Filter-Based Feedback Control for a Class of Markovian Open Quantum Systems

This letter considers target state preparation for Markovian open quantum systems subject to continuous measurement. Conditions on invariant and attractive subspaces are investigated, which ensure the stabilization of the target state/subspace. For a class of open quantum systems with time delay in the feedback loop, a bang-bang-like control law is proposed, and the stability of the feedback control strategy is proved. An example of four-level Markovian open quantum systems is presented to demonstrate the effectiveness of the proposed control strategy.