AI 中文总结
本综述总结了量子蒙特卡洛（QMC）方法适配多体量子信息领域的最新进展，以量子比特系统为具体场景，提出了提取非线性诊断量的统一视角，拓展了QMC的应用范围。
AI 中文摘要
量子蒙特卡洛（QMC）方法是研究强关联量子多体系统的核心数值工具之一，尤其适用于高维系统。随着量子信息为多体物理学引入了新的信息论视角与诊断手段，QMC方法也相应得到扩展，不再局限于传统线性可观测量的测量。本综述总结了QMC适配多体量子信息领域的最新进展，以量子比特或自旋-1/2系统为具体研究场景，同时确保讨论内容广泛适用于量子位元（qudit）和玻色子系统。我们提出了提取非线性诊断量的统一视角，涵盖纠缠熵、纠缠谱、混合态纠缠的Rényi负性、量子 magic 的稳定子熵，以及退相干驱动的现象，如虚时演化与退相干的相互作用、强-弱自发对称性破缺等。
英文摘要
Quantum Monte Carlo (QMC) methods are among the central numerical tools for studying strongly correlated quantum many-body systems, particularly in higher dimensions. As quantum information has introduced new information-theoretic perspectives and diagnostics into many-body physics, QMC methods have accordingly been extended beyond the measurement of conventional linear observables. This review summarizes recent progress in adapting QMC to many-body quantum-information, focusing on qubit or spin-$1/2$ systems as a concrete setting while keeping the discussion broadly applicable to qudit and bosonic systems. We present a unified perspective on the extraction of nonlinear diagnostics, including entanglement entropies and entanglement spectra, Rényi negativities for mixed-state entanglement, stabilizer entropies for quantum magic, and decoherence-driven phenomena such as the interplay between imaginary-time evolution and decoherence and strong-to-weak spontaneous symmetry breaking.
Comments44 pages; 20 figures
