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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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ResultIn-situ characterization of quantum devices with error correctionPreprint
Combes, J., Ferrie, C., Cesare, C., Tiersch, M., Milburn, G. J., Briegel, H. J., & Caves, C. M. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1405.5656 · Cited by 17
“Since the early days of the Shor [1] and Steane [2] codes, quantum error correction has seen many developments, notably Gottes-man’s stabilizer formalism [3] and Kitaev’s topological codes [4].”
BackgroundMatsumoto, R., & Uyematsu, T. (1999) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/9911011 · Cited by 21
“The error correction method presented in this subsection is not explicitly mentioned in the papers [2, 3, 6].”
InfluentialAlways-On Quantum Error Tracking with Continuous Parity Measurements
Mohseninia, R., Yang, J., Siddiqi, I., Jordan, A. N., & Dressel, J. (2020) · Quantum · doi:10.22331/q-2020-11-04-358 · Cited by 16
“Examples of this model include the Shor [6], Steane [7], and Calderbank-Steane-Shor (CSS) codes [8, 9], as well as more general stabilizer codes [10–14].”
MethodError-correcting Bacon-Shor code with continuous measurement of noncommuting operators
Atalaya, J., Korotkov, A. N., & Whaley, K. B. (2020) · Physical Review A · doi:10.1103/physreva.102.022415 · Cited by 16
Stability of quantum concatenated-code Hamiltonians
Bacon, D. (2008) · Physical Review A · doi:10.1103/physreva.78.042324 · Cited by 17
“Stabilizer codes [32] are defined by the use of a particular subgroup of the Pauli group known as a stabilizer group.”
Method
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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