Optimization and thermodynamics of classical problems from a quantum perspective
Rolando D. Somma, Cristian D. Batista, Gerardo Ortíz · Journal of Physics Conference Series · 2008
We present two approaches to study the thermodynamic properties of d -dimensional classical systems in equilibrium. In the first approach we reduce this problem to the computation of the 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. Particularly, we extend the quantum annealing method to study classical systems at finite temperatures. We derive the rates to assure convergence to the optimal thermodynamic state using the adiabatic theorem of quantum mechanics. In the second approach we present a quantum algorithm that performs numerical integration and computes, for example, the partition function of the system under study. We show that this quantum algorithm provides a quadratic speed-up with respect to the classical algorithm that samples with the uniform distribution and computes physical quantities of interest. Other quantum strategies, as well as their potential speed-up, are also discussed.