<p>Optically addressed atomic defects in the solid state are widely used as single-photon sources and memories for quantum network applications. The solid-state environment allows for a high density of electron and nuclear spins with the potential to form registers for coherent information processing. Interactions between the spins could enable computational gates, but it is challenging to reliably address individual spins at nanometre separations at which interactions are large. Rare-earth ions offer a promising solution, as their narrow homogeneous optical linewidth allows the frequency-domain resolution of a large number of emitters independent of their spatial separation. Here we realize the coherent optical and spin control of a pair of interacting Er³⁺ ions, together with a nearby nuclear spin ancilla. We demonstrate two-qubit electron–electron gates and use them to perform repeated quantum non-demolition measurements on one of the Er³⁺ ions. We also use electron–nuclear gates to coherently store and retrieve qubit information in a nuclear spin, and show that the nuclear spin coherence survives read-out of the electron spin. These techniques can be readily scaled to larger numbers of electron and nuclear spins, providing a platform for massively multiplexed quantum network nodes.</p>