more general class of QECCs, which are called symplectic codes or stabilizer codes [3], [4], [5].”
BackgroundLattice Quantum Codes and Exotic Topological Phases of Matter
Haah, J. (2013) · CaltechTHESIS (California Institute of Technology) · doi:10.48550/arxiv.1305.6973 · Cited by 19
“tinguishable. It did not take too long for people to realize that the Shor’s error correcting code can be generalized and studied in an analogous way that one studies classical error correcting codes [38,39,40,41]. The connection is due to the observation that the encoded state can be described as the eigenstate of pa…”
BackgroundInfluentialQuantum circuit dynamics via path integrals: Is there a classical action for discrete-time paths?
Penney, M. D., Koh, D. E., & Spekkens, R. W. (2017) · New Journal of Physics · doi:10.1088/1367-2630/aa61ba · Cited by 13
“Clifford circuits were first introduced in the context of qubits [8], but were subsequently generalized to continuous variable systems [9] and d-level systems for d > 2 (qudits) [10, 11].”
Background
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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