Erasures, or errors with known locations, are a more favorable type of error
for quantum error-correcting codes than Pauli errors. Converting physical noise
into erasures can significantly improve the performance of quantum error
correction. Here we apply the idea of performing erasure conversion by encoding
qubits into metastable atomic states, proposed by Wu, Kolkowitz, Puri, and
Thompson [Nat. Comm. 13, 4657 (2022)], to trapped ions. We suggest an
erasure-conversion scheme for metastable trapped-ion qubits and develop a
detailed model of various types of errors. We then compare the logical
performance of ground and metastable qubits on the surface code under various
physical constraints, and conclude that metastable qubits may outperform ground
qubits when the achievable laser power is larger for metastable qubits.Comment: 20 pages, 8 figure