On Robust Control Of Single-qubit Systems

The target of quantum control is to control quantum objectives in order to satisfy requirements in the fields such as quantum computation and quantum communication. Real quantum systems usually suffers from decoherence induced by environment disturbance. This effect, together with inaccurate modeling, usually leads to uncertainties in system models, which will destroy systems’ excellent quantum properties. Hence it is significant to study quantum robust control to enhance control performance in reality.This thesis studies robust control for a single qubit system via periodical sampling and estab-lishes control strategies based on sliding mode control. According to single-qubit system’s bilinear and antisymmetric properties under the Bloch representation, an alternative method is proposed to exclude the existence of singular arc in quantum optimal control, which makes the proof of opti-mal control in no-decoherence situation stricter. To avoid high frequency disturbance brought by frequent measurements, the sampling periods should be prolonged under the prerequisite that the system’s robustness is satisfied. Therefore, for the situation of amplitude damping decoherence and phase damping decoherence, this thesis first designs longer sampling periods under the as-sumption that variable indices are ideal enough, and then gives results on longer sampling periods via more accurate estimation method without any assumption, which are more viable for physical realization.Together with collaborators, this thesis also investigates the problem of robust control for a single qubit with operator errors, which enlarges the field of quantum robust control. It establishes control models on the basis of sliding mode control, and defines control performance with indices as fidelity, coherence and purity that have real physical meanings. It divides decoherence situations into three ones, i.e. approximate amplitude damping decoherence, approximate phase damping decoherence and approximate depolarizing decoherence, and designs detailed control laws and sampling periods, respectively.