Near-deterministic quantum search algorithm without phase design

TL;DR

This paper introduces a near-deterministic quantum search algorithm that improves success probability without requiring precise phase design, using a rescaled diffusion operator to enhance Grover's algorithm.

Contribution

It proposes a novel quantum search algorithm that avoids complex phase design by incorporating a rescaled diffusion operator, achieving near-deterministic performance.

Findings

Success probability is improved with minimal additional queries.

The algorithm works for search spaces of size 8, 16, and 32.

No precise phase tuning is required, simplifying implementation.

Abstract

Grover's algorithm solves the unstructured search problem. Grover's algorithm can find the target state with certainty only if searching one out of four. Designing the deterministic search algorithm can avoid any repetition of the algorithm, especially when Grover's algorithm is a subroutine in other algorithms. 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. A near-deterministic quantum search algorithm without the phase design is proposed. The 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. The success probability of Grover's algorithm is improved by the partial diffusion operator in two different ways. The possible cost is one or two more queries to the oracle. The deterministic search algorithm is also designed when searching one out of eight, sixteen, and thirty-two.