A Robust Scheme for Two－Qubit Grover Quantum Search Alogrithm Based on the Motional and Internal States of a Single Cold Trapped Ion

We propose a scheme to implement a two-qubit Grover quantum search algorithm. The novelty in the proposal is that the motional state is introduced into the computation and the internal state within a single cold trapped ion.The motional and internal states of the ion are manipulated as two qubits by the laser pulses to accomplish anexample of a Grover algorithm based on the two qubits. The composite laser pulses that are applied to implementthe Grover algorithm have been designed in detail. The issues concerning measurement and decoherence arediscussed.