Quantum Monte Carlo Integration for Simulation-Based Optimisation

TL;DR

This paper explores the integration of quantum Monte Carlo algorithms into financial simulation-based optimization, analyzing errors, resource requirements, and the impact of quantum noise on practical financial problems.

Contribution

It provides a comprehensive error analysis, resource estimation, and benchmarking of quantum Monte Carlo methods applied to financial optimization problems, including error mitigation strategies.

Findings

Quantum algorithms can estimate financial risk measures with potential efficiency gains.

Error mitigation improves the accuracy of quantum amplitude estimation in noisy environments.

Quantum Monte Carlo methods are feasible for certain financial optimization tasks with current or near-term quantum devices.

Abstract

We investigate the feasibility of integrating quantum algorithms as subroutines of simulation-based optimisation problems with relevance to and potential applications in mathematical finance. To this end, we conduct a thorough analysis of all systematic errors arising in the formulation of quantum Monte Carlo integration in order to better understand the resources required to encode various distributions such as a Gaussian, and to evaluate statistical quantities such as the Value-at-Risk (VaR) and Conditional-Value-at-Risk (CVaR) of an asset. Finally, we study the applicability of quantum Monte Carlo integration for fundamental financial use cases in terms of simulation-based optimisations, notably Mean-Conditional-Value-at-Risk (Mean-CVaR) and (risky) Mean-Variance (Mean-Var) optimisation problems. In particular, we study the Mean-Var optimisation problem in the presence of noise on a quantum device, and benchmark a quantum error mitigation method that applies to quantum amplitude estimation -- a key subroutine of quantum Monte Carlo integration -- showcasing the utility of such an approach.