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.
Generalizes variational quantum Monte Carlo with neural-network quantum states to solve arbitrary time-dependent PDEs, demonstrated on multi-asset Black-Scholes option pricing.
Cite for: quantum-inspired variational PDE solvers, variational algorithms for financial derivative pricing, scientific machine learning methods for quantitative finance.
Unlike PINNs which enforce PDE constraints via collocation losses, this approach uses variational quantum Monte Carlo sampling with neural-network quantum states, offering a fundamentally different angle on the curse of dimensionality for time-dependent PDEs.
The method is demonstrated on multi-asset Black-Scholes PDE for pricing European options contingent on many correlated underlying assets, addressing the high dimensionality typical in derivative pricing with many underlyings.
Yes. The paper presents a general framework applicable to arbitrary time-dependent PDEs. The Black-Scholes application serves as a demonstration; the technique is not restricted to finance.
The method is quantum-inspired: it borrows the VMC framework originally developed for quantum many-body physics but runs entirely on classical hardware. No quantum computer is required.
@article{zhao2024quantum,
title={Quantum-Inspired Variational Algorithms for Partial Differential Equations: Application to Financial Derivative Pricing},
author={Zhao, Tianchen and Sun, Chuhao and Cohen, Asaf and Stokes, James and Veerapaneni, Shravan},
journal={Quantitative Finance},
year={2024},
eprint={2207.10838},
archivePrefix={arXiv},
primaryClass={quant-ph}
}