发表机构
Lawrence Technological University; North Carolina State University（劳伦斯理工大学; 北卡罗来纳州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究评估混合量子-经典模型用于脑变形场降阶预测，发现经典网络在静态回归和时间预测中均优于量子变体，确立降阶物理场学习为QML测试平台。
AI 中文摘要
我们评估了混合量子-经典机器学习在高维时空脑变形场降阶预测中的应用。为缓解高维位移场带来的计算不可行性，我们采用本征正交分解（POD）将数据投影到紧凑的潜在空间中。在此框架下，我们提出了两个不同的学习目标：静态的时间到潜在回归和自回归潜在状态预测。我们系统地将紧凑的经典基线模型与最小及增强的混合量子架构进行基准比较。结果表明，在当前设定下，经典网络提供了最强的基线。对于静态回归，经典POD-MLP在所有评估的量子变体中表现最佳，尽管增强的变分量子电路（VQC）相比最小VQC基线有显著改进。对于时间预测，经典POD-LSTM在变化的历史窗口和随机初始化下，相比增强的量子LSTM（QLSTM）提供了更优越的预测准确性和统计稳健性。总体而言，本研究将降阶物理场学习确立为近期量子机器学习（QML）的严格测试平台，强调虽然混合增强能成功恢复弱量子电路的表达能力，但经典架构在保真度和稳定性方面仍保持决定性优势。
英文摘要
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.
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