Simulated annealing and quantum detailed balance

Abstract

The analogue of simulated annealing is considered for time-inhomogeneous evolutions of a von Neumann algebra of operators, whose instantaneous generator at each timet satisfies the quantum detailed balance condition with respect to a faithful normal state which depends on time through a suitable cooling schedule. Convergence to the (nonfaithful) limiting state is proved under the usual kinds of assumptions. The approach is interesting in view of possible applications to stochastic Ising models and to Boltzmann machines.