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
吴宇航 1张凤荣 2唐国尧 1韦永壮 3王保仓2
作者信息
- 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
- 折叠
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.
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.
关键词
Bernstein-Vazirani算法/向量值函数/线性结构Key words
Bernstein-Vazirani algorithm/vector-valued function/linear structure引用本文复制引用
出版年
2024
NETL
NSTL
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