Notes on Sampled-data Design for Robust Control of a Single Qubit

This paper presents several notes on the robust control method proposed in [Dong et al (2013), Sampled-data design for robust control of a single qubit. IEEE Transactions on Automatic Control, in press] and furthermore improves the original sampling periods so that this control method can be better and more easily realized. 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 both of the above two cases under the same assumption as that in [Dong et al (2013), Sampled-data design for robust control of a single qubit. IEEE Transactions on Automatic Control, in press].