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arXiv · 0910.4129

Graph Concatenation for Quantum Codes

Salman Beigi·Isaac Chuang·Markus Grassl·Peter Shor·Bei Zeng
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Abstract

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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Salman Beigi, Isaac Chuang, Markus Grassl, Peter Shor, Bei Zeng. 2010-02-03. Graph Concatenation for Quantum Codes. https://doi.org/10.1063/1.3534799

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