Quantum-inspired variational algorithms for partial differential equations: application to financial derivative pricing

Tianchen Zhao, Chuhao Sun, Asaf Cohen, James Stokes and Shravan Veerapaneni

Quantitative Finance, 2024, vol. 24, issue 1, 1-11

Abstract: Variational quantum Monte Carlo (VMC) combined with neural-network quantum states offers a novel angle of attack on the curse-of-dimensionality encountered in a particular class of partial differential equations (PDEs); namely, the real- and imaginary time-dependent Schrödinger equation. In this paper, we present a simple generalization of VMC applicable to arbitrary time-dependent PDEs, showcasing the technique in the multi-asset Black-Scholes PDE for pricing European options contingent on many correlated underlying assets.

Date: 2024
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DOI: 10.1080/14697688.2023.2259954

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