Abstract
We suggest a fast two-qubit quantum logic gates for trapped ions in thermal motion via geometric phase shifts. In the scheme, several vibrational modes are simultaneously displaced by driving the ions with a single off-resonant standing-wave laser. Under certain conditions, all the vibrational modes simultaneously return to the original points in the phase spaces along corresponding closed paths depending on the electronic states, producing a geometric phase gate. During the gate operation, the ions undergo no electronic transitions and the gate time might be shorter than the period of the center-of-mass vibration.
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