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 http://resolver.caltech.edu/CaltechAUTHORS:20110318-145128732
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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 nonbinary concatenated quantum codes as well as their generalizations.
| Item Type: | Article | ||||||||||||||
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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. | ||||||||||||||
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| Subject Keywords: | graph theory, quantum computing | ||||||||||||||
| Classification Code: | PACS: 03.67.Lx; 02.10.Ox | ||||||||||||||
| Record Number: | CaltechAUTHORS:20110318-145128732 | ||||||||||||||
| Persistent URL: | http://resolver.caltech.edu/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 | ||||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||||
| Deposited By: | Ruth Sustaita | ||||||||||||||
| Deposited On: | 22 Mar 2011 18:21 | ||||||||||||||
| Last Modified: | 26 Dec 2012 13:05 |
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