Quantum Algorithm for Determining a Complex Number String

Here, we discuss the generalized Bernstein-Vazirani algorithm for determining a complex number string. The generalized algorithm presented here has the following structure. Given the set of complex values {a₁, a₂, a₃,…, a_N} and a special function g: C→ C, we determine N real parts of values of the function l(a₁), l(a₂), l(a₃),…, l(a_N) and N imaginary parts of values of the function h(a₁), h(a₂), h(a₃),…, h(a_N) simultaneously. That is, we determine the N complex values g(a_j) = l(a_j) + ih(a_j) simultaneously. We mention the two computing can be done in parallel computation method simultaneously. The speed of determining the string of complex values is shown to outperform the best classical case by a factor of N. Additionally, we propose a method for calculating many different matrices A, B, C,.. into g(A), g(B), g(C),.. simultaneously. The speed of solving the problem is shown to outperform the classical case by a factor of the number of the elements of them. We hope our discussions will give a first step to the quantum simulation problem.