可训练嵌入的量子物理信息框架用于多物种反应扩散系统
A Trainable-Embedding Quantum Physics-Informed Framework for Multi-Species Reaction-Diffusion Systems
AI总结：
本文提出了一种可训练嵌入的量子物理信息框架，用于解决多物种反应扩散系统问题，通过比较经典与量子嵌入方法，展示了量子嵌入在精度和优化性能上的优势。
摘要：
物理信息神经网络（PINNs）和混合量子-经典扩展提供了解决偏微分方程（PDEs）的有希望的框架，通过将物理定律直接嵌入到学习过程中。在本工作中，我们研究了可训练嵌入量子物理信息神经网络（TE-QPINNs）在非线性反应扩散（RD）系统中的嵌入策略。我们引入了一种扩展的TE-QPINN（x-TE-QPINN）架构，支持经典和完全量子嵌入，使能够对基于前馈神经网络的特征映射和参数化量子电路嵌入进行受控比较。第一种架构是基于经典嵌入前馈神经网络的TE-QPINN（FNN-TE-QPINN），而后者变体是一种纯量子的，称为基于量子嵌入神经网络的TE-QPINN（QNN-TE-QPINN）。所提出的框架利用硬件高效的变分量子电路和物种特异性读取操作符来近似耦合多场动力学，同时通过物理信息损失函数强制执行控制方程、边界条件和初始条件。通过隔离嵌入机制，同时保持变分ansatz、损失公式和优化过程不变，我们分析了嵌入设计对梯度结构、参数缩放和量子资源需求的影响。对一维和二维RD方程的数值实验表明，量子嵌入可以替代经典嵌入，而不会降低解的精度，在某些情况下，比经典PINNs和具有固定嵌入的混合量子模型表现出改进的优化行为。这些结果为混合量子PDE求解器提供了架构见解，并指导了资源高效的量子物理信息学习方法的设计。
英文摘要：
Physics-informed neural networks (PINNs) and hybrid quantum-classical extensions provide a promising framework for solving partial differential equations (PDEs) by embedding physical laws directly into the learning process. In this work, we study embedding strategies for trainable embedding quantum physics-informed neural networks (TE-QPINNs) in the context of nonlinear reaction-diffusion (RD) systems. We introduce an extended TE-QPINN (x-TE-QPINN) architecture that supports both classical and fully quantum embeddings, enabling a controlled comparison between feedforward neural network-based feature maps and parameterized quantum circuit embeddings. The first architecture is the classical embedding feed-forward neural network-based TE-QPINN (FNN-TE-QPINN), while the latter variant is a purely quantum one, referred to as quantum embedding neural network-based TE-QPINN (QNN-TE-QPINN). The proposed framework employs hardware-efficient variational quantum circuits and species-specific readout operators to approximate coupled multi-field dynamics while enforcing governing equations, boundary conditions, and initial conditions through a physics-informed loss function. By isolating the embedding mechanism while keeping the variational ansatz, loss formulation, and optimization procedure fixed, we analyze the impact of embedding design on gradient structure, parameter scaling, and quantum resource requirements. Numerical experiments on one- and two-dimensional RD equations demonstrate that quantum embeddings can replace classical embeddings without degradation in solution accuracy and, in certain regimes, exhibit improved optimization behavior compared to classical PINNs and hybrid quantum models with fixed embeddings. These results provide architectural insight into hybrid quantum PDE solvers and inform the design of resource-efficient quantum physics-informed learning methods.
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