  We investigate quantum computation with neutral atoms in optical microtraps
where the qubit is implemented in the motional states of the atoms, i.e., in
the two lowest vibrational states of each trap. The quantum gate operation is
performed by adiabatically approaching two traps and allowing tunneling and
cold collisions to take place. We demonstrate the capability of this scheme to
realize a square-root of swap gate, and address the problem of double
occupation and excitation to other unwanted states. We expand the two-particle
wavefunction in an orthonormal basis and analyze quantum correlations
throughout the whole gate process. Fidelity of the gate operation is evaluated
as a function of the degree of adiabaticity in moving the traps. Simulations
are based on rubidium atoms in state-of-the-art optical microtraps with quantum
gate realizations in the few tens of milliseconds duration range.
