The Parallel Quantum Algorithm for the Class of Optimization.

For the given n numbers without any other prior information, how to obtain the minimum norm of them only by assigning their signs before them? Moreover, how to know one number is the multiplication of which ones in the given n numbers? In classical solutions, enumeration is the only way via trying one by one, whose complexity is about [Formula: see text] and this is a NP problem. In this paper, the parallel quantum algorithm is proposed to solve the two questions shown in above. Through the quantum design of linear expressions of angles in parallel circuits, only [Formula: see text] time’s quantum operations and about [Formula: see text] times’ quantum measurements in the average will give the correct answer in the successful probability of 0.97 instead of the traditional [Formula: see text] times. The example and theoretical analysis demonstrate the efficiency of the proposed method.