Superpositional wavefunction oscillations for the implementation of quantum algorithms modify the desired interference required for the quantum computation. We propose a scheme with trapped ultracold ion-pairs beingqubits to diminish the detrimental effect of the wavefunction oscillations, which is applied to the two-qubitGrovers search. It can be also found that the qubits in our scheme are more robust against the decoherencecaused by the environment, and the model is scalable.