  We report the implementation of universal two- and three-qubit entangling
gates on neutral atom qubits encoded in long-lived hyperfine ground states. The
gates are mediated by excitation to strongly interacting Rydberg states, and
are implemented in parallel on several clusters of atoms in a one-dimensional
array of optical tweezers. Specifically, we realize the controlled-phase gate,
enacted by a novel, fast protocol involving only global coupling of two qubits
to Rydberg states. We benchmark this operation by preparing Bell states with
fidelity $\mathcal{F} \ge 95.0(2)\%$, and extract gate fidelity $\ge
97.4(3)\%,$ averaged across five atom pairs. In addition, we report a
proof-of-principle implementation of the three-qubit Toffoli gate, in which two
control atoms simultaneously constrain the behavior of one target atom. These
experiments demonstrate key ingredients for high-fidelity quantum information
processing in a scalable neutral atom platform.
