Quantum Monte Carlo Integration for Simulation-Based Optimisation

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Hauptverfasser: Cui, Jingjing, de Brouwer, Philippe J. S., Herbert, Steven, Intallura, Philip, Kargi, Cahit, Korpas, Georgios, Krajenbrink, Alexandre, Shoosmith, William, Williams, Ifan, Zheng, Ban
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Veröffentlicht: 2024
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author Cui, Jingjing
de Brouwer, Philippe J. S.
Herbert, Steven
Intallura, Philip
Kargi, Cahit
Korpas, Georgios
Krajenbrink, Alexandre
Shoosmith, William
Williams, Ifan
Zheng, Ban
author_facet Cui, Jingjing
de Brouwer, Philippe J. S.
Herbert, Steven
Intallura, Philip
Kargi, Cahit
Korpas, Georgios
Krajenbrink, Alexandre
Shoosmith, William
Williams, Ifan
Zheng, Ban
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2410_03926
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Quantum Monte Carlo Integration for Simulation-Based Optimisation
Cui, Jingjing
de Brouwer, Philippe J. S.
Herbert, Steven
Intallura, Philip
Kargi, Cahit
Korpas, Georgios
Krajenbrink, Alexandre
Shoosmith, William
Williams, Ifan
Zheng, Ban
Quantum Physics
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.
title Quantum Monte Carlo Integration for Simulation-Based Optimisation
topic Quantum Physics
url https://arxiv.org/abs/2410.03926