Quantum Physics Informed Neural Networks

Abstract

In this work, we propose a method to implement a quantum version of the physics informed neural network (QPINN) to solve differential equations. We use quantum circuits that can be modelled as Fourier series approximation of the desired function to encode the solution of a differential equation. We resort to parameter shift rules to compute the exact derivatives of this quantum circuit and hence to define a physics loss. Further we enforce the boundary conditions of our differential equations in the loss function of the QPINN to obtain a unique solution to the given differential equation. We present our preliminary results for two instances of 1D Poisson equation.