The DOI matches its Crossref record; 3 of the 3 references it cites were found in a registry or an index.
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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Citations
Cites
Scheme for reducing decoherence in quantum computer memory
Shor, P. W. (1995) · Physical Review A · doi:10.1103/physreva.52.r2493 · Cited by 4,479
Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
Bennett, C. H., Brassard, G., Popescu, S., Schumacher, B., Smolin, J. A., & Wootters, W. K. (1996) · Physical Review Letters · doi:10.1103/physrevlett.76.722 · Cited by 2,961
Good quantum error-correcting codes exist
Calderbank, A. R., & Shor, P. W. (1996) · Physical Review A · doi:10.1103/physreva.54.1098 · Cited by 2,516
Cited by
Sorted by citations
Items 1,001–1,003 of 1,003
Quantum error correction and fault tolerance: A comprehensive tutorial
Spencer, D. J., Jain, S. P., Tanggara, A., Sun, Z., Haug, T., Khu, D., & Bharti, K. (2026) · arXiv
The Heisenberg Representation of Quantum Computers
Gottesman, D. (1998) · arXiv · doi:10.48550/arxiv.quant-ph/9807006 · Cited by 489
“The set of such operators is closed under multiplication, and therefore forms a group, known as the stabilizer S [4, 5].”
BackgroundThe Physical Implementation of Quantum Computation
DiVincenzo, D. P. (2000) · Fortschritte der Physik · doi:10.1002/1521-3978(200009)48:9/11
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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