  We investigate a hybrid quantum system consisting of spatially separated
resonant exchange qubits, defined in three-electron semiconductor triple
quantum dots, that are coupled via a superconducting transmission line
resonator. Drawing on methods from circuit quantum electrodynamics and
Hartmann-Hahn double resonance techniques, we analyze three specific approaches
for implementing resonator-mediated two-qubit entangling gates in both
dispersive and resonant regimes of interaction. We calculate entangling gate
fidelities as well as the rate of relaxation via phonons for resonant exchange
qubits in silicon triple dots and show that such an implementation is
particularly well-suited to achieving the strong coupling regime. Our approach
combines the favorable coherence properties of encoded spin qubits in silicon
with the rapid and robust long-range entanglement provided by circuit QED
systems.
