Sliding mode control of two-level quantum systems with bounded uncertainties

This paper proposes a robust control method based on sliding mode design for two-level quantum systems with bounded uncertainties. An eigenstate of the two-level quantum system is identified as a sliding mode. The objective is to design a control law to steer the system into the sliding mode domain and then maintain it in that domain when bounded uncertainties exist in the system Hamiltonian. For different uncertainties, we give conditions for designing a control law, which can guarantee the desired robustness in the presence of the uncertainties. The sliding mode control method has potential applications to quantum information processing with uncertainties.