Quantum Algorithms for Finding Linear Structures of Vector-Valued Functions
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.
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