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Abstract: of a paper submitted to ISIT 2002, Lausanne, Switzerland Abstract| We show that any stabilizer code over a nite eld is equivalent to a graphical quantum code. Furthermore we prove that a graphical quantum code over a nite eld 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. (Update)
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BibTeX entry: (Update)
@misc{ grassl-graphs,
author = "Markus Grassl and Andreas Klappenecker and Martin Rötteler",
title = "Graphs, Quadratic Forms, and Quantum Codes (Extended Abstract)",
url = "citeseer.ist.psu.edu/grassl02graphs.html" }
Citations (may not include all citations):52 Good quantum errorcorrecting codes exist - Calderbank, Shor - 1996
35 Quantum Error Correction Via Codes over GF - Calderbank, Rains et al. - 1998
20 Error Correcting Codes in Quantum Theory (context) - Steane - 1996
9 Nonbinary quantum stabilizer codes - Ashikhhmin, Knill - 2000
5 Beyond Stabilizer Codes I: Nice Error Bases (context) - Klappenecker, otteler
4 Quantum error-correcting codes associated with graphs (context) - Schlingemann, Werner - 2000
2 Algorithmic Aspects of Quantum Error-correcting Codes (context) - Grassl - 2001
2 IEEE Transactions on Information Theory (context) - Rains, Codes - 1999
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