Theory of Quantum Error Correction for General Noise
Open accessAbstract
A measure of quality of an error-correcting code is the maximum number of errors that it is able to correct. We show that a suitable notion of "number of errors" e makes sense for any quantum or classical system in the presence of arbitrary interactions. Thus, e-error-correcting codes protect information without requiring the usual assumptions of independence. We prove the existence of large codes for both quantum and classical information. By viewing error-correcting codes as subsystems, we relate codes to irreducible representations of operator algebras and show that noiseless subsystems are infinite-distance error-correcting codes.
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The vanishing of an energy scale for degenerate qubits holds, strictly speaking, only for fully adiabatic techniques, e.g., HQC.
“Indeed, the vanishing of an energy scale for degenerate qubits holds, strictly speaking, only for fully adiabatic techniques, e.g., HQC [53, 54].”
From Internal consistency of fault-tolerant quantum error correction in light of rigorous derivations of the quantum Markovian limit (2006) · cites this paper as [53]
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- Authors
- Knill, E., Laflamme, R., & Viola, L.
- Affiliations
- Los Alamos National Laboratory (US)
- Massachusetts Institute of Technology (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2000-03-13
- Volume
- 84
- Issue
- 11
- Pages
- 2525-2528
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2087256203
- Cited by
- 866
- References
- 36
- Citations by year
- 2026: 31 · 2025: 53 · 2024: 41 · 2023: 35 · 2022: 35 · 2021: 39 · 2020: 32 · 2019: 36 · 2018: 26 · 2017: 24 · 2016: 30 · 2015: 17 · 2014: 30 · 2013: 31 · 2012: 22
- FWCI
- 36.13
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Computer Science › Artificial Intelligence › Coding theory and cryptography
- Keywords
- quantum error correction, error-correcting codes, classical error-correcting codes, subsystem codes, noiseless subsystems, irreducible representations, operator algebras, code existence
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