Further results on sampled-data design for robust control of a single qubit

Abstract

This paper presents further results on the robust control method for qubit systems in Dong et al. (2013). Based on the properties of an antisymmetric system, an alternative method is presented to analyse and exclude singularity intervals in the proof of partial original results. For the case of amplitude damping decoherence, a larger sampling period is presented when the upper bound of the probability of failure is small enough. For the case of phase damping decoherence, a larger sampling period is given when the lower bound of the target coherence is large enough. Furthermore, we provide improved sampling periods for amplitude damping decoherence and phase damping decoherence without the above prior constraints.

Keywords:

• quantum control
• qubit
• sampled-data design
• sliding mode control
• robust decoherence control

Acknowledgements

D. Dong would like to thank Ian Petersen and Herschel Rabitz for their helpful discussions. The authors would also like to thank the editor and anonymous reviewers for helpful comments and suggestions.

Additional information

Funding

This research was supported under Australian Research Council’s Discovery Projects funding scheme (project DP130101658) and by the Natural Science Foundation of China [grant number 61273327], [grant number 61374092].