  We consider the time evolution of simple quantum systems under the influence
of random fluctuations of the control parameters. We show that when the
parameters fluctuate sufficiently fast, there is a cancellation effect of the
noise. We propose that such an effect could be experimentally observed by
performing a simple experiment with trapped ions. As a byproduct of our
analysis, we provide an explanation of the robustness against random
perturbations of adiabatic population transfer techniques in atom optics.
