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We investigate quantum computation with neutral atoms in optical microtrapswhere the qubit is implemented in the motional states of the atoms, i.e., inthe two lowest vibrational states of each trap. The quantum gate operation isperformed by adiabatically approaching two traps and allowing tunneling andcold collisions to take place. We demonstrate the capability of this scheme torealize a square-root of swap gate, and address the problem of doubleoccupation and excitation to other unwanted states. We expand the two-particlewavefunction in an orthonormal basis and analyze quantum correlationsthroughout the whole gate process. Fidelity of the gate operation is evaluatedas a function of the degree of adiabaticity in moving the traps. Simulationsare based on rubidium atoms in state-of-the-art optical microtraps with quantumgate realizations in the few tens of milliseconds duration range.

Quantum computing in optical microtraps based on the motional states of neutral atoms