Research

Quantum Physics-Informed Neural Networks

In financial mathematics, partial differential equations (PDEs) are fundamental to the modeling and valuation of financial derivatives, risk management, and optimal portfolio strategies. Classical numerical methods, such as finite difference methods (FDM), finite element methods (FEM), and Monte Carlo simulations, often struggle with high-dimensional PDEs, non-linearity, and path-dependency inherent in modern financial models. Recently, Physics-Informed Neural Networks (PINNs) have emerged as a promising mesh-free alternative that leverages deep learning to solve PDEs by embedding physical laws into the loss function. However, the computational cost and scalability issues remain a bottleneck for large-scale financial applications.

Quantum computing, with its ability to represent and process information in high-dimensional Hilbert spaces, offers a new frontier for accelerating scientific computing tasks. Quantum Neural Networks (QNNs), especially in hybrid quantum-classical frameworks, have demonstrated potential in optimization and differential equation solving. We aim to investigate or demonstrate quantum advantage, if any, of QPINN over classical PINNs. This proposal introduces a novel research direction: Quantum Physics-Informed Neural Networks (QPINNs) for solving PDEs in quantitative finance. The central idea is to exploit quantum computing capabilities to address limitations in current PINN models and offer new, efficient methodologies for computational finance.