X. L. Lei

A simple alternative scheme for implementing quantum gates with a single trapped cold two-level ion beyond the Lamb-Dicke (LD) limit is proposed. Basing on the quantum dynamics for the laser-ion interaction described by a generalized Jaynes-Cummings model, one can introduce two kinds of elementary quantum operations i.e., the simple rotation on the bare atomic state, generated by applying a resonant pulse, and the joint operation on the internal and external degrees of the ion, performed by using an off-resonant pulse. Several typical quantum gates, including Hadamard gate, controlled-Z and controlled-NOT gates $etc.$, can thus be implemented exactly by using these elementary operations. The experimental parameters including the LD parameter and the durations of the applied laser pulses, for these implementation are derived analytically and numerically. Neither the LD approximation for the laser-ion interaction nor the auxiliary atomic level is needed in the present scheme.

We propose a simple scheme for implementing quantum logic gates with a string of two-level trapped cold ions outside the Lamb-Dicke limit. Two internal states of each ion are used as one computational qubit (CQ) and the collective vibration of ions acts as the information bus, i.e., bus qubit (BQ). Using the quantum dynamics for the laser-ion interaction as described by a generalized Jaynes-Cummings model, we show that quantum entanglement between any one CQ and the BQ can be coherently manipulated by applying classical laser beams. As a result, universal quantum gates, i.e. the one-qubit rotation and two-qubit controlled gates, can be implemented exactly. The required experimental parameters for the implementation, including the Lamb-Dicke (LD) parameter and the durations of the applied laser pulses, are derived. Neither the LD approximation for the laser-ion interaction nor the auxiliary atomic level is needed in the present scheme.