Model robustness for feedback stabilization of open quantum systems
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.
Cite
@article{arxiv.2205.01961,
title = {Model robustness for feedback stabilization of open quantum systems},
author = {Weichao Liang and Nina H. Amini},
journal= {arXiv preprint arXiv:2205.01961},
year = {2022}
}