Contributions to Quantum Control and Statistical Physics

Abstract

This thesis consists of two parts. The first part is on the complexity of controlling quantum systems. Specifically, we present results on sufficient conditions under which control of quantum systems is efficient. We introduce a new family of graphs defining the interaction of subsystems, on which control is feasible. The second part explores two problems in statistical physics. A mean field equation for bosons interacting via bounded many-body potentials is rigorously derived. An error bound is obtained for the error between the actual and mean field evolution equations. The mean field error bounds are relevant to numerical integration of non-linear differential equations on quantum computers. We also study the conditions under which a classical particle subject to a random force behaves quantum mechanically. The results are achieved through the application of method of averaging to the stochastic formulation of quantum mechanics.