Research on Quantum Searching Algorithms Based on Phase Shifts

One iterative in Grover's original quantum search algorithm consists of two Hadamard–Walsh transformations, a selective amplitude inversion and a diffusion amplitude inversion. We concentrate on the relation among the probability of success of the algorithm, the phase shifts, the number of target items and the number of iterations via replacing the two amplitude inversions by phase shifts of an arbitrary φ = φ(0 ≤ φ, φ ≤ 2π). Then, according to the relation we find out the optimal phase shifts when the number of iterations is given. We present a new quantum search algorithm based on the optimal phase shifts of 1.018 after 0.5π/√M/N iterations. The new algorithm can obtain either a single target item or multiple target items in the search space with the probability of success at least 93.43%. (general)