  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.
