  Leakage errors take qubits out of the computational subspace and will
accumulate if not addressed. A leaked qubit will reduce the effectiveness of
quantum error correction protocols due to the cost of implementing leakage
reduction circuits and the harm caused by interacting leaked states with qubit
states. Ion trap qubits driven by Raman gates have a natural choice between
qubits encoded in magnetically insensitive hyperfine states that can leak and
qubits encoded in magnetically sensitive Zeeman states of the electron spin
that cannot leak. In our previous work, we compared these two qubits in the
context of the toric code with a depolarizing leakage error model and found
that for magnetic field noise with a standard deviation less than 32 $\mu$G
that the $^{174}$Yb$^+$ Zeeman qubit outperforms the $^{171}$Yb$^+$ hyperfine
qubit. Here we examine a physically motivated leakage error model based on ions
interacting via the Molmer-Sorenson gate. We find that this greatly improves
the performance of hyperfine qubits but the Zeeman qubits are more effective
for magnetic field noise with a standard deviation less than 10 $\mu$G. At
these low magnetic fields, we find that the best choice is a mixed qubit scheme
where the hyperfine qubits are the ancilla and the leakage is handled without
the need of an additional leakage reduction circuit.
