  We have demonstrated transport of Be+ ions through a 2D Paul-trap array that
incorporates an X-junction, while maintaining the ions near the motional
ground-state of the confining potential well. We expand on the first report of
the experiment [1], including a detailed discussion of how the transport
potentials were calculated. Two main mechanisms that caused motional excitation
during transport are explained, along with the methods used to mitigate such
excitation. We reduced the motional excitation below the results in Ref. [1] by
a factor of approximately 50. The effect of a mu-metal shield on qubit
coherence is also reported. Finally, we examined a method for exchanging energy
between multiple motional modes on the few-quanta level, which could be useful
for cooling motional modes without directly accessing the modes with lasers.
These results establish how trapped ions can be transported in a large-scale
quantum processor with high fidelity.
