Assembly and coherent control of a register of nuclear spin qubits

We introduce an optical tweezer platform for assembling and individually manipulating a two-dimensional register of nuclear spin qubits. Each nuclear spin qubit is encoded in the ground $^{1}S_{0}$ manifold of $^{87}$Sr and is individually manipulated by site-selective addressing beams. We observe that spin relaxation is negligible after 5 seconds, indicating that $T_1gg5$ s. Furthermore, utilizing simultaneous manipulation of subsets of qubits, we demonstrate significant phase coherence over the entire register, estimating $T_2^star = left(21pm7right)$ s and measuring $T_2^text{echo}=left(42pm6right)$ s.