  We propose a scheme to realize quantum logic and entanglement for qutrit
systems via state-dependent forces on trapped ions. By exploiting the laser-ion
coupling in the presence of Coulomb interactions, the set of quantum gate
operations including the conditional phase shifts on two qutrits as well as
arbitrary SU(3) rotations on single qutrits are derived for universal quantum
manipulation. As an illustration, we demonstrate in detail how these gate
resources could be used to generate the maximally entangled state of two
qutrits. Besides being insensitive to vibrational heating of the trapped ions,
the present scheme is also shown to be scalable through designing appropriately
the pulse configuration of the laser-ion interactions.
