用流模型提升量子态采样，更准更快求解复杂量子系统基态。
Improved Ground State Estimation in Quantum Field Theories via Normalising Flow-Assisted Neural Quantum States
- 用连续流模型替代传统采样，分离采样与变分参数优化。
- 50自旋系统下误差低于自回归神经量子态，且收敛稳定。
- 适合长程关联和体积律纠缠的量子系统，可扩展性强。
我们提出一种混合变分框架，将归一化流采样器融入神经量子态（NQS），以提升多体量子波函数的表达能力和训练性。该方法通过学习一个连续流模型，将采样任务从变分答案中解耦，聚焦于希尔伯特空间中由振幅支持的离散子空间。相比马尔可夫链蒙特卡洛（MCMC）和自回归方法，尤其在具有长程关联和体积律纠缠的区域表现更优。应用于具有短程与长程相互作用的横向场伊辛模型，本方法在地面态能量误差上达到与最优矩阵乘积态相当的水平，且低于自回归型NQS。对于最多50个自旋的系统，我们在广泛耦合强度范围内实现了高精度与鲁棒收敛，甚至在其他方法失效的区域仍表现良好。结果表明，流辅助采样是可扩展的量子模拟工具，为高维希尔伯特空间中学习表达性量子态提供了新路径。
原文摘要 · Abstract (English)
We propose a hybrid variational framework that enhances Neural Quantum States (NQS) with a Normalising Flow-based sampler to improve the expressivity and trainability of quantum many-body wavefunctions. Our approach decouples the sampling task from the variational ansatz by learning a continuous flow model that targets a discretised, amplitude-supported subspace of the Hilbert space. This overcomes limitations of Markov Chain Monte Carlo (MCMC) and autoregressive methods, especially in regimes with long-range correlations and volume-law entanglement. Applied to the transverse-field Ising model with both short- and long-range interactions, our method achieves comparable ground state energy errors with state-of-the-art matrix product states and lower energies than autoregressive NQS. For systems up to 50 spins, we demonstrate high accuracy and robust convergence across a wide range of coupling strengths, including regimes where competing methods fail. Our results showcase the utility of flow-assisted sampling as a scalable tool for quantum simulation and offer a new approach toward learning expressive quantum states in high-dimensional Hilbert spaces.
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