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.
| Original language | English |
|---|---|
| Article number | 042318 |
| Journal | Physical Review A - Atomic, Molecular, and Optical Physics |
| Volume | 86 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 2012 Oct 15 |
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics