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Design of strict control-Lyapunov functions for Quantum systems with QND measurements

Authors: H. Amini, P. Rouchon, M. Mirrahimi, 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC) 2011, pp. 8193 - 8198, 12-15 Dec. 2011, Orlando, USA DOI: 10.1109/CDC.2011.6160433
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.
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BibTeX:
@Proceedings{,
author = {H. Amini, P. Rouchon, M. Mirrahimi},
editor = {},
title = {Design of strict control-Lyapunov functions for Quantum systems with QND measurements},
booktitle = {50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC) 2011},
volume = {},
publisher = {},
address = {Orlando},
pages = {8193 - 8198},
year = {2011},
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 = {}}