Gradient-based feedback control of quantum systems

Abstract

The paper proposes a gradient method for feedback control and stabilization of quantum systems using Schroodinger's and Lindblad's descriptions. The eigenstates of the quantum system are defined by the spin model. First, a gradient-based control law is computed using Schroodinger's description. Next, an estimate of state of the quantum system is obtained using Lindblad's differential equation. In the latter case, by applying Lyapunov's stability theory and LaSalle's invariance principle one can compute a gradient control law which assures that the quantum system's state will track the desirable state within acceptable accuracy levels. The performance of the control loop is studied through simulation experiments for the case of a two-qubit quantum system.