Evaluating Hybrid Quantum-Classical Models for Reduced-Order Brain Deformation Dynamics

We evaluate hybrid quantum-classical machine learning for the reduced-order prediction of spatiotemporal brain deformation fields. To mitigate the computational intractability of high-dimensional displacement fields, we employ Proper Orthogonal Decomposition (POD) to project the data into a compact latent space. Within this framework, we formulate two distinct learning objectives: static temporal-to-latent regression and autoregressive latent state forecasting. We systematically benchmark compact classical baselines against both minimal and enhanced hybrid quantum architectures. Our results demonstrate that classical networks provide the strongest baselines in the present setting. For static regression, a classical POD-MLP outperforms all evaluated quantum variants, although an enhanced Variational Quantum Circuit (VQC) substantially improves upon a minimal VQC baseline. For temporal forecasting, a classical POD-LSTM delivers superior predictive accuracy and statistical robustness compared to an enhanced Quantum LSTM (QLSTM) across varying history windows and random initializations. Overall, this study establishes reduced-order physical field learning as a rigorous testbed for near-term QML, highlighting that while hybrid enhancements successfully recover expressivity in weak quantum circuits, classical architectures retain a definitive advantage in both fidelity and stability.