A Quantum Walk Enhanced Grover Search Algorithm for Global Optimization

TL;DR

This paper introduces a hybrid quantum algorithm combining continuous-time quantum walks with Grover's search to enhance global optimization efficiency by leveraging quantum tunneling effects.

Contribution

It proposes a novel hybrid approach that accelerates search and improves threshold selection in Grover's algorithm using quantum walks.

Findings

The hybrid algorithm outperforms traditional Grover search.

Quantum tunneling improves early-stage threshold estimation.

Results surpass classical heuristic algorithms.

Abstract

One of the significant breakthroughs in quantum computation is Grover's algorithm for unsorted database search. Recently, the applications of Grover's algorithm to solve global optimization problems have been demonstrated, where unknown optimum solutions are found by iteratively improving the threshold value for the selective phase shift operator in Grover rotation. In this paper, a hybrid approach that combines continuous-time quantum walks with Grover search is proposed so that the search is accelerated with improved threshold values. By taking advantage of the quantum tunneling effect, better threshold values can be found at the early stage of the search process so that the sharpness of probability improves. The results between the new algorithm, existing Grover search, and classical heuristic algorithms are compared.