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arXiv:quant-ph/9911011

Constructing quantum error-correcting codes for p^m-state systems from classical error-correcting codes

Ryutaroh Matsumoto, Tomohiko Uyematsu

Published Nov 4, 1999• 17 citations
arXivHTMLPDF

Abstract

We generalize the construction of quantum error-correcting codes from GF(4)-linear codes by Calderbank et al. to p^m-state systems. Then we show how to determine the error from a syndrome. Finally we discuss a systematic construction of quantum codes with efficient decoding algorithms.
DOI
10.48550/arxiv.quant-ph/9911011

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Abstract : We consider quantum error-correcting codes over alphabets of arbitrary size. We generalize quantum stabilizer codes and develop Calderbank-Shor-Steane construction over quantum systems of arbitrary dimensions using the group structure of alphabets. We also develop a methodology systematically conjoining error-correcting codes into a new class of error-correcting codes. With the help of these methods we give several ways to construct quantum maximum distance separable (MDS) codes and present many families of quantum MDS codes.
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