Graphs, Quadratic Forms, and Quantum Codes
arXiv:quant-ph/0703112 · doi:10.1109/ISIT.2002.1023317
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.
5 pages, 2 figures, paper presented at the 2002 IEEE International Symposium on Information Theory