发表机构
Imperial College London; RWTH Aachen University（帝国理工学院; 亚琛工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对快速林德布拉德动力学，提出可观测量特有的混合时间，证明局域可观测量平衡时间与系统大小无关，缩短耗散量子算法运行时间，还开发了对应量子启发经典算法，模拟验证了理论预测的有效性。
AI 中文摘要
马尔可夫开放系统动力学在量子信息科学中应用广泛，包括算法态制备，其收敛性通常用演化态与稳态之间的最坏情况全局迹距离量化。但当仅关注物理相关的可观测量时，该准则可能过于严格。本文引入并研究可观测量特有的混合时间，证明对于准局域、快速混合的林德布拉德（Lindbladian），几何局域可观测量之和的平衡时间与系统大小无关，这与全局态混合的对数依赖形成鲜明对比。这种分离缩短了耗散量子算法（包括量子吉布斯采样器）的运行时间，用于估计吉布斯态能量、局域序参量等量时，整体缩放与系统大小呈线性关系。作为该量子结果的补充，本文开发了一种受量子启发的经典算法来估计相同量，其运行时间同样与系统大小呈线性关系，但缩放为指数级，形式为$\big(\frac{1}{\boldsymbol{\text{ε}}}\big)^D$，其中$D$表示晶格的空间维度。本文进一步分析了多体量子位、费米子和玻色子上的非相互作用林德布拉德，证明可观测量的局域性并非定性更快混合的必要条件。对量子吉布斯采样器的小规模模拟显示，渐近分析中不存在大的隐藏常数，且理论预测能很好地匹配有限大小的动力学。
英文摘要
Markovian open-system dynamics have widespread applications throughout quantum information science, including algorithmic state preparation. Their convergence is commonly quantified using the worst case global trace distance between the evolving and stationary states. However, this criterion can be unnecessarily stringent when only physically relevant observables are of interest. Here we introduce and study observable-specific mixing times. We prove that, for quasi-local, rapidly mixing Lindbladians, sums of geometrically local observables equilibrate in a time independent of system size, in contrast to the logarithmic dependence of global state mixing. This separation reduces the runtime of dissipative quantum algorithms, including quantum Gibbs samplers, for estimating quantities such as the Gibbs state energy and local order parameters, yielding an overall scaling that is linear in system size. Complementing this quantum result, we develop a quantum-inspired classical algorithm for estimating the same quantities. Its runtime is likewise linear in system size, but scaling exponentially in $\mathcal{O}\big(\log(1/ε)^D\big)$, where $D$ denotes the spatial dimension of the lattice. We further analyse non-interacting Lindbladians over qudits, fermions, and bosons, demonstrating that locality of observables is not always necessary for a qualitatively faster mixing. Small-scale simulations of quantum Gibbs samplers reveal no large hidden constants in our asymptotic analysis and show that the theoretical predictions closely capture the finite-size dynamics.
Comments24 pages, 6 figures. Version 2 adds tensor network simulations and new corollaries for 1D systems
