Quantum Physics-Informed Neural Network for Scattered Wavefields

Quantum Machine Learning has emerged as a promising paradigm for scientific computing, particularly when combined with Physics-Informed Neural Networks (PINNs) to solve partial differential equations. In this work, we introduce a Quantum Physics-Informed Neural Network (QPINN) framework for solving the Helmholtz equation in the context of scattered wavefield modeling. To overcome the numerical instabilities associated with point-source singularities commonly encountered in classical PINNs, we adopt the Lippmann-Schwinger integral formulation. The proposed hybrid architecture couples a classical neural-network encoder with a variational quantum circuit, enabling the learning of expressive, dynamically generated feature embeddings. Numerical experiments conducted on a heterogeneous velocity model demonstrate that the proposed QPINN achieves high solution accuracy while requiring significantly fewer trainable parameters compared to analogous classical neural network architectures. Our results highlight the potential of hybrid quantum-classical approaches as efficient and scalable alternatives for wavefield simulation and for solving wave-based inverse problems.