发表机构
Forschungszentrum Jülich GmbH, Peter Grünberg Institute; University of Regensburg（于利希研究中心彼得·格林伯格研究所; 雷根斯堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过一维量子Ising模型淬火动力学基准，发现神经量子态模拟的困难源于量子几何张量核的动态旋转导致小偏差几何膨胀，而非表示能力限制，并提出QGT零空间旋转作为改进TDVP算法的诊断目标。
AI 中文摘要
神经量子态（NQS）已成为模拟强关联量子系统非平衡动力学的强大框架，为高度纠缠态提供可扩展的变分表示。然而，在一些复杂度有限的物理区域中，精确的NQS模拟被发现出人意料地具有挑战性。在此，我们将一维量子Ising模型的典型淬火动力学作为受控基准进行研究。通过监督式态重构，我们建立了比先前估计更严格的经验参数数量上界，从而排除了表示能力限制作为关键障碍。相反，我们揭示了小偏差的几何膨胀这一迄今被忽视的挑战，它阻碍了无穷小时变变分原理（TDVP）的精确求解：量子几何张量（QGT）核的动态旋转可能突然赋予先前无关的参数偏差以物理意义。同一TDVP的矩阵乘积态解的稳定性表明，神经网络拟设的非线性是这种敏感性的根源。这些结果将QGT零空间旋转确定为敏感NQS动力学的几何诊断指标，并作为改进TDVP算法的具体目标。
英文摘要
Neural quantum states (NQS) have emerged as a powerful framework for simulating non-equilibrium dynamics in strongly correlated quantum systems, offering scalable variational representations of highly entangled states. Yet, accurate NQS simulations have been found to be surprisingly challenging in some physical regimes of limited complexity. Here, we address paradigmatic quench dynamics of a one-dimensional quantum Ising model as a controlled benchmark. Through supervised state reconstruction we establish substantially tighter empirical upper bounds on the required parameter count than previous estimates, ruling out representational limitations as the key obstruction. Instead, we uncover a geometric inflation of small deviations as a hitherto overlooked challenge for accurate solutions of the infinitesimal time-dependent variational principle (TDVP): the dynamical rotation of the kernel of the quantum geometric tensor (QGT) can suddenly lend physical significance to previously irrelevant parameter deviations. The stability of matrix product state solutions of the same TDVP suggests that the non-linearity of the neural network ansatz is the origin of the sensitivity. These results identify QGT-null-space rotation as a geometric diagnostic of sensitive NQS dynamics and as a concrete target for improving TDVP algorithms
Comments18 pages, 13 figures
