Design of Strict Control-Lyapunov Functions for Quantum Systems with QND Measurements

Details Design of Strict Control-Lyapunov Functions for Quantum Systems with QND Measurements Design of Strict Control-Lyapunov Functions for Quantum Systems with QND Measurements

2011-03-07

arxiv.org/abs/1103.1365v2

Mathematics

Optimization and Control

Scientific paper

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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