Title :
Concatenated Quantum Codes Constructible in Polynomial Time: Efficient Decoding and Error Correction
Author_Institution :
PRESTO, Japan Sci. & Technol. Agency, Kawaguchi
Abstract :
A method for concatenating quantum error-correcting codes is presented. The method is applicable to a wide class of quantum error-correcting codes known as Calderbank-Shor-Steane (CSS) codes. As a result, codes that achieve a high rate in the Shannon-theoretic sense and that are decodable in polynomial time are presented. The rate is the highest among those known to be achievable by CSS codes. Moreover, the best known lower bound on the greatest minimum distance of codes constructible in polynomial time is improved for a wide range.
Keywords :
computational complexity; concatenated codes; error correction codes; Calderbank-Shor-Steane codes; concatenated quantum codes; error-correcting codes; polynomial time; Cascading style sheets; Concatenated codes; Decoding; Error correction; Error correction codes; Galois fields; Geometry; Hilbert space; Information theory; Quantum mechanics; Achievable rates; concatenation; constructible; geometric Goppa codes; polynomial time; symplectic codes; syndrome decoding;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2008.2006416
