FOKKER–PLANCK-BASED CONTROL OF A TWO-LEVEL OPEN QUANTUM SYSTEM

Abstract

The control of a two-level open quantum system subject to dissipation due to environment interaction is considered. The evolution of this system is governed by a Lindblad master equation which is augmented by a stochastic term to model the effect of time-continuous measurements. In order to control this stochastic master equation model, a Fokker–Planck control framework is investigated. Within this strategy, the control objectives are defined based on the probability density functions of the two-level stochastic process and the controls are computed as minimizers of these objectives subject to the constraints represented by the Fokker–Planck equation. This minimization problem is characterized by an optimality system including the Fokker–Planck equation and its adjoint. This optimality system is approximated by a second-order accurate, stable, conservative and positive-preserving discretization scheme. The implementation of the resulting open-loop controls is realized with a receding-horizon algorithm over a sequence of time windows. Results of numerical experiments demonstrate the effectiveness of the proposed approach.