Quantum-Enhanced Simulation-Based Optimization

TL;DR

This paper presents a quantum-enhanced algorithm that leverages Quantum Amplitude Estimation to significantly speed up simulation-based optimization, applicable to both continuous and discrete problems, demonstrated on portfolio and inventory management tasks.

Contribution

It introduces a novel quantum algorithm combining QAE with quantum optimization techniques for improved simulation-based optimization.

Findings

Quadratic speed-up over classical Monte Carlo methods.

Successful demonstration on portfolio optimization with Value at Risk.

Effective application to inventory management problems.

Abstract

In this paper, we introduce a quantum-enhanced algorithm for simulation-based optimization. Simulation-based optimization seeks to optimize an objective function that is computationally expensive to evaluate exactly, and thus, is approximated via simulation. Quantum Amplitude Estimation (QAE) can achieve a quadratic speed-up over classical Monte Carlo simulation. Hence, in many cases, it can achieve a speed-up for simulation-based optimization as well. Combining QAE with ideas from quantum optimization, we show how this can be used not only for continuous but also for discrete optimization problems. Furthermore, the algorithm is demonstrated on illustrative problems such as portfolio optimization with a Value at Risk constraint and inventory management.