自回归投影量子蒙特卡洛：从厄米到非厄米视角
Autoregressive Projective Quantum Monte Carlo: From a Hermitian to a Non-Hermitian Perspective
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中文总结 AI 辅助
本研究提出自回归投影量子蒙特卡洛（PQMC）框架，以循环神经网络引导随机动力学，经基准测试，该方法在各类系统中精度更高且计算成本可控，为量子多体系统低能态模拟提供了新途径。
中文摘要 AI 辅助
精确确定量子多体系统的基态性质仍是核心挑战。本研究引入自回归投影量子蒙特卡洛（PQMC）框架，利用循环神经网络（RNN）引导随机动力学。通过在PQMC中融入自回归采样，与标准无引导PQMC相比，我们的方法在保留多项式计算成本的同时，实现了精度的大幅提升。我们将该方法与传统变分RNN ansatz（变分近似）进行基准测试，发现无论系统规模、哈密顿量是否为厄米或非厄米，自回归PQMC始终能达到更低的能量和更高的保真度。研究结果凸显了神经引导PQMC方法的通用性与强大性，为复杂量子多体系统低能态的可扩展模拟铺平了道路。
英文摘要
Accurately determining the ground-state properties of quantum many-body systems remains a central challenge. In this work, we introduce an autoregressive projective quantum Monte Carlo (PQMC) framework that leverages recurrent neural networks (RNNs) to guide the stochastic dynamics. By incorporating autoregressive sampling into PQMC, we demonstrate substantial improvements in accuracy compared to standard unguided PQMC, while retaining polynomial computational cost. We benchmark our approach against conventional variational RNN ansätze and find that the autoregressive PQMC consistently achieves lower energies and higher fidelity, regardless of system size or whether the Hamiltonian is Hermitian or non-Hermitian. Our results highlight the versatility and power of neural-guided PQMC methods, paving the way for promising scalable simulations of low-energy states in complex quantum many-body systems.
