Identification and control of a two-level open quantum system

To make full use of the amazing characteristics of quantum states, control of open quantum systems is of great significance in practical applications. This paper studies a more practical control problem where the decoherence parameter is not known exactly. The problem is considered in two phases. First, the unknown decoherence strength is estimated based on continuous measurements and an appropriately designed control. Then, Markovian feedback control is designed to deal with the decoherence effect based on the accurate parameter estimation. It is shown that state transfer with a high probability can be achieved by designing the feedback gains and the measurement. Moreover, good state transfer performance can be guaranteed even there exists an estimation error on the decoherence strength. Simulation studies are included to demonstrate the effectiveness of the proposed approach.