An optimized quantum minimum searching algorithm with sure-success probability and its experiment simulation with Cirq

TL;DR

This paper introduces an optimized quantum minimum searching algorithm that guarantees success probability, improves accuracy and efficiency over previous methods, and is validated through Cirq-based simulations.

Contribution

It presents a novel quantum minimum search algorithm with sure-success probability using Grover-Long search and dynamic strategies, along with optimized oracle circuits.

Findings

Higher success rate than DHA algorithm

Reduced number of gates in oracle circuit

Validated feasibility through Cirq simulation

Abstract

Finding a minimum is an essential part of mathematical models, and it plays an important role in some optimization problems. Durr and Hoyer proposed a quantum searching algorithm (DHA), with a certain probability of success, to achieve quadratic speed than classical ones. In this paper, we propose an optimized quantum minimum searching algorithm with sure-success probability, which utilizes Grover-Long searching to implement the optimal exact searching, and the dynamic strategy to reduce the iterations of our algorithm. Besides, we optimize the oracle circuit to reduce the number of gates by the simplified rules. The performance evaluation including the theoretical success rate and computational complexity shows that our algorithm has higher accuracy and efficiency than DHA algorithm. Finally, a simulation experiment based on Cirq is performed to verify its feasibility.