Design of Strict Control-Lyapunov Functions for Quantum Systems with QND Measurements
Abstract
We consider discrete-time quantum systems subject to Quantum Non-Demolition (QND) measurements and controlled by an adjustable unitary evolution between two successive QND measures. In open-loop, such QND measurements provide a non-deterministic preparation tool exploiting the back-action of the measurement on the quantum state. We propose here a systematic method based on elementary graph theory and inversion of Laplacian matrices to construct strict control-Lyapunov functions. This yields an appropriate feedback law that stabilizes globally the system towards a chosen target state among the open-loop stable ones, and that makes in closed-loop this preparation deterministic. We illustrate such feedback laws through simulations corresponding to an experimental setup with QND photon counting.
Keywords
Cite
@article{arxiv.1103.1365,
title = {Design of Strict Control-Lyapunov Functions for Quantum Systems with QND Measurements},
author = {Hadis Amini and Pierre Rouchon and Mazyar Mirrahimi},
journal= {arXiv preprint arXiv:1103.1365},
year = {2011}
}