  Executing quantum algorithms on error-corrected logical qubits is a critical
step for scalable quantum computing, but the requisite numbers of qubits and
physical error rates are demanding for current experimental hardware. Recently,
the development of error correcting codes tailored to particular physical noise
models has helped relax these requirements. In this work, we propose a qubit
encoding and gate protocol for ${}^{171}$Yb neutral atom qubits that converts
the dominant physical errors into erasures, that is, errors in known locations.
The key idea is to encode qubits in a metastable electronic level, such that
gate errors predominantly result in transitions to disjoint subspaces whose
populations can be continuously monitored via fluorescence. We estimate that
98% of errors can be converted into erasures. We quantify the benefit of this
approach via circuit-level simulations of the surface code, finding a threshold
increase from 0.937% to 4.15%. We also observe a larger code distance near the
threshold, leading to a faster decrease in the logical error rate for the same
number of physical qubits, which is important for near-term implementations.
Erasure conversion should benefit any error correcting code, and may also be
applied to design new gates and encodings in other qubit platforms.
