A two-step strategy for stabilizing control of quantum systems with uncertainties

As a matter of course, designed control laws are to be acted on actual systems. However, most designed control laws are proven to be effective when performed on ideal models of the systems as opposed to the actual systems themselves. One fundamental problem is how to ensure the satisfactory performance of the designed control laws when they are performed on actual systems. Focusing on the state stabilization of quantum systems, a two-step strategy is proposed to solve this problem. A feedback strategy and the open-loop control technique of dynamical decoupling are combined therein to deal with the inevitable differences between an actual system and its model, by taking advantage of the distinct quantum characteristics: the measurement-induced-state-transfer and the tensor product structure, with the structure characterizing the coupling between a quantum system and its environment. Specifically, in the first step, a measurement-based feedback control strategy is selected according to a model of the actual system. In the second step, by identifying the differences between the actual system and the established model as decoherence noise, a specific control procedure is designed through dynamical decoupling. This procedure allows the realization of the chosen control strategy so as to deal with the differences.