发表机构
University of Bologna（博洛尼亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为量子物理信息神经网络（QPINNs）建立了非渐近的懒惰训练理论，证明在足够大的电路宽度下，其非线性梯度流可被线性化NTK模型定量逼近，界依赖于量子比特数、电路深度、光锥几何及PDE解域维度。
AI 中文摘要
我们研究了量子物理信息神经网络（QPINNs）在求解具有Dirichlet边界条件的二阶椭圆型偏微分方程时的梯度流训练动态。我们考虑将参数化量子电路作为函数逼近器，并通过神经正切核（NTK）的视角分析其过参数化机制。我们的贡献在于为QPINNs及其变分形式建立了一个非渐近的懒惰训练理论：我们证明了，对于足够大的电路宽度，非线性梯度流可以被线性化的NTK模型定量逼近，其显式界取决于量子比特数、电路深度、电路光锥几何以及偏微分方程解的定义域的维度。
英文摘要
We study the gradient-flow training dynamics of quantum physics-informed neural networks (QPINNs) for the solution of second-order elliptic partial differential equations with Dirichlet boundary conditions. We consider parameterized quantum circuits as function approximators and analyze their overparameterized regime through the lens of the neural tangent kernel (NTK). Our contribution is a nonasymptotic lazy-training theory for QPINNs and their variational formulation: we prove that, for sufficiently large circuit width, the nonlinear gradient flow is quantitatively approximated by a linearized NTK model, with explicit bounds depending on the number of qubits, circuit depth, circuit light-cone geometry, and the dimension of the domain of the solution to the PDE.
