We describe a method for creating small quantum processors in a crystal stoichiometric in an optically active rare-earth ion. The crystal is doped with another rare earth, creating an ensemble of identical clusters of surrounding ions, whose optical and hyperfine frequencies are uniquely determined by their spatial position in the cluster. Ensembles of ions in each unique position around the dopant serve as qubits, with strong local interactions between ions in different qubits. These ensemble qubits can each be used as a quantum memory for light, and we show how the interactions between qubits can be used to perform linear operations on the stored photonic state. We also describe how these ensemble qubits can be used to enact, and study, error correction.R.L.A. acknowledges support from an Australian
Research Council Discovery Early Career Researcher Award
(Project No. DE170100099). This work was supported by the
Australian Research Council Centre of Excellence for Quantum Computation and Communication Technology (Grant No.
CE110001027)
