Codeword-stabilized quantum codes on subsystems
- Authors
- Shin, Jeonghwan; Heo, Jun
- Issue Date
- 15-10월-2012
- Publisher
- AMER PHYSICAL SOC
- Citation
- PHYSICAL REVIEW A, v.86, no.4
- Indexed
- SCIE
SCOPUS
- Journal Title
- PHYSICAL REVIEW A
- Volume
- 86
- Number
- 4
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/107212
- DOI
- 10.1103/PhysRevA.86.042318
- ISSN
- 1050-2947
- Abstract
- Codeword-stabilized quantum codes provide a unified approach to constructing quantum error-correcting codes, including both additive and nonadditive quantum codes. Standard codeword-stabilized quantum codes encode quantum information into subspaces. The more general notion of encoding quantum information into a subsystem is known as an operator (or subsystem) quantum error-correcting code. Most operator codes studied to date are based in the usual stabilizer formalism. We introduce operator quantum codes based on the codeword-stabilized quantum code framework. Based on the necessary and sufficient conditions for operator quantum error correction, we derive an error-correction condition for operator codeword-stabilized quantum codes. Based on this condition, the word operators of a operator codeword-stabilized quantum code are constructed from a set of classical binary errors induced by generators of the gauge group. We use this scheme to construct examples of both additive and nonadditive codes that encode quantum information into a subsystem.
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