  Nuclear spins in the solid state are both a cause of decoherence and a
valuable resource for spin qubits. In this work, we demonstrate control of
isolated 29Si nuclear spins in silicon carbide (SiC) to create an entangled
state between an optically active divacancy spin and a strongly coupled nuclear
register. We then show how isotopic engineering of SiC unlocks control of
single weakly coupled nuclear spins and present an ab initio method to predict
the optimal isotopic fraction which maximizes the number of usable nuclear
memories. We bolster these results by reporting high-fidelity electron spin
control (F=99.984(1)%), alongside extended coherence times (T2=2.3 ms,
T2DD>14.5 ms), and a >40 fold increase in dephasing time (T2*) from isotopic
purification. Overall, this work underlines the importance of controlling the
nuclear environment in solid-state systems and provides milestone
demonstrations that link single photon emitters with nuclear memories in an
industrially scalable material.
