  We examine the detailed scenario for implementing n-control-qubit Toffoli
gates and select gates on ion-trap quantum computers, especially those that
shuttle ions into interaction zones. We determine expected performance of these
gates with realistic parameters for an ion-trap quantum computer and taking
into account the time variation of the exchange integrals. This allows us to
estimate the errors due to spin-phonon entanglement as well. While there are
challenges with implementing these gates, because their performance always has
some degree of error, they should be feasible on current hardware, but they may
be too slow to be used efficiently in quantum codes on noisy intermediate scale
quantum computers.
