  Superconducting transmon qubits comprise one of the most promising platforms
for quantum information processing due to their long coherence times and to
their scalability into larger qubit networks. However, their weakly anharmonic
spectrum leads to spectral crowding in multiqubit systems, making it
challenging to implement fast, high-fidelity gates while avoiding leakage
errors. To address this challenge, we use a protocol known as SWIPHT [Phys.
Rev. B 91, 161405(R) (2015)], which yields smooth, simple microwave pulses
designed to suppress leakage without sacrificing gate speed through spectral
selectivity. Here, we determine the parameter regimes in which SWIPHT is
effective and demonstrate that in these regimes it systematically produces
two-qubit gate fidelities for cavity-coupled transmons in the range 99.6%-99.9%
with gate times as fast as 23 ns. Our results are obtained from full numerical
simulations that include current experimental levels of relaxation and
dephasing. These high fidelities persist over a wide range of system parameters
that encompass many current experimental setups and are insensitive to small
parameter variations and pulse imperfections.
