Entanglement and control of single nuclear spins in isotopically engineered silicon carbide.

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 Si 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 that 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 (Hahn-echo T = 2.3 ms, dynamical decoupling T > 14.5 ms), and a >40-fold increase in Ramsey spin dephasing time (T*) from isotopic purification. Overall, this work underlines the importance of controlling the nuclear environment in solid-state systems and links single photon emitters with nuclear registers in an industrially scalable material.