发表机构
Universität Ulm; Center for Integrated Quantum Science and Technology (IQST)（乌尔姆大学; 集成量子科学与技术中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出态自适应Krylov框架，利用几何广义平均场投影将多体可观测量压缩到低体子空间，实现稳定高效的海森堡动力学模拟，并验证于三维大晶格。
AI 中文摘要
在海森堡绘景中，当演化的可观测量在低维结构内允许紧凑的算子表示时，量子多体模拟可以变得高效。传统的泡利弦传播和截断技术利用了这种结构，但在相干哈密顿动力学中，其误差控制往往是启发式的，且稳定性可能较差。我们引入了一个态自适应的Krylov框架，该框架基于几何广义平均场投影，将多体可观测量投影到低体算子子空间上。由此产生的动力学近似期望值，不会将空间支持扩展到Lieb-Robinson界限所规定的范围之外，并将高体关联压缩到其态相关的低体代表上，而不是简单地丢弃它们。我们推导了低体表示的必要算子纠缠障碍，以及涉及非稳定性和受控高体尾部的表示误差和动力学误差的条件充分界限。数值基准测试显示了改进的、稳定的有限$m$层级，以及在大规模三维晶格上的模拟，为传统的海森堡绘景泡利弦权重截断建立了一种可扩展的态自适应替代方案。
英文摘要
The Heisenberg picture can make quantum many-body simulation efficient when evolved observables admit compact operator representation within low-dimensional structures. Conventional Pauli-string propagation and truncation techniques exploit this structure, but in coherent Hamiltonian dynamics their error control is often heuristic and their stability can be poor. We introduce a state-adapted Krylov framework based on geometric generalized mean-field projections of many-body observables onto low-body operator subspaces. The resulting dynamics approximate expectation values, do not extend spatial support beyond that prescribed by Lieb-Robinson bounds, and compress high-body correlations onto their state-relevant low-body representatives rather than simply discarding them. We derive necessary operator-entanglement obstructions to low-body representation and conditional sufficient bounds on representation and dynamical errors involving nonstabilizerness and controlled high-body tails. Numerical benchmarks show improved, stable finite-$m$ hierarchies and simulations on large three-dimensional lattices, establishing a scalable state-adapted alternative to conventional Heisenberg-picture weight-truncation of Pauli strings.
Comments10 pages, 5 figures. Comments and suggestions are welcome
