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QUANTUM ERROR CORRECTION AND STABILIZER CODES

TitleQUANTUM ERROR CORRECTION AND STABILIZER CODES
Publication TypeJournal Article
Year of Publication2015
AuthorsElezi, A
JournalInternational Electronic Journal of Pure and Applied Mathematics
Volume9
Issue3
Start Page181
Pagination10
Date Published05/2015
Type of ArticleScientific article
ISSN1314-0744
Keywordslinear codes, quantum error-correcting codes, self-orthogonal codes, stabilizer codes
Abstract

The goal of this paper is to provide a self contained detailed and rigorous mathematical introduction to some aspects of the quantum error-correcting codes and especially  quantum stabilizer codes without venturing much, if at all,  into the world of physics. While most of the results presented are not new, it is not easy to extract a precise mathematical formulation of results and to provide their rigorous proofs by reading the vast number of papers in the field, quite a few of which are written by computer scientists or physicists. It is this formulation and proofs - quite a few of of them new -  that we present here. The connections between (a) quantum stabilizer codes and classical self-orthogonal codes and (b) between error correction and error detection have been established in details. Techniques from algebra of finite fields as well as representations of finite abelian groups have been employed here.

URLhttp://www.e.ijpam.eu/contents/articles/201500903007.pdf
DOI10.12732/iejpam.v9i3.7
Short TitleQUANTUM ERROR CORRECTION AND STABILIZER CODES
Alternate JournalIeJPAM
Refereed DesignationRefereed
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