Due to the influence of decoherence, the quantum state probably evolves from the initial pure state to the mixed state, resulting in loss of fidelity, coherence and purity, which is deteriorating for quantum information transmission. Thus, in quantum engineering, quantum control should not only realize the transfer and track of quantum states through manipulation of the external electromagnetic field but also enhance the robustness against decoherence. In this paper, we aim to design a control law to steer the system into the sliding mode domain and maintain it in that domain when bounded uncertainties exist in the system Hamiltonian. We first define the required control performance by fidelity, degree of coherence and purity in terms of the uncertainty of the Hamiltonian in Markovian open quantum system. By characterizing the required robustness using a sliding mode domain, a sampled-data design method is introduced for decoherence control in the quantum system. Furthermore, utilizing the sampled data, a control scheme has been designed on the basis of sliding mode control, and the choice of sampling operator and driving of quantum state during the sampling by the Lyapunov control method are discussed.
Numerical estimation of reachable and controllability sets for a two-level open quantum system driven by coherent and incoherent controls