Near-deterministic quantum search algorithm without phase control

Grover's algorithm solves the unstructured search problem. Grover's algorithm can find the target item with certainty only if searching one out of four. Grover's algorithm can be deterministic if the phase of the oracle or the diffusion operator is delicately designed. The precision of the phases could be a problem. We propose a near-deterministic quantum search algorithm without the phase control. Our algorithm has the same oracle and diffusion operators as Grover's algorithm. One additional component is the rescaled diffusion operator. It acts partially on the database. We show how to improve the success probability of Grover's algorithm by the partial diffusion operator in two different ways. The possible cost is one or two more queries to the oracle. We also design the deterministic search algorithm when searching one out of eight, sixteen, and thirty-two.