  We investigate theoretically the speed limit of quantum gate operations for
ion trap quantum information processors. The proposed methods use laser pulses
for quantum gates which 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 frequency of
the relevant electronic transition, and the vibrational frequency in the trap.
We have experimentally studied the gate operations below and above this speed
limit. In the latter case, the fidelity is reduced, in agreement with our
theoretical findings. //
  Changes: a) error in equ. 24 and table III repaired b) reference Jonathan et
al, quant-ph/ 0002092, added (proposes fast quantum gates using the AC-Stark
effect)
