  Neutral atom arrays are a rapidly developing platform for quantum science. In
this work, we demonstrate a universal set of quantum gate operations on a new
type of neutral atom qubit: a nuclear spin in an alkaline earth-like atom
(AEA), $^{171}$Yb. We present techniques for cooling, trapping and imaging
using a newly discovered magic trapping wavelength at $\lambda = 486.78$ nm. We
implement qubit initialization, readout, and single-qubit gates, and observe
long qubit lifetimes, $T_1 \approx 20$ s and $T^*_2 = 1.24(5)$ s, and a
single-qubit operation fidelity $\mathcal{F}_{1Q} = 0.99959(6)$. We also
demonstrate two-qubit entangling gates using the Rydberg blockade, as well as
coherent control of these gate operations using light shifts on the Yb$^+$ ion
core transition at 369 nm. These results are a significant step towards highly
coherent quantum gates in AEA tweezer arrays.
