  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.
