Solving Differential Equation with Quantum-Circuit Enhanced Physics-Informed Neural Networks

2025/09/17 by Rachana Soni, Soni, Rachana
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Model Reduction and Neural Networks #Neural Networks and Applications #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2509.16247

openalex publication_date 2025/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

I present a simple hybrid framework that combines physics informed neural networks (PINNs) with features generated from small quantum circuits. As a proof of concept, a first-order equation is solved by feeding quantum measurement probabilities into the neural model. The architecture enforces the initial condition exactly, and training is guided by the ODE residual loss. Numerical results show that the hybrid model reproduces the analytical solution, illustrating the potential of quantum-enhanced PINNs for differential equation solving.

Citations

• Physics-informed machine learning
• Fourier Neural Operator for Parametric Partial Differential Equations
• Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Quantum Computation by Adiabatic Evolution

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