  Neutral atom arrays have recently emerged as a promising platform for quantum
information processing. One important remaining roadblock for the large-scale
application of these systems is the ability to perform error-corrected quantum
operations. To entangle the qubits in these systems, atoms are typically
excited to Rydberg states, which could decay or give rise to various correlated
errors that cannot be addressed directly through traditional methods of
fault-tolerant quantum computation. In this work, we provide the first complete
characterization of these sources of error in a neutral-atom quantum computer
and propose hardware-efficient, fault-tolerant quantum computation schemes that
mitigate them. Notably, we develop a novel and distinctly efficient method to
address the most important errors associated with the decay of atomic qubits to
states outside of the computational subspace. These advances allow us to
significantly reduce the resource cost for fault-tolerant quantum computation
compared to existing, general-purpose schemes. Our protocols can be implemented
in the near-term using state-of-the-art neutral atom platforms with qubits
encoded in both alkali and alkaline-earth atoms.
