  Selective control of qubits in a quantum register for the purposes of quantum
information processing represents a critical challenge for dense spin ensembles
in solid state systems. Here we present a protocol that achieves a complete set
of selective single and two-qubit gates on nuclear spins in such an ensemble in
diamond facilitated by a nearby NV center. The protocol suppresses internuclear
interactions as well as unwanted coupling between the NV center and other spins
of the ensemble to achieve quantum gate fidelities well exceeding 99% .
Notably, our method can be applied to weakly coupled, distant, spins and
therefore represents a scalable procedure that exploits the exceptional
properties of nuclear spins in diamond as robust quantum memories.
