A scheme for the implementation of unconventional geometric phase gates with trapped ions

We propose a scheme for the realization of unconventional geometric two-qubit phase gates with two identicaltwo-level ions. In the present scheme, the two ions are simultaneously illuminated by a standing-wave laser pulse withits pulse frequency being tuned to the ionic transition. The gate operation time can be much shorter, making the systemrobust against decoherence. In addition, we choose the appropriate experimental parameters to construct the geometricphase gate in one step, and thus avoid implementing the pure geometric single qubit operation.