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Luo Y, Zhen YZ, Liu X, Ebler D, Dahlsten O. General limit to thermodynamic annealing performance. Phys Rev E 2023; 108:L052105. [PMID: 38115520 DOI: 10.1103/physreve.108.l052105] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2023] [Accepted: 10/13/2023] [Indexed: 12/21/2023]
Abstract
Annealing has proven highly successful in finding minima in a cost landscape. Yet, depending on the landscape, systems often converge towards local minima rather than global ones. In this Letter, we analyze the conditions for which annealing is approximately successful in finite time. We connect annealing to stochastic thermodynamics to derive a general bound on the distance between the system state at the end of the annealing and the ground state of the landscape. This distance depends on the amount of state updates of the system and the accumulation of nonequilibrium energy, two protocol and energy landscape-dependent quantities which we show are in a trade-off relation. We describe how to bound the two quantities both analytically and physically. This offers a general approach to assess the performance of annealing from accessible parameters, both for simulated and physical implementations.
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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 Laboratory, Central Research Institute, 2012 Labs, Huawei Technology Company Limited, 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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