Graph Concatenation for Quantum Codes

Details Graph Concatenation for Quantum Codes Graph Concatenation for Quantum Codes

2009-10-21

arxiv.org/abs/0910.4129v2

Journal of Mathematical Physics, vol. 52, no. 2, February 2011, 022201

Physics

Quantum Physics

26 pages, 12 figures. Figures of concatenated [[5,1,3]] and [[7,1,3]] are added. Submitted to JMP

Scientific paper

10.1063/1.3534799

Graphs are closely related to quantum error-correcting codes: every stabilizer code is locally equivalent to a graph code, and every codeword stabilized code can be described by a graph and a classical code. For the construction of good quantum codes of relatively large block length, concatenated quantum codes and their generalizations play an important role. We develop a systematic method for constructing concatenated quantum codes based on "graph concatenation", where graphs representing the inner and outer codes are concatenated via a simple graph operation called "generalized local complementation." Our method applies to both binary and non-binary concatenated quantum codes as well as their generalizations.

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