求解向量值函数线性结构的量子算法  

Quantum Algorithms for Finding Linear Structures of Vector-Valued Functions

作　　者：吴宇航 张凤荣[2] 唐国尧 韦永壮[3] 王保仓[2] WU Yuhang;ZHANG Fengrong;TANG Guoyao;WEI Yongzhuang;WANG Baocang(School of Computer Science and Technology,China University of Mining and Technology,Xuzhou 221116,China;State Key Laboratory of Integrated Services Networks,Xidian University,Xi’an 710071,China;Guangxi Key Laboratory of Cryptography and Information Security,Guilin University of Electronic Technology,Guilin 541004,China)

机构地区：[1]中国矿业大学计算机科学与技术学院,徐州221116 [2]西安电子科技大学空天地一体化综合业务网全国重点实验室,西安710071 [3]桂林电子科技大学广西密码学与信息安全重点实验室,桂林541004

出　　处：《北京邮电大学学报》2024年第6期44-49,共6页Journal of Beijing University of Posts and Telecommunications

基　　金：国家自然科学基金项目(62372346)。

摘　　要：为求解向量值函数线性结构的广义Bernstein-Vazirani算法,研究了利用Bernstein-Vazirani算法求解向量值函数线性结构量子算法的可行性。首先,根据单周期单陪集的特性,重新证明了利用Bernstein-Vazirani算法求解原始Simon问题的正确性;其次,对多弱周期多陪集等拓展的Simon问题进行分析,证明了利用Bernstein-Vazirani算法求解拓展Simon问题的可行性;最后,证明了利用Bernstein-Vazirani算法能以极大的概率获取向量值函数的线性结构。To solve the generalized Bernstein-Vazirani algorithm for the linear structure of vector-valued functions,this paper studied the feasibility of using the Bernstein-Vazirani algorithm to solve such quantum algorithms.Firstly,according to the characteristics of single period and single coset,the correctness of solving the original Simon’s problem by applying the Bernstein-Vazirani algorithm is reproved.Secondly,extended Simon’s problems such as multiple weak periods and multiple cosets are analyzed,and the feasibility of using the Bernstein-Vazirani algorithm to solve the extended Simon’s problems is proved.Finally,it is demonstrated that by the Bernstein-Vazirani algorithm,it is possible with great probability to determine whether there is a linear structure for a vector-valued function.

关 键 词：Bernstein-Vazirani算法 向量值函数 线性结构 

分 类 号：TN918.4[电子电信—通信与信息系统]