Graphs, Quadratic Forms, and Quantum Codes

Published 13 Mar 2007 in quant-ph, cs.IT, and math.IT | (0703112v1)

Abstract: We show that any stabilizer code over a finite field is equivalent to a graphical quantum code. Furthermore we prove that a graphical quantum code over a finite field is a stabilizer code. The technique used in the proof establishes a new connection between quantum codes and quadratic forms. We provide some simple examples to illustrate our results.

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