Graphs, Quadratic Forms, and Quantum Codes

  • Markus Grassl ,
  • Andreas Klappenecker ,
  • Martin Roetteler

Proceedings 2002 IEEE International Symposium on Information Theory (ISIT 2002), Lausanne, Switzerland, June/July 2002, p. 45 |

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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.