Quantum Monte Carlo Integration for Simulation-Based Optimisation
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.
Cite
@article{arxiv.2410.03926,
title = {Quantum Monte Carlo Integration for Simulation-Based Optimisation},
author = {Jingjing Cui and Philippe J. S. de Brouwer and Steven Herbert and Philip Intallura and Cahit Kargi and Georgios Korpas and Alexandre Krajenbrink and William Shoosmith and Ifan Williams and Ban Zheng},
journal= {arXiv preprint arXiv:2410.03926},
year = {2024}
}