Graph concatenation for quantum codes
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Chuang_Graph concatenation.pdf
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Author(s)
Beigi, Salman
Chuang, Isaac L.
Grassl, Markus
Zeng, Bei
Shor, Peter W.
Date Issued
February 2011
Journal
Journal of Mathematical Physics
Publisher
American Institute of Physics (AIP)
Citation
Beigi, Salman, Isaac Chuang, Markus Grassl, Peter Shor, and Bei Zeng. “Graph Concatenation for Quantum Codes.” Journal of Mathematical Physics 52, no. 2 (2011): 022201.
Version
Original manuscript
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.
Description
Original article: February 3, 2010
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Department of Mathematics
Massachusetts Institute of Technology. Department of Physics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1063/1.3534799
