Graphs, Quadratic Forms, and Quantum Codes
<|reference_start|>Graphs, Quadratic Forms, and Quantum Codes: 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.<|reference_end|>
@article{grassl2007graphs,,
    title={Graphs, Quadratic Forms, and Quantum Codes},
    author={Markus Grassl, Andreas Klappenecker, Martin Roetteler},
    journal={Proceedings 2002 IEEE International Symposium on Information
  Theory (ISIT 2002), Lausanne, Switzerland, June/July 2002, p. 45},
    year={2007},
    doi={10.1109/ISIT.2002.1023317},
    archivePrefix={arXiv},
    eprint={quant-ph/0703112},
    primaryClass={quant-ph cs.IT math.IT}
}