Model robustness for feedback stabilization of open quantum systems

TL;DR

This paper extends feedback stabilization techniques for multi-measurement quantum systems, proving the effectiveness of simplified filters for high-dimensional systems and paving the way for robust control methods.

Contribution

It provides a complete proof for using simplified filters in feedback stabilization of quantum systems with multiple measurements, enhancing practical applicability.

Findings

Validated the use of simplified filters for feedback control

Established robustness of stabilization against filter approximations

Extended stabilization results to systems with multiple measurement operators

Abstract

This paper generalizes the results in [30] concerning feedback stabilization of target states for N-level quantum angular momentum systems undergoing quantum non-demolition measurements (QND) in absence of the knowledge about initial states and parameters. Here we consider multiple measurement operators and study the stabilization toward a chosen target subspace which is a common eigenspace of measurement operators. Under the QND conditions, we show that this analysis provides necessary tools to ensure feedback stabilization based on a simplified filter whose state is a N-dimensional vector. A numerical analysis has been proposed in [18]. This paper provides a complete proof for the use of a simplified filter in feedback stabilization. This has important practical use as the dimension of quantum systems is usually high. This paper opens the way toward a complete proof concerning the robustness of a stabilizing feedback with respect to approximate filters, which is lacking.