The effect of sample property on optimum search by quantum computing

Quantum computers are designed based on quantum mechanics. They have special features such as entanglement and parallelism, which do not exist in classic mechanics-based computers. Therefore, quantum algorithms have their own privilege for solving some problems compare to classic ones such as finding the minimum value of a function in optimization problems. For instance, finding the minimum of N elements in quantum method is faster than classic method. In this case, having information about N elements of distribution does not reduce the cost of finding the minimum value in classic method due to linear search of each element. But in quantum method, all elements are simultaneously considered as well as distribution information, which is related to the whole elements. This distribution information effectively influences on finding the minimum value. Numerical simulations show having mean and variance of N elements can reduces the cost of minimum finding through quantum method by %40. Furthermore, it is shown the greater variance causes less cost.