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