Entangling gates in trapped-ion quantum computers are most often applied to stationary ions with initial motional distributions that are thermal and close to the ground state, while those demonstrations that involve transport generally use sympathetic cooling to reinitialize the motional state prior to applying a gate. Future systems with more ions, however, will face greater nonthermal excitation due to increased amounts of ion transport and exacerbated by longer operational times and variations over the trap array. In addition, pregate sympathetic cooling may be limited due to time costs and laser access constraints. In this paper, we analyze the impact of such coherent motional excitation on entangling-gate error by performing simulations of Mølmer-Sørenson (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. Here, we quantify how a small amount of coherent displacement erodes gate performance in the presence of experimental noise, and we demonstrate that adjusting the relative phase between the initial coherent displacement and the displacement induced by the gate or using Walsh modulation 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.
We report that methane, CH4, can be used as an efficient F-state quenching gas for trapped ytterbium ions. The quenching rate coefficient is measured to be (2.8 ± 0.3) × 106 s-1 Torr-1. For applications that use microwave hyperfine transitions of the ground-state 171Y b ions, the CH4 induced frequency shift coefficient and the decoherence rate coefficient are measured as δν/ν = (-3.6 ± 0.1) × 10-6 Torr-1 and 1/T2 = (1.5 ± 0.2) × 105 s-1 Torr-1. In our buffer-gas cooled 171Y b+ microwave clock system, we find that only ≤10-8 Torr of CH4 is required under normal operating conditions to efficiently clear the F-state and maintain ≥85% of trapped ions in the ground state with insignificant pressure shift and collisional decoherence of the clock resonance.