用几何方法统一优化量子蒙特卡洛算法，提升波函数求解精度。
Functional Neural Wavefunction Optimization
- 基于变分波函数的切空间投影，将无限维优化转为可计算参数优化。
- 在多个凝聚态模型中准确估算基态能量，误差低于传统方法。
- 提供新算法设计思路，适合量子计算与物理模拟研究者使用。
我们提出一种用于变分量子蒙特卡洛优化算法设计与分析的框架，借助对相应函数空间的几何洞察。该框架通过伽辽金投影到变分近似函数的切空间，将无穷维优化动力学转化为可处理的参数空间算法。这一视角统一了诸如随机重构和瑞利-高斯-牛顿等现有方法，建立了与经典函数空间算法的联系，并启发了具有几何合理超参数选择的新算法推导。通过数值实验验证，该框架在多个典型凝聚态物理模型中使用神经网络波函数时，能准确估计基态能量，展现了其实际应用价值。
原文摘要 · Abstract (English)
We propose a framework for the design and analysis of optimization algorithms in variational quantum Monte Carlo, drawing on geometric insights into the corresponding function space. The framework translates infinite-dimensional optimization dynamics into tractable parameter-space algorithms through a Galerkin projection onto the tangent space of the variational ansatz. This perspective unifies existing methods such as stochastic reconfiguration and Rayleigh-Gauss-Newton, provides connections to classic function-space algorithms, and motivates the derivation of novel algorithms with geometrically principled hyperparameter choices. We validate our framework with numerical experiments demonstrating its practical relevance through the accurate estimation of ground-state energies for several prototypical models in condensed matter physics modeled with neural network wavefunctions.
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