  Ion trap systems are a leading platform for large scale quantum computers.
Trapped ion qubit crystals are fully-connected and reconfigurable, owing to
their long range Coulomb interaction that can be modulated with external
optical forces. However, the spectral crowding of collective motional modes
could pose a challenge to the control of such interactions for large numbers of
qubits. Here, we show that high-fidelity quantum gate operations are still
possible with very large trapped ion crystals, simplifying the scaling of ion
trap quantum computers. To this end, we present analytical work that determines
how parallel entangling gates produce a crosstalk error that falls off as the
inverse cube of the distance between the pairs. We also show experimental work
demonstrating entangling gates on a fully-connected chain of seventeen
$^{171}{\rm{Yb}}^{+}$ ions with fidelities as high as $97(1)\%$.
