Feedback stabilization via a quantum projection filter

TL;DR

This paper introduces a feedback stabilization method for open quantum systems using a quantum projection filter, ensuring exponential convergence to a target state under QND measurements.

Contribution

It presents a novel feedback control approach based on a quantum projection filter for stabilizing quantum states in open systems.

Findings

Feedback guarantees exponential convergence to the target state.

The method is effective for systems with QND measurements.

The approach leverages the structure of the exponential family in the projection process.

Abstract

This paper considers a simplified model of open quantum systems undergoing imperfect measurements obtained via a projection filter approach. We use this approximate filter in the feedback stabilization problem specifically in the case of Quantum Non-Demolition (QND) measurements. The feedback design relies on the structure of the exponential family utilized for the projection process. We demonstrate that the introduced feedback guarantees exponential convergence of the original filter equation toward a predefined target state, corresponding to an eigenstate of the measurement operator.