The problem of equilibration and the computation of correlation   functions on a quantum computer
  We address the question of how a quantum computer can be used to simulate experiments on quantum systems in thermal equilibrium. We present two approaches for the preparation of the equilibrium state on a quantum computer. For both approaches, we show that the output state of the algorithm, after long enough time, is the desired equilibrium. We present a numerical analysis of one of these approaches for small systems. We show how equilibrium (time)-correlation functions can be efficiently estimated on a quantum computer, given a preparation of the equilibrium state. The quantum algorithms that we present are hard to simulate on a classical computer. This indicates that they could provide an exponential speedup over what can be achieved with a classical device. 
Barbara M. Terhal and David P. DiVincenzo