Microsoft Quantum, Microsoft（微软量子）；Department of Physics, Brandeis University（布兰迪斯大学物理系）；Department of Physics, University of Massachusetts, Amherst（马萨诸塞大学阿默斯特分校物理系）；Santa Fe Institute（圣塔菲研究所）
Amin Barzegar, Firas Hamze, Christopher Amey, Jonathan Machta
退火算法（如模拟退火和种群退火）广泛用于采样吉布斯分布和解决优化问题（即寻找基态）。对于统计力学和优化，通常需要温度以外的额外参数，如化学势、外场或施加约束的拉格朗日乘子。本文利用非平衡统计力学方法，推导了多维参数空间中退火算法的最优调度形式。结果与热力学系统最优控制的工作密切相关[Sivak and Crooks, PRL 108, 190602 (2012)]。在该形式中，我们比较了种群退火和模拟退火的加权多次运行（“退火重要性采样”）的效率，并讨论了非遍历性对两种算法的影响。理论结果得到了自旋玻璃数值模拟的支持。
英文摘要：
Annealing algorithms such as simulated annealing and population annealing are widely used both for sampling the Gibbs distribution and solving optimization problems (i.e. finding ground states). For both statistical mechanics and optimization, additional parameters beyond temperature are often needed such as chemical potentials, external fields or Lagrange multipliers enforcing constraints. In this paper we derive a formalism for optimal annealing schedules in multidimensional parameter spaces using methods from non-equilibrium statistical mechanics. The results are closely related to work on optimal control of thermodynamic systems [Sivak and Crooks, PRL 108, 190602 (2012)]. Within the formalism, we compare the efficiency of population annealing and multiple weighted runs of simulated annealing ("annealed importance sampling") and discuss the effects of non-ergodicity on both algorithms. Theoretical results are supported by numerical simulations of spin glasses.
Population Annealing as a Discrete-Time Schrödinger Bridge
Graduate School of Information Sciences, Tohoku University（东北大学信息科学研究院）；Department of Physics, Tokyo Institute of Technology（东京工业大学物理系）；Research and Education Institute for Semiconductors and Informatics, Kumamoto University（熊本大学半导体与信息学研究与教育学院）；Sigma-i Co., Ltd.（Sigma-i有限公司）
