  Increasing quantum circuit fidelity requires an efficient instruction set to
avoid errors from decoherence. The choice of a two-qubit (2Q) hardware basis
gate depends on a quantum modulator's native Hamiltonian interactions and
applied control drives. In this paper, we propose a collaborative design
approach to select the best ratio of drive parameters that determine the best
basis gate for a particular modulator. This requires considering the
theoretical computing power of the gate along with the practical speed limit of
that gate, given the modulator drive parameters. The practical speed limit
arises from the couplers' tolerance for strong driving when one or more pumps
is applied, for which some combinations can result in higher overall speed
limits than others. Moreover, as this 2Q basis gate is typically applied
multiple times in succession, interleaved by 1Q gates applied directly to the
qubits, the speed of the 1Q gates can become a limiting factor for the quantum
circuit. We propose a parallel-drive approach that drives the modulator and
qubits simultaneously, allowing a richer capability of the 2Q basis gate and in
some cases for this 1Q drive time to be absorbed entirely into the 2Q
operation. This allows increasingly short duration 2Q gates while mitigating a
significant source of overhead in some quantum systems. On average, this
approach can decrease circuit duration by 17.84% and decrease infidelity for
random 2Q gates by 10.5% compared to the best basic 2Q gate,
$\sqrt{\texttt{iSWAP}}$.
