Quantum Approach to Classical Statistical Mechanics
Open accessAbstract
We present a new approach to study the thermodynamic properties of d-dimensional classical systems by reducing the problem to the computation of ground state properties of a d-dimensional quantum model. This classical-to-quantum mapping allows us to extend the scope of standard optimization methods by unifying them under a general framework. The quantum annealing method is naturally extended to simulate classical systems at finite temperatures. We derive the rates to assure convergence to the optimal thermodynamic state using the adiabatic theorem of quantum mechanics. For simulated and quantum annealing, we obtain the asymptotic rates of T(t) approximately (pN)/(k(B)logt) and gamma(t) approximately (Nt)(-c/N), for the temperature and magnetic field, respectively. Other annealing strategies are also discussed.
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These connections enable one to phrase statistical physics problems naturally in a quantum mechanical setting.
“For one, these connections enable one to phrase statistical physics problems naturally in a quantum mechanical setting 87,92,95,96,99-102 .”
From Measurement-based quantum computation (2009) · cites this paper as [101]
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- Authors
- Somma, R. D., Batista, C. D., & Ortiz, G.
- Affiliations
- Los Alamos National Laboratory (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2007-07-20
- Volume
- 99
- Issue
- 3
- Pages
- 030603-030603
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2049371556
- Cited by
- 87
- References
- 21
- Citations by year
- 2026: 3 · 2025: 3 · 2024: 3 · 2023: 3 · 2022: 4 · 2021: 7 · 2020: 7 · 2019: 3 · 2018: 2 · 2017: 4 · 2016: 2 · 2015: 3 · 2014: 3 · 2013: 5 · 2012: 6
- FWCI
- 9.07
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Keywords
- quantum annealing, simulated annealing, adiabatic theorem, ground-state properties, convergence rate, finite temperature, optimization methods
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