Quantum Grover Adaptive Search for Discrete Simulation Optimization

TL;DR

This paper introduces SOGAS, a quantum algorithm leveraging Grover search for discrete simulation optimization, achieving quadratic speedup and demonstrating empirical quantum advantage.

Contribution

It presents the first Grover-search-based quantum algorithm for discrete simulation optimization with a novel quantum oracle and binary-search framework.

Findings

SOGAS achieves quadratic speedup in query complexity.

Numerical experiments show SOGAS outperforms classical methods.

Empirical evidence suggests quantum advantage in the problem domain.

Abstract

Quantum computing has advanced rapidly in recent years and has shown advantages in a variety of domains. In this paper, we investigate its potential for discrete simulation optimization in the fixed-confidence setting, a fundamental problem in the simulation literature. We first introduce a quantum simulation oracle that prepares a coherent superposition over all candidate solutions and provides the foundation for quantum algorithm design. Based on this oracle, we develop the first Grover-search-based quantum algorithm for discrete simulation optimization, called SOGAS. In particular, SOGAS uses a binary-search framework to progressively eliminate suboptimal solutions while carefully controlling the error probability, and eventually identifies a set of near-optimal solutions. We prove that SOGAS returns a near-optimal solution with probability at least the prescribed confidence level and achieves a quadratic speedup in the dependence of query complexity on the number of candidate solutions. Numerical experiments further show that SOGAS substantially outperforms classical benchmarks and provide empirical evidence for quantum advantage in discrete simulation optimization.