新的最优非对称量子纠错码的构造

非对称量子纠错码是量子纠错码中一类重要的码。因为量子比特翻转的错误概率小于量子相位翻转的错误概率,所以量子纠错需要考虑到非对称的量子信道。文章利用有限域上的经典常循环码,通过非对称量子纠错码的 CSS 构造法构造了 2 类非对称量子纠错码。所构造的非对称量子纠错码是新的,同时达到了非对称量子纠错码的 Singleton 界,因而也是最优的。

Asymmetric quantum error-correcting codes form an important class of quantum codes. Since the error probability of bit-flip is less than the error probability of phase reversal, quantum error correction should take into account the asymmetric quantum channel. In this paper, based on typical constacyclic codes over finite field, two classes of asymmetric quantum error-correcting codes are obtained according to the CSS construction. These asymmetric quantum error-correcting codes are new in the sense that their parameters are not covered by the codes available in the literature and they are also optimal due to the fact that they achieve the Singleton bound of asymmetric quantum error-correcting codes.