On Physics-Informed Neural Networks for Quantum Computers

TL;DR

This paper explores the development and performance of Quantum Physics-Informed Neural Networks (PINNs) using Quantum Processing Units to solve the Poisson problem, highlighting differences from classical PINNs and future research directions.

Contribution

It introduces a quantum PINN framework, analyzes optimizer impacts, and compares quantum and classical PINN methods for solving PDEs.

Findings

Basic SGD outperforms advanced optimizers in quantum PINNs.

Quantum PINNs show different training landscape characteristics than classical PINNs.

Identifies future challenges in quantum PINN development.

Abstract

Physics-Informed Neural Networks (PINN) emerged as a powerful tool for solving scientific computing problems, ranging from the solution of Partial Differential Equations to data assimilation tasks. One of the advantages of using PINN is to leverage the usage of Machine Learning computational frameworks relying on the combined usage of CPUs and co-processors, such as accelerators, to achieve maximum performance. This work investigates the design, implementation, and performance of PINNs, using the Quantum Processing Unit (QPU) co-processor. We design a simple Quantum PINN to solve the one-dimensional Poisson problem using a Continuous Variable (CV) quantum computing framework. We discuss the impact of different optimizers, PINN residual formulation, and quantum neural network depth on the quantum PINN accuracy. We show that the optimizer exploration of the training landscape in the case of quantum PINN is not as effective as in classical PINN, and basic Stochastic Gradient Descent (SGD) optimizers outperform adaptive and high-order optimizers. Finally, we highlight the difference in methods and algorithms between quantum and classical PINNs and outline future research challenges for quantum PINN development.