Graph Concatenation for Quantum Codes
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.
Cite
@article{arxiv.0910.4129,
title = {Graph Concatenation for Quantum Codes},
author = {Salman Beigi and Isaac Chuang and Markus Grassl and Peter Shor and Bei Zeng},
journal= {arXiv preprint arXiv:0910.4129},
year = {2011}
}
Comments
26 pages, 12 figures. Figures of concatenated [[5,1,3]] and [[7,1,3]] are added. Submitted to JMP