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arXiv · 2410.03926

Quantum Monte Carlo Integration for Simulation-Based Optimisation

Jingjing Cui·Philippe J. S. de Brouwer·Steven Herbert·Philip Intallura·Cahit Kargi·Georgios Korpas·Alexandre Krajenbrink·William Shoosmith·Ifan Williams·Ban Zheng
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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.

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Jingjing Cui, Philippe J. S. de Brouwer, Steven Herbert, Philip Intallura, Cahit Kargi, Georgios Korpas, Alexandre Krajenbrink, William Shoosmith, Ifan Williams, Ban Zheng. 2024-10-04. Quantum Monte Carlo Integration for Simulation-Based Optimisation. https://arxiv.org/abs/2410.03926

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