| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,600,000)
Fiscal Year 2000: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1999: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1998: ¥1,200,000 (Direct Cost: ¥1,200,000)
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| Research Abstract |
Quantum error-correcting codes have been developed as one of the promising methods for protecting quantum information against quantum errors. One of the most important families of quantum error-correcting codes has been provided by Steane and Calderbank ＆ Shor. In general, the resulting quantum error-correcting codes are commonly referred to as Calderbank-Shor-Steane (CSS) codes. A great deal of effort has been made to construct efficient quantum error-correcting codes from classical linear codes, and various code constructions have been proposed based on the CSS code construction. Especially, Vatan, Roychowdhury and Anantram have presented two types of revised versions of the CSS code construction, and have also provided an exhaustive procedure for determining bases of quantum error-correcting codes. Their results are very attractive because they can be applied to any set of quantum errors such as quantum random errors, quantum burst errors, and so on.
In this research, we have investigated in details the results and the searching procedure given by Vatan et al. As a result, we have pointed out that there is no essential difference between those revised versions. Moreover, by utilizing some fundamental properties of classical linear codes, we have proposed an efficient algorithm for searching for bases of CSS type quantum error-correcting codes. The proposed algorithm has much lower complexity than Vatan et al.'s procedure, and seems to be very useful in determining bases of quantum error-correcting codes constructed from classical linear codes which are not weakly self-dual. We have also shown some results of a computer search for new CSS type quantum burst-error-correcting codes obtained from classical cyclic codes of length 30 or less.
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