Constructing quantum error-correcting codes for p^m-state systems from classical error-correcting codes
Quantum Physics
2007-05-23 v3
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.
Cite
@article{arxiv.quant-ph/9911011,
title = {Constructing quantum error-correcting codes for p^m-state systems from classical error-correcting codes},
author = {Ryutaroh Matsumoto and Tomohiko Uyematsu},
journal= {arXiv preprint arXiv:quant-ph/9911011},
year = {2007}
}
Comments
10 pages, LaTeX2e. To appear in IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences (ISSN 0916-8508), vol. E83-A, no. 10, Oct. 2000. Revision on Dec. 14, 1999: Added a note on a systematic construction of quantum codes with efficient decoding algorithms. Revision on June 26, 2000: Corrected lots of errors, and added a review on the overall error correction process. No original materials were added