Abstract
This paper presents further results on the robust control method for qubit systems in Dong et al. Citation(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.
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.