Bound on annealing performance from stochastic thermodynamics, with application to simulated annealing

Yutong Luo; Yi-Zheng Zhen; Xiangjing Liu; Daniel Ebler; Oscar Dahlsten

doi:10.1103/PhysRevE.108.054119

Bound on annealing performance from stochastic thermodynamics, with application to simulated annealing

Phys Rev E. 2023 Nov;108(5-1):054119. doi: 10.1103/PhysRevE.108.054119.

Authors

Yutong Luo^{1

2}, Yi-Zheng Zhen^{3

4}, Xiangjing Liu², Daniel Ebler^{5

6}, Oscar Dahlsten^{7

8

9}

Affiliations

¹ Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom.
² Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China.
³ Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China.
⁴ Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China.
⁵ Theory Lab, Central Research Institute, 2012 Labs, Huawei Technology Co. Ltd., Hong Kong Science Park, Hong Kong SAR, China.
⁶ Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China.
⁷ Department of Physics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong SAR, China.
⁸ Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China.
⁹ Institute of Nanoscience and Applications, Southern University of Science and Technology, Shenzhen 518055, China.

PMID: 38115542
DOI: 10.1103/PhysRevE.108.054119

Abstract

Annealing is the process of gradually lowering the temperature of a system to guide it towards its lowest energy states. In an accompanying paper [Y. Luo et al., Phys. Rev. E 108, L052105 (2023)10.1103/PhysRevE.108.L052105], we derived a general bound on annealing performance by connecting annealing with stochastic thermodynamics tools, including a speed limit on state transformation from entropy production. We here describe the derivation of the general bound in detail. In addition, we analyze the case of simulated annealing with Glauber dynamics in depth. We show how to bound the two case-specific quantities appearing in the bound, namely the activity, a measure of the number of microstate jumps, and the change in relative entropy between the state and the instantaneous thermal state, which is due to temperature variation. We exemplify the arguments by numerical simulations on the Sherrington-Kirkpatrick (SK) model of spin glasses.