非对称量子乘积-张量积码

Asymmetric quantum product and tensor product codes

针对绝大多数量子信道模型中发生量子比特翻转错误概率远小于发生量子相位翻转错误概率这一非对称的物理现象,基于经典乘积码与张量积码构造了非对称量子乘积-张量积码.利用经典乘积码来纠正量子比特翻转错误,利用经典张量积码来纠正量子相位翻转错误.当2个组成子码皆满足对偶包含条件时,经典乘积码与张量积码满足对偶包含条件.基于3类满足对偶包含条件的经典纠错码,构造了具有新的参数非对称量子纠错码.结果表明,该类非对称量子乘积-张量积码具有显著的非对称性.通过与已存在的非对称量子纠错码对比可以发现,所构造的部分非对称量子乘积-张量积码的参数优于其他已知的非对称量子纠错码.

To solve the physical phenomenon that the probability of the quantum qubit-flipping errors is much less than that of the phase-flipping errors in many quantum channel models,the asymmetric quantum error-correcting codes(AQECCs),called as asymmetric quantum product and tensor product codes,are constructed based on classical product codes and tensor product codes.The product codes are used to correct the qubit-flipping errors and the tensor product codes are used to correct the phase-flipping errors.If the two component codes satisfy the dual containing conditions,then the resultant product codes and tensor product codes satisfy the dual containing conditions.A new class of AQECCs is constructed based on three classes of classical error-correcting codes satisfying the dual containing restrictions.The results show that that the proposed asymmetric quantum product and tensor product codes have obvious asymmetries.Compared with the known AQECCs,parts of the asymmetric quantum product and tensor product codes have better parameters than the known AQECCs.