Rapid incoherent control of a simple quantum system via two-step optimization

A rapid incoherent control scheme for driving a simple qubit system from an initial mixed state to an arbitrary target pure state is proposed. This scheme consists of two main steps: rapid purification of the initial mixed state and time optimal transition from the conditional state to the target state. The first step rapidly purifies the initial mixed state into an almost-pure state of the simple qubit system through continuous measurements and feedback control by the protocol proposed in Jacobs 2003 Physical Review A 67 030301(R). The second step finds a set of suitable time optimal controls to drive the simple qubit system from the conditional state to the target state. The switching time between the first step and the second step is determined by the expected purity and the resultant state is an almost-pure state with a high fidelity with the target state. This rapid incoherent control scheme provides an alternative quantum engineering strategy for the rapid preparation of arbitrary pure states of a simple qubit system.