  We design a quantum repeater architecture using individual $^{167}$Er ions
doped into Y$_2$SiO$_5$ crystal. This ion is a promising candidate for a
repeater protocol because of its long hyperfine coherence time in addition to
its ability to emit photons within the telecommunication wavelength range. To
distribute entanglement over a long distance, we propose two different swapping
gates between nearby ions using the exchange of virtual cavity photons and the
electric dipole-dipole interaction. We analyze their expected performance, and
discuss their strengths and weaknesses. Then, we show that a post-selection
approach can be implemented to improve the gate fidelity of the virtual photon
exchange scheme by monitoring cavity emission. Finally, we use our results for
the swapping gates to estimate the end-to-end fidelity and distribution rate
for the protocol.
