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

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.