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

TL;DR

This paper investigates how coherent quantum feedback can be used to suppress noise in finite-dimensional quantum systems, providing conditions for effective noise mitigation and illustrating with a two-qubit example.

Contribution

It introduces new conditions for designing coherent feedback protocols that counteract transient and persistent noise in quantum systems.

Findings

Protocols can asymptotically drive trajectories towards desired states.

Conditions ensure long-term suppression of persistent noise.

A constructive example with a two-qubit system demonstrates the approach.

Abstract

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.