Embodiment of quantum physics informed neural networks to solve differential equation over a continuous-wave quantum computer

Physics-Informed Neural Networks (PINNs) embed physical laws into neural networks to solve differential equations. Recent advancements extend PINNs into the quantum domain as Quantum Physics-Informed Neural Networks (QPINNs).

The goal of our work is to assess the potential of QPINNs by simulating continuous variable quantum computers, specifically photonic architectures where information is carried through qumodes in waveguides. In a specific instance involving the solution of a trivial ordinary differential equation, used primarily to observe the initial results, we observed that QPINNs provided significantly better accuracy compared to classical PINNs, while using comparable architectures, hinting at their potential as a more precise alternative.

Our results demonstrate QPINN's effectiveness in solving multi-dimensional and higher-order differential equations, showcasing their capability to handle problems beyond state of the art. We applied QPINNs to various specific problems to address their strengths and limitations. The findings indicate a promising pathway for QPINNs, especially in addressing more complex problems, such as Navier-Stokes or Schroedinger's equations.

These findings highlight the utility of QPINNs, emphasizing their potential to handle native continuous quantum data and suggesting improvements like hybrid and fully quantum subroutines. This positions QPINNs as valuable tools in the NISQ era, with significant implications for computational methods in quantum physics and engineering.