北京邮电大学学报

  • EI核心期刊

北京邮电大学学报 ›› 2024, Vol. 47 ›› Issue (6): 44-49.

• • 上一篇    

求解向量值函数线性结构的量子算法

吴宇航1,张凤荣2,唐国尧1,韦永壮3,王保仓2   

  1. 1.中国矿业大学 计算机科学与技术学院
    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
    3.桂林电子科技大学 广西密码学与信息安全重点实验室


  • 收稿日期:2024-02-29 修回日期:2024-04-28 出版日期:2024-12-28 发布日期:2024-10-29
  • 通讯作者: 张凤荣 E-mail:zhfl203@163.com
  • 基金资助:
     国家自然科学基金项目(62372346)

Quantum Algorithms for Finding Linear Structures of Vector-valued Functions

  • Received:2024-02-29 Revised:2024-04-28 Online:2024-12-28 Published:2024-10-29

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判定向量值函数是否具有线性结构。

关键词: Bernstein-Vazirani算法, 向量值函数, 线性结构

Abstract: 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 re-proved. 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.

Key words: Bernstein-Vazirani algorithm, vector-valued function, linear structure

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