具有量子数对称性的自回归神经量子态
Autoregressive Neural Quantum States with Quantum Number Symmetries
AI总结：
针对自回归神经量子态难以纳入量子数对称性的问题，提出适配任意数量该类对称性的通用框架，在分子电子结构计算中实现超一个数量级加速且全分子达到化学精度，拓展了变分拟设的对称性工具。
摘要：
神经量子态已成为量子多体系统变分蒙特卡罗模拟中一类强大且通用的拟设（ansatz）。其中尤为突出的是自回归神经网络量子态（ANQS），它兼具深度神经网络的表达能力，还具备快速无偏采样的流程。然而，自回归采样的非选择性使得纳入量子数对称性颇具挑战。本研究中，我们开发了一个通用框架，使自回归采样能够适配任意数量的量子数对称性。我们通过对一系列具有此类多重对称性的分子开展电子结构计算，展示了该框架的优势。我们达到了先前工作中报道的精度水平，同时实现了超过一个数量级的加速，并且对所有研究的分子都达到了化学精度，这是此前未有报道的里程碑成果。结合现有纳入空间对称性的研究工作，我们的方法拓展了对所有变分拟设都至关重要的对称性工具箱，让ANQS更有望成为研究复杂量子多体系统的有竞争力的选择。
英文摘要：
Neural quantum states have established themselves as a powerful and versatile family of ansatzes for variational Monte Carlo simulations of quantum many-body systems. Of particular prominence are autoregressive neural quantum states (ANQS), which enjoy the expressibility of deep neural networks, and are equipped with a procedure for fast and unbiased sampling. Yet, the non-selective nature of autoregressive sampling makes incorporating quantum number symmetries challenging. In this work, we develop a general framework to make the autoregressive sampling compliant with an arbitrary number of quantum number symmetries. We showcase its advantages by running electronic structure calculations for a range of molecules with multiple symmetries of this kind. We reach the level of accuracy reported in previous works with more than an order of magnitude speedup and achieve chemical accuracy for all studied molecules, which is a milestone unreported so far. Combined with the existing effort to incorporate space symmetries, our approach expands the symmetry toolbox essential for any variational ansatz and brings the ANQS closer to being a competitive choice for studying challenging quantum many-body systems.
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