生成量子稳定子码的种子生成器  

Generate seed generators for quantum stabilizer codes

作　　者：肖芳英[1] 陈汉武[1] 

机构地区：[1]东南大学计算机科学与工程学院,南京210096

出　　处：《东南大学学报（自然科学版）》2010年第1期52-57,共6页Journal of Southeast University：Natural Science Edition

基　　金：国家自然科学基金资助项目(60572071;60873101);江苏省自然科学基金资助项目(BK2007104;BK2008209);东南大学优秀博士论文基金资助项目(YBJJ0820)

摘　　要：为了解决生成量子稳定子码的码字时需先找出种子生成器的问题,将寻找种子生成器转化为解线性方程组及线性空间中向量组线性相关和线性无关问题,提出了快速判决法、排序查找法和求解方程组方法来验证找到的算子是否为合法的种子生成器.将稳定子与种子生成器同时标准化可以快速得到量子稳定子码的编码电路.给出了稳定子码种子生成器总数和编码电路所需要的2-qubit和1-qubit门数量.该方法既能用于同时包含Ⅰ型和Ⅱ型生成元的量子稳定子码,又能用于仅含Ⅰ型生成元的量子稳定子码,得到的种子生成器仅含X算子,故编码电路简单.In order to generate the quantum error-correcting codes based on the stabilizer it is needed to generate seed generator at first. The problem of finding seed generators is transformed into the problems of determining linear independence or linear dependence of vectors and finding the solutions of equation. Quick determinant method, sort and find method and solve equations method are presented to verify the validity of the operators. Through standardizing the generator of the stabilizer and the seed generators at the same time the quantum encoding circuit can be obtained quickly. The total number of seed generators of the stabilizer code and the number of 2-qubit gates and 1-qubit gates needed for the encoding circuit are given. The method introduced in this paper can be applied to the quantum stabilizer code containing both type I and type 11 generator, and it can also be ap- plied to the quantum stabilizer code containing only type I generators. The encoding circuit is simple for the seed generators only contain X operators.

关 键 词：量子纠错码 稳定子 种子生成器 编码电路 

分 类 号：TP387[自动化与计算机技术—计算机系统结构]