Robust incoherent control of qubit systems via switching and optimisation

Abstract

A robust incoherent quantum control scheme via projective measurements plus unitary transformations is proposed for driving a qubit system from an unknown initial mixed state to an arbitrary target pure state. This scheme consists of two main steps: projective measurement on the initial mixed state and optimal control between two pure states. The first step projects the initial state into an eigenstate of the qubit system by projective measurement and guarantees that the proposed scheme is robust to different initial mixed states. The second step finds a set of suitable optimal controls to drive the qubit system from the conditional eigenstate to the target pure state. The connection between the two steps is accomplished by a switching strategy. To accomplish the second step, two approaches are presented in detail. These approaches are time-optimal transition with unbounded control and bang-bang control with minimal switches. The minimal time and minimal number of switches in these approaches can be calculated by simple analytical expressions. The proposed approaches provide two relatively straightforward optimal design methods.

Keywords:

• incoherent control
• quantum control
• projective measurement
• switching control
• qubit system
• optimal control

Acknowledgements

The authors would like to thank three anonymous reviewers for helpful comments which have improved the readability of this article. D. Dong would also like to thank Bo Qi, Hao Pan and Jianwu Wu for helpful suggestions. This work was supported by the Australian Research Council and was supported in part by the National Natural Science Foundation of China under Grant No. 60703083 and HKU CRCG 10400030.