Connecting atomic qubit arrays by a cavity

We analyze an architecture for quantum computers and networks where arrays of atoms are hosted in a centimeters-scale optical cavity. The cavity has two spatially separated focal regions hosting two arrays of atoms, and non-local entangling gates between any atom pair is executed by reflecting single photons off the cavity. We analyze two representative geometries, that of a double bowtie running-wave cavity and a linear standing-wave cavity, as examples of the proposed architecture. For realistic cavity QED and atomic parameters, entangling gates with fidelities > 0.99 and gate times ~100 us may be realized between any atom pair in these cavities, which can host ~500 atoms.