Noise Suppression via Coherent Quantum Feedback: a Schr{\"o}dinger Picture Approach

In this article, we explore the possibility of achieving noise suppression for finite-dimensional quantum systems through coherent feedback. For a quantum plant which is expected to evolve according to a target trajectory, noise effect potentially deforms the plant state trajectory from the desired one. It is then hoped that a coherent feedback protocol can be designed that counteracts noise. In terms of coping with transient noise, we present several conditions on coherent feedback protocols under which noise-affected trajectories can be driven back towards desired ones asymptotically. As for rejecting persistent noise, conditions on protocols are given which ensure that the error between the target and feedback-corrected trajectories in the long-time limit can be effectively suppressed. Moreover, a possible construction of coherent feedback protocols which satisfies the given conditions is provided. Our theoretical results are illustrated by an example which involves a two-qubit plant and a two-level controller.