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Graph concatenation for quantum codes

Beigi, Salman and Chuang, Isaac and Grassl, Markus and Shor, Peter and Zeng, Bei (2011) Graph concatenation for quantum codes. Journal of Mathematical Physics, 52 (2). Art. No. 022201. ISSN 0022-2488.

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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 nonbinary concatenated quantum codes as well as their generalizations.

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Additional Information:© 2011 American Institute of Physics. Received 3 February 2010; accepted 15 December 2010; published online 16 February 2011. We thank Runyao Duan for helpful discussions. S.B. is supported in part by NSF under Grant No. PHY-0803371 and by NSA/ARO under Grant No. W911NF-09-1-0442. B.Z. is supported by NSERC and QuantumWorks. The Centre for Quantum Technologies is a Research Centre of Excellence funded by the Ministry of Education and the National Research Foundation of Singapore.
Funding AgencyGrant Number
National Security Agency (NSA)/Army Research Office (ARO)W911NF-09-1-0442
Natural Sciences and Engineering Research Council of Canada (NSERC )UNSPECIFIED
Ministry of Education (Singapore)UNSPECIFIED
National Research Foundation of SingaporeUNSPECIFIED
Subject Keywords:graph theory, quantum computing
Issue or Number:2
Classification Code:PACS: 03.67.Lx; 02.10.Ox
Record Number:CaltechAUTHORS:20110318-145128732
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Official Citation:Graph concatenation for quantum codes Salman Beigi, Isaac Chuang, Markus Grassl, Peter Shor, and Bei Zeng J. Math. Phys. 52, 022201 (2011); doi:10.1063/1.3534799
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:22981
Deposited By: Ruth Sustaita
Deposited On:22 Mar 2011 18:21
Last Modified:03 Oct 2019 02:42

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