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 nonbinary concatenated quantum codes as well as their generalizations.
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.Attached Files
Published - Beigi2011p13107J_Math_Phys.pdf
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Additional details
- Eprint ID
- 22981
- Resolver ID
- CaltechAUTHORS:20110318-145128732
- PHY-0803371
- NSF
- W911NF-09-1-0442
- National Security Agency (NSA)/Army Research Office (ARO)
- Natural Sciences and Engineering Research Council of Canada (NSERC )
- QuantumWorks
- Ministry of Education (Singapore)
- National Research Foundation of Singapore
- Created
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2011-03-22Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field