  We show that for any finite-dimensional quantum systems the conserved
quantities can be characterized by their robustness to small perturbations: for
fragile symmetries small perturbations can lead to large deviations over long
times, while for robust symmetries their expectation values remain close to
their initial values for all times. This is in analogy with the celebrated
Kolmogorov-Arnold-Moser (KAM) theorem in classical mechanics. To prove this
remarkable result, we introduce a resummation of a perturbation series, which
generalizes the Hamiltonian of the quantum Zeno dynamics.
