Error Correcting Codes in Quantum Theory
Abstract
A new type of uncertainty relation is presented, concerning the information-bearing properties of a discrete quantum system. A natural link is then revealed between basic quantum theory and the linear error correcting codes of classical information theory. A subset of the known codes is described, having properties which are important for error correction in quantum communication. It is shown that a pair of states which are, in a certain sense, "macroscopically different," can form a superposition in which the interference phase between the two parts is measurable. This provides a highly stabilized "Schrödinger cat" state.Received 4 October 1995DOI:https://doi.org/10.1103/PhysRevLett.77.793©1996 American Physical Society
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Depending on the scheme being used, typically between 7 and 9 physical qubits are needed to represent the state of one qubit.
“Depending on the scheme being used, typically between 7 [55] and 9 [56][57][58] physical qubits are needed to represent the state of one qubit.”
From Neutral atom quantum computing hardware: performance and end-user perspective (2023) · cites this paper as [55]
Since R'_xz is in the Clifford group, it can be performed fault-tolerantly.
“Since R ′ xz is in the Clifford group, it can be performed fault-tolerantly.”
From Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations (1999) · cites this paper as [17]
Through an appropriate sequence of gates and measurements, any C2 operation can be performed on any stabilizer code.
“Through an appropriate sequence of gates and measurements, any C 2 operation can also be performed on any stabilizer code [17].”
From Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations (1999) · cites this paper as [17]
Operators from the Pauli group can easily be performed on logical qubits encoded with a stabilizer code.
“Operators from the Pauli group (such as X , Y , and Z ) can easily be performed on logical qubits which are encoded with a stabilizer code [17].”
From Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations (1999) · cites this paper as [17]
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“The universally accepted approach to remedy effects of noise and decoherence in quantum computing is the use of quantum error correction [36, 39, 9].”
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- Authors
- Steane, A. M.
- Affiliations
- University of Oxford (GB)
- Corresponding author
- Steane, A. M.
- ORCID
- Steane, A. M.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1996-07-29
- Volume
- 77
- Issue
- 5
- Pages
- 793-797
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2042474962
- Semantic Scholar
- db5c47769e7b1a852303220fb75b8e9d6e2086ce
- Cited by
- 2,677
- References
- 13
- Citations by year
- 2026: 120 · 2025: 180 · 2024: 119 · 2023: 179 · 2022: 119 · 2021: 110 · 2020: 113 · 2019: 120 · 2018: 80 · 2017: 74 · 2016: 84 · 2015: 72 · 2014: 95 · 2013: 92 · 2012: 94
- FWCI
- 65.40
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- quantum error-correcting codes, uncertainty relations, discrete quantum systems, quantum communication, Schrödinger cat states, superposition, linear codes
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