  Dynamically correcting for unwanted interactions between a quantum system and
its environment is vital to achieving the high-fidelity quantum control
necessary for a broad range of quantum information technologies. In recent
work, we uncovered the complete solution space of all possible driving fields
that suppress transverse quasistatic noise errors while performing single-qubit
operations. This solution space lives within a simple geometrical framework
that makes it possible to obtain globally optimal pulses subject to a set of
experimental constraints by solving certain geometrical optimization problems.
In this work, we solve such a geometrical optimization problem to find the
fastest possible pulses that implement single-qubit gates while cancelling
transverse quasistatic noise to second order. Because the time-optimized pulses
are not smooth, we provide a method based on our geometrical approach to obtain
experimentally feasible smooth pulses that approximate the time-optimal ones
with minimal loss in gate speed. We show that in the presence of realistic
constraints on pulse rise times, our smooth pulses significantly outperform
sequences based on ideal pulse shapes, highlighting the benefits of building
experimental waveform constraints directly into dynamically corrected gate
designs.
