Realization of Quantum Logic Gates in Ion Traps Without Any Requirement on the Lamb-Dicke Parameter

A scheme is presented for realizing quantum logic gate in an ion trap. In the scheme the state of the mth ion is first replicated onto the collective motion. Then a transformation, conditional on the motional state, is performed on the nth ion. Finally the motional state is replicated back onto the mth ion. By this way the quantum logic-gate between the mth and the nth ions is realized. The scheme does not put any requirement on the Lamb-Dicke parameter.