# On Physics-Informed Neural Networks for Quantum Computers

arXiv: https://arxiv.org/abs/2209.14754 · HTML: https://mlsanity.com/paper/2209.14754/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Sep 2022.

## Built on by (most cited first, 5 of 5)

- [QCPINN: Quantum-Classical Physics-Informed Neural Networks for Solving PDEs](https://mlsanity.com/paper/2503.16678/) (2025)
- [Partitioned Hybrid Quantum Fourier Neural Operators for Scientific Quantum Machine Learning](https://mlsanity.com/paper/2507.08746/) (2025)
- [A Quantum Neural Network Transfer-Learning Model for Forecasting Problems with Continuous and Discrete Variables](https://mlsanity.com/paper/2503.07633/) (2025)
- [Wavelet-Accelerated Physics-Informed Quantum Neural Network for Multiscale Partial Differential Equations](https://mlsanity.com/paper/2512.08256/) (2025)
- [Quantum-Classical Physics-Informed Kolmogorov-Arnold Networks for Solving Fuzzy Differential Equations](https://mlsanity.com/paper/2608.08782/) (2026)

## Abstract (arXiv)

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.