  We show that a thermally isolated system driven across a quantum phase
transition by a noisy control field exhibits anti-Kibble-Zurek behavior,
whereby slower driving results in higher excitations. We characterize the
density of excitations as a function of the ramping rate and the noise
strength. The optimal driving time to minimize excitations is shown to scale as
a universal power law of the noise strength. Our findings reveal the
limitations of adiabatic protocols such as quantum annealing and demonstrate
the universality of the optimal ramping rate.
