We investigate theoretically the speed limit of quantum gate operations for
ion trap quantum information processors. The proposed methods use laser pu
lses for quantum gates that entangle the electronic and vibrational degrees
of freedom of the trapped ions. Two of these methods are studied in detail
and for both of them the speed is limited by a combination of the recoil f
requency of the relevant electronic transition, and the vibrational frequen
cy in the trap. We have experimentally studied the gate operations below an
d above this speed limit. In the latter case, the fidelity is reduced, in a
greement with our theoretical findings.