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Stabilizer Formalism for Operator Quantum Error Correction
Open accessAbstract
Operator quantum error correction is a recently developed theory that provides a generalized and unified framework for active error correction and passive error avoiding schemes. In this Letter, we describe these codes using the stabilizer formalism. This is achieved by adding a gauge group to stabilizer codes that defines an equivalence class between encoded states. Gauge transformations leave the encoded information unchanged; their effect is absorbed by virtual gauge qubits that do not carry useful information. We illustrate the construction by identifying a gauge symmetry in Shor's 9-qubit code that allows us to remove 3 of its 8 stabilizer generators, leading to a simpler decoding procedure and a wider class of logical operations without affecting its essential properties. This opens the path to possible improvements of the error threshold of fault-tolerant quantum computing.
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Cites
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Cited by
Quantum error correction for quantum memories
Terhal, B. M. (2015) · Reviews of Modern Physics · doi:10.1103/revmodphys.87.307 · Cited by 1,354
An introduction to quantum error correction and fault-tolerant quantum computation
Gottesman, D. (2010) · Proceedings of Symposia in Applied Mathematics · doi:10.1090/psapm/068/2762145 · Cited by 370
A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes
Bravyi, S., & Terhal, B. (2009) · New Journal of Physics · doi:10.1088/1367-2630/11/4/043029 · Cited by 255
Gauge color codes: optimal transversal gates and gauge fixing in topological stabilizer codes
Bombín, H. (2015) · New Journal of Physics · doi:10.1088/1367-2630/17/8/083002 · Cited by 217
Subsystem Fault Tolerance with the Bacon-Shor Code
Aliferis, P., & Cross, A. W. (2007) · Physical Review Letters · doi:10.1103/physrevlett.98.220502 · Cited by 203
Metadata
- Authors
- Poulin, D.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2005-12-01
- Volume
- 95
- Issue
- 23
- Pages
- 230504-230504
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2095025840
- Cited by
- 342
- References
- 20
- FWCI
- 16.15
- Type
- journal article
- Language
- en
- Open access
- green
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