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 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 an example of Grover algorithm based on the two qubits. The composite laser pulses which are applied to implement the Grover algorithm have been designed in details. The issues concerning measurement and decoherence are discussed.