Graph concatenation for quantum codes
Author(s)Beigi, Salman; Chuang, Isaac L.; Grassl, Markus; Zeng, Bei; Shor, Peter W.
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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.
Original article: February 3, 2010
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Department of Mathematics; Massachusetts Institute of Technology. Department of Physics
Journal of Mathematical Physics
American Institute of Physics (AIP)
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.