标题： 最优量子算法用于吉布斯态制备 显示英文标题

标题： Optimal quantum algorithm for Gibbs state preparation

摘要： 理解开放量子多体系统的热化过程，以及量子计算机如何能够高效地模拟该过程，具有重要意义。 一种最近引入的耗散演化过程，受到现有开放系统热化模型的启发，已被证明可以在量子计算机上高效实现。 在此，我们证明，在足够高的温度下，这种演化过程的时间与系统大小的对数成比例地达到吉布斯态。 该结果适用于满足李-罗宾逊界限的哈密顿量，例如格点上的局部哈密顿量，也包括长程系统。 据我们所知，这些是首次严格确立高温量子吉布斯采样器的快速混合性质的结果，已知该性质在多体情况下给出了最快的热化速度。 随后，我们将我们的结果应用于高温下估计分区函数的问题，展示了比之前经典和量子算法更好的性能。 显示英文摘要

摘要： It is of great interest to understand the thermalization of open quantum many-body systems, and how quantum computers are able to efficiently simulate that process. A recently introduced disispative evolution, inspired by existing models of open system thermalization, has been shown to be efficiently implementable on a quantum computer. Here, we prove that, at high enough temperatures, this evolution reaches the Gibbs state in time scaling logarithmically with system size. The result holds for Hamiltonians that satisfy the Lieb-Robinson bound, such as local Hamiltonians on a lattice, and includes long-range systems. To the best of our knowledge, these are the first results rigorously establishing the rapid mixing property of high-temperature quantum Gibbs samplers, which is known to give the fastest possible speed for thermalization in the many-body setting. We then employ our result to the problem of estimating partition functions at high temperature, showing an improved performance over previous classical and quantum algorithms.