  The ability to perform entangling quantum operations with low error rates in
a scalable fashion is a central element of useful quantum information
processing. Neutral atom arrays have recently emerged as a promising quantum
computing platform, featuring coherent control over hundreds of qubits and
any-to-any gate connectivity in a flexible, dynamically reconfigurable
architecture. The major outstanding challenge has been to reduce errors in
entangling operations mediated through Rydberg interactions. Here we report the
realization of two-qubit entangling gates with 99.5% fidelity on up to 60 atoms
in parallel, surpassing the surface code threshold for error correction. Our
method employs fast single-pulse gates based on optimal control, atomic dark
states to reduce scattering, and improvements to Rydberg excitation and atom
cooling. We benchmark fidelity using several methods based on repeated gate
applications, characterize the physical error sources, and outline future
improvements. Finally, we generalize our method to design entangling gates
involving a higher number of qubits, which we demonstrate by realizing
low-error three-qubit gates. By enabling high-fidelity operation in a scalable,
highly connected system, these advances lay the groundwork for large-scale
implementation of quantum algorithms, error-corrected circuits, and digital
simulations.
