  We study numerically the effects of measurements on dynamical localization in
the kicked rotator model simulated on a quantum computer. Contrary to the
previous studies, which showed that measurements induce a diffusive probability
spreading, our results demonstrate that localization can be preserved for
repeated single-qubit measurements. We detect a transition from a localized to
a delocalized phase, depending on the system parameters and on the choice of
the measured qubit.
