  Optimal control theory provides recipes to achieve quantum operations with
high fidelity and speed, as required in quantum technologies such as quantum
sensing and computation. While technical advances have achieved the ultrastrong
driving regime in many physical systems, these capabilities have yet to be
fully exploited for the precise control of quantum systems, as other
limitations, such as the generation of higher harmonics or the finite bandwidth
of the control fields, prevent the implementation of theoretical time-optimal
control. Here we present a method to achieve time-optimal control of qubit
systems that can take advantage of fast driving beyond the rotating wave
approximation. We exploit results from optimal control theory to design driving
protocols that can be implemented with realistic, finite-bandwidth control and
we find a relationship between bandwidth limitations and achievable control
fidelity.
