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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.
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https://hal-mines-paristech.archives-ouvertes.fr/hal-00683461
Contributor : François Chaplais <>
Submitted on : Wednesday, March 28, 2012 - 5:46:32 PM
Last modification on : Wednesday, January 13, 2021 - 5:02:03 PM
Long-term archiving on: : Friday, June 29, 2012 - 2:27:52 AM

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Hadis Amini, Pierre Rouchon, Mazyar Mirrahimi. Design of strict control-Lyapunov functions for Quantum systems with QND measurements. CDC-ECC 2011 : 50th IEEE Conference on Decision and Control and European Control Conference, Dec 2011, Orlando, United States. pp.8193 - 8198, ⟨10.1109/CDC.2011.6160433⟩. ⟨hal-00683461⟩

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