Hybrid quantum physics-informed neural network: Towards efficient learning of high-speed flows

This study benchmarks hybrid quantum physics-informed neural network (HQPINN) to model high-speed flows, compared against classical physics-informed neural networks (PINNs) and fully quantum neural networks (QNNs). The HQPINN architecture integrates a parameterized quantum circuit (PQC) with a classical neural network in parallel, trained via a physics-informed loss. Across harmonic, non-harmonic, and transonic benchmarks, HQPINNs demonstrate balanced performance, offering competitive accuracy and stability with reduced parameter cost. Quantum PINNs are highly efficient for harmonic problems achieving the lowest loss with minimal parameters due to their Fourier structure, but struggle to generalize in non-harmonic settings involving shocks and discontinuities. HQPINNs mitigate such artifacts, and with sufficient parameterization, can match the performance of classical models in more complex regimes. Although constrained by current quantum emulation costs and scalability, HQPINNs show promise as general-purpose solvers, offering parameter efficiency with robust fallback behavior, particularly suited for problems where the nature of the solution is not known a-priori.