Sampling-based learning control of quantum systems via path planning

Robust control design is a central problem for quantum systems in practical implementation and applications. In this study, the authors present a systematic methodology of sampling-based learning control via path planning for state transfer of quantum systems with uncertainties and bounded controls. The authors formulate the control problem of a quantum system with bounded uncertainties as the problem of steering this system to a target state with bounded controls via an optimised evolution path to achieve a satisfactory level of fidelity. To find the optimised path (controls), the authors present a combined design method of sampling-based learning control and path planning. The numerical results on an example of a four-level quantum system show the effectiveness of the proposed learning control design method. The method provides a useful design approach for learning control of quantum systems with uncertainties.