Quantum Approach to Classical Statistical Mechanics

R. D. Somma, C. D. Batista, and G. Ortiz
Phys. Rev. Lett. 99, 030603 – Published 20 July 2007

Abstract

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)(pN)/(kBlogt) and γ(t)(Nt)c¯/N, for the temperature and magnetic field, respectively. Other annealing strategies are also discussed.

  • Received 11 October 2006

DOI:https://doi.org/10.1103/PhysRevLett.99.030603

©2007 American Physical Society

Authors & Affiliations

R. D. Somma* and C. D. Batista

  • Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

G. Ortiz

  • Department of Physics, Indiana University, Bloomington, Indiana 47405, USA

  • *somma@lanl.gov

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Issue

Vol. 99, Iss. 3 — 20 July 2007

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