Physics Maths Engineering

On physics-informed neural networks for quantum computers


  Peer Reviewed

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.

Key Questions about 'On Physics-Informed Neural Networks for Quantum Computers'

The article "On Physics-Informed Neural Networks for Quantum Computers" by Stefano Markidis, published in Frontiers in Applied Mathematics and Statistics in September 2022, investigates the design, implementation, and performance of Physics-Informed Neural Networks (PINNs) using Quantum Processing Units (QPUs). Source

1. How can Quantum Processing Units (QPUs) enhance the performance of Physics-Informed Neural Networks (PINNs)?

The study explores the integration of QPUs with PINNs to potentially accelerate computations and improve the accuracy of solutions to differential equations, leveraging quantum computing's capabilities. Source

2. What is the impact of different optimizers on the accuracy of Quantum PINNs?

The research examines how various optimization algorithms affect the performance of Quantum PINNs, aiming to identify the most effective methods for training these networks on quantum hardware. Source

3. How does the depth of quantum neural networks influence the accuracy of Quantum PINNs?

The article investigates the relationship between the depth of quantum neural networks and the accuracy of Quantum PINNs, seeking to determine optimal network architectures for solving specific problems. Source