2,171 research outputs found
Concatenated Quantum Codes Constructible in Polynomial Time: Efficient Decoding and Error Correction
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.Comment: 16 pages, 3 figures. Ver.4: Title changed. Ver.3: Due to a request of
the AE of the journal, the present version has become a combination of
(thoroughly revised) quant-ph/0610194 and the former quant-ph/0610195.
Problem formulations of polynomial complexity are strictly followed. An
erroneous instance of a lower bound on minimum distance was remove
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