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

Hadis Amini (1) , Pierre Rouchon (1) , Mazyar Mirrahimi (2)

1 CAS - Centre Automatique et Systèmes
2 SISYPHE - SIgnals and SYstems in PHysiology & Engineering

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.

Domaines: Automatique / Robotique

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⟩