Quantum Approach to Classical Statistical Mechanics

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)/(k_Blog⁡t) and γ(t)≈(Nt)^{-c̅ /N}, for the temperature and magnetic field, respectively. Other annealing strategies are also discussed.