Rapid incoherent control of quantum systems based on continuous measurements and reference model

A rapid incoherent control scheme is proposed for driving a quantum system from an initial mixed state to a final state having a high fidelity with a target pure state. This scheme consists of two main steps: rapid purification of the initial mixed state and time-optimal control of the conditional state. The first step rapidly purifies the initial mixed state into an almost-pure state (conditional state) through continuous measurements and feedback control. The second step finds a set of suitable time-optimal controls through the control design of a reference model to drive the quantum system from the conditional state to the final state. The switching time between the two steps is determined by the expected purity or fidelity and the resultant state is an almost-pure state having a high fidelity with the target pure state. As an illustrative example, the authors apply the present rapid incoherent control scheme to a spin system. The potential applications of model predictive control to quantum systems are also discussed briefly.