  Entangling gates in trapped-ion quantum computing have primarily targeted
stationary ions with initial motional distributions that are thermal and close
to the ground state. However, future systems will likely incur significant
non-thermal excitation due to, e.g., ion transport, longer operational times,
and increased spatial extent of the trap array. In this paper, we analyze the
impact of such coherent motional excitation on entangling-gate error by
performing simulations of Molmer-Sorenson (MS) gates on a pair of trapped-ion
qubits with both thermal and coherent excitation present in a shared motional
mode at the start of the gate. We discover that a small amount of coherent
displacement dramatically erodes gate performance in the presence of
experimental noise, and we demonstrate that applying only limited control over
the phase of the displacement can suppress this error. We then use experimental
data from transported ions to analyze the impact of coherent displacement on
MS-gate error under realistic conditions.
