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.
“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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Topological Computation without Braiding
Bombín, H., & Martin-Delgado, M. A. (2007) · Physical Review Letters · doi:10.1103/physrevlett.98.160502 · Cited by 191 · see citing works
Decoherence, Pointer Engineering, and Quantum State Protection
Carvalho, A. R. R., Milman, P., Filho, R. L. D. M., & Davidovich, L. (2001) · Physical Review Letters · doi:10.1103/physrevlett.86.4988 · Cited by 179 · see citing works
Efficient fault-tolerant quantum computing
Steane, A. M. (1999) · Nature · doi:10.1038/20127 · Cited by 186 · see citing works
Self-organized error correction in random unitary circuits with measurement
Fan, R., Vijay, S., Vishwanath, A., & You, Y. (2021) · Physical review. B./Physical review. B · doi:10.1103/physrevb.103.174309 · Cited by 181 · see citing works
Optimal resources for topological two-dimensional stabilizer codes: Comparative study
Bombin, H., & Martin-Delgado, M. A. (2007) · Physical Review A · doi:10.1103/physreva.76.012305 · Cited by 178 · see citing works
“A suitable formalism to study quantum error correction codes is the stabilizer formalism [4].”
MethodAnalog Quantum Error Correction
Lloyd, S., & Slotine, J.-J. E. (1998) · Physical Review Letters · doi:10.1103/physrevlett.80.4088 · Cited by 169 · see citing works
Single-Shot Fault-Tolerant Quantum Error Correction
Bombín, H. (2015) · Physical Review X · doi:10.1103/physrevx.5.031043 · Cited by 165 · see citing works
“Stabilizer codes [26] are defined in systems composed of a number of physical qubits.”
BackgroundExperimental Application of Decoherence-Free Subspaces in an Optical Quantum-Computing Algorithm
Mohseni, M., Lundeen, J. S., Resch, K. J., & Steinberg, A. M. (2003) · Physical Review Letters · doi:10.1103/physrevlett.91.187903 · Cited by 160 · see citing works
- 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 › Computer Science › Artificial Intelligence › Coding theory and cryptography
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Keywords
- quantum error-correcting codes, code construction, single error correction, qubit encoding, code rate, quantum information
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