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Luo Y, Zhen YZ, Liu X, Ebler D, Dahlsten O. Bound on annealing performance from stochastic thermodynamics, with application to simulated annealing. Phys Rev E 2023; 108:054119. [PMID: 38115542 DOI: 10.1103/physreve.108.054119] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2023] [Accepted: 10/13/2023] [Indexed: 12/21/2023]
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.
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Affiliation(s)
- Yutong Luo
- Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
- Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
| | - Yi-Zheng Zhen
- 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
- 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
| | - Xiangjing Liu
- Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
| | - Daniel Ebler
- Theory Lab, Central Research Institute, 2012 Labs, Huawei Technology Co. Ltd., Hong Kong Science Park, Hong Kong SAR, China
- Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China
| | - Oscar Dahlsten
- Department of Physics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong SAR, China
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- Institute of Nanoscience and Applications, Southern University of Science and Technology, Shenzhen 518055, China
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