High-fidelity control of a $^{13}$C nuclear spin coupled to a tin-vacancy center in diamond

Nuclear spins near group-IV defects in diamond are promising candidates for quantum memories in quantum network applications. Here, we demonstrate high-fidelity control of a single $^{13}$C nuclear spin coupled to a tin-vacancy center in diamond. We perform a combination of optical and microwave pumping to achieve initialization into a combined electronuclear spin state with a fidelity of 99.74(3)%. Harnessing a superconducting waveguide for radio-frequency driving, we demonstrate precise nuclear-spin control: Ramsey measurements reveal a coherence time of 𝑇*$_2$=1.5⁢(1)  ms , and we use dynamical decoupling to extend it to 1.35(3) s. We perform randomized benchmarking, yielding a single-qubit gate fidelity of 99.92(1)%. This demonstrates a coherent spin-photon system with promising properties for quantum network nodes.