摘要： 根据由简单无向图构造的量子纠错码与量子稳定子码的关系，利用与图对应的对称矩阵直接给出量子稳定子码的稳定子，由此提出一种基于矩阵方法的量子纠错码构造方法，通过将子矩阵变换为循环矩阵，找到满足特殊性质的矩阵，并证明对任意素数p>3，量子MDS码［［9,5,3］］p和［［8,4,3］］p存在，对任意素数p>7，量子MDS码［［9,3,4］］p存在。

关键词: 非二元量子码, 量子MDS码, 量子稳定子码

Abstract: According to the relationship between quantum code corresponding to simple undirected graph and quantum stabilizer code, this paper gives the stabilizer of the constructed quantum stabilizer code by the matrix corresponding to the simple undirected graph, and proposes a construction method of quantum errorcorrecting code based on matrix method. It is proved that nonbinary quantum MDS codes ［［9,5,3］］p and ［［8,4,3］］p exist for all primes p>3 and ［［9,3,4］］p exist for all primes p>7 by using matrix method.

Key words: nonbinary quantum code, quantum MDS code, quantum stabilizer code

中图分类号: 

• TN918.1