  Implementing two-qubit gates via strong coupling between quantum-dot qubits
and a superconducting microwave cavity requires achieving coupling rates that
are much faster than decoherence rates. Typically, this involves tuning the
qubit either to a sweet spot, where it is relatively insensitive to charge
noise, or to a point where it is resonant with the microwave cavity.
Unfortunately, such operating points seldom coincide. Here, we theoretically
investigate several schemes for performing gates between two quantum-dot hybrid
qubits, mediated by a microwave cavity. The rich physics of the quantum dot
hybrid qubit gives rise to two types of sweet spots, which can occur at
operating points with strong charge dipole moments. Such strong interactions
provide new opportunities for off-resonant gating, thereby removing one of the
main obstacles for long-distance two-qubit gates. Our results suggest that the
numerous tuning knobs of quantum dot hybrid qubits make them good candidates
for strong coupling. In particular, we show that off-resonant
red-sideband-mediated two-qubit gates can exhibit fidelities $>$95\% for
realistic operating parameters, and we describe improvements that could
potentially yield gate fidelities $>$99\%.
