发表机构
University of Cambridge; Inria, ENS Lyon, UCBL, LIP; Inria, Télécom Paris - LTCI, Institut Polytechnique de Paris; University of Copenhagen（剑桥大学; 法国国家信息与自动化研究所，里昂高等师范学校，里昂第一大学，计算与图像实验室; 法国国家信息与自动化研究所，巴黎电信学院-信息与通信系，巴黎理工学院; 哥本哈根大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为开放量子系统传播算法建立快速收敛条件，证明在噪声足够强或高温下可高效经典模拟，并将无噪声可模拟时间尺度提升至1/u。
AI 中文摘要
我们建立了传播算法在量子多体系统中计算局部可观测量期望值时快速收敛的一般条件，涵盖自旋系统和费米子系统。我们的结果适用于充分压缩的演化，提供了一种一般机制，通过该机制，压缩性控制由局部相互作用产生的增长，并使得有效的经典模拟成为可能。作为第一个应用，我们考虑了由任意相互作用图上的局部哈密顿量生成的含噪声时间演化。我们证明，当噪声强度$\lambda$相对于相互作用图的度足够大时，动力学可以被高效模拟。更一般地，对于相互作用强度为$u$的系统，我们的界确定了时间范围$t_{\text{max}}$，该范围是相互作用强度$u$、噪声强度$\lambda$以及相互作用结构的函数，在此范围之下算法是高效的。在无噪声极限$\lambda=0$下，我们的分析将Facelli、Fawzi和Fawzi（2026）证明的高效可模拟时间尺度从$\log(1/u)$扩展到$t_{\text{max}} \sim 1/u$，与Zhao、Marvian和Tong（2026）最近的改进相匹配。作为第二个应用，我们将相同的框架应用于局部哈密顿量吉布斯态中局部可观测量的计算。我们考虑一个稳态为吉布斯态的伪林德布拉德算符，并证明在足够高的温度下，其传播算法快速收敛。特别是，对于相互作用强度为$u$的弱相互作用系统，我们的结果适用于逆温度$\beta\sim\log(1/u)$。
英文摘要
We establish general conditions for the rapid convergence of propagation algorithms for computing expectation values of local observables in quantum many-body systems, covering both spin and fermionic systems. Our results apply to evolutions that are sufficiently contractive, providing a general mechanism by which contractivity controls the growth generated by local interactions and enables efficient classical simulation. As a first application, we consider noisy time evolution generated by local Hamiltonians on arbitrary interaction graphs. We show that the dynamics can be efficiently simulated when the noise strength $λ$ is sufficiently large compared to the degree of the interaction graph. More generally, for systems with an interaction strength $u$, our bounds determine a time horizon $t_{\text{max}}$ as a function of the interaction strength $u$, the noise strength $λ$, and the interaction structure below which the algorithm is efficient. In the noiseless limit, $λ=0$, our analysis extends the efficiently simulable time scale from $\log(1/u)$ proved in Facelli, Fawzi, and Fawzi (2026) to $t_{\text{max}} \sim 1/u$ matching the recent improvement by Zhao, Marvian and Tong (2026). As a second application, we apply the same framework to the computation of local observables in Gibbs states of local Hamiltonians. We consider a pseudo-Lindbladian whose steady state is the Gibbs state and show that, at sufficiently high temperature, its propagation algorithm converges rapidly. In particular, for weakly-interacting systems with interaction strength $u$, our result applies up to inverse temperatures $β\sim\log(1/u)$.
Comments31 pages
