Graphs, Quadratic Forms, and Quantum Codes
Quantum Physics
2009-05-24 v1 Information Theory
math.IT
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.
Cite
@article{arxiv.quant-ph/0703112,
title = {Graphs, Quadratic Forms, and Quantum Codes},
author = {Markus Grassl and Andreas Klappenecker and Martin Roetteler},
journal= {arXiv preprint arXiv:quant-ph/0703112},
year = {2009}
}
Comments
5 pages, 2 figures, paper presented at the 2002 IEEE International Symposium on Information Theory