Non-binary quasi-cyclic quantum LDPC codes

Author

Kasai, Kenta ; Hagiwara, Manabu ; Imai, Hideki ; Sakaniwa, Kohichi

Author_Institution

Dept. of Commun. & Integrated Syst., Tokyo Inst. of Technol., Tokyo, Japan

fYear

2011

fDate

July 31 2011-Aug. 5 2011

Firstpage

653

Lastpage

657

Abstract

In this paper, we propose a construction method for two-level quantum error-correcting codes via non-binary LDPC codes over an extended field of order 2^p, p an integer p >; 1. The proposed quantum error-correcting codes are based on binary quasi-cyclic LDPC codes which have almost achieved a “Bounded Distance Decoding (BDD)” limit but have not surpassed the limit yet. Quantum codes constructed from the proposed method surpass the BDD limit. Furthermore the codes outperform the efficiently-decodable state-of-the-art quantum codes.

Keywords

cyclic codes; decoding; error correction codes; parity check codes; quantum communication; binary quasicyclic LDPC codes; bounded distance decoding; nonbinary quasi-cyclic quantum LDPC codes; two-level quantum error-correcting codes; Cascading style sheets; Equations; Error correction codes; Indexes; Mathematical model; Parity check codes; Sparse matrices; CSS codes; Galois field; LDPC code; belief propagation; iterative decoding; non-binary LDPC codes; quantum error-correcting codes;

fLanguage

English

Publisher

ieee

Conference_Titel

Information Theory Proceedings (ISIT), 2011 IEEE International Symposium on

Conference_Location

St. Petersburg

ISSN

2157-8095

Print_ISBN

978-1-4577-0596-0

Electronic_ISBN

2157-8095

Type

conf

DOI

10.1109/ISIT.2011.6034212

Filename

6034212