Implementation of many-qubit Grover search with trapped ultracold ions

We propose a potentially practical scheme for realization of an n-qubit (n>2) conditional phase flip (CPF) gate and implementation of Grover search algorithm in the ion-trap system. We demonstrate both analytically and numerically that, our scheme could be achieved efficiently to find a marked state with high fidelity and high success probability. We also show the merits of the proposal that the increase of the ion number can improve the fidelity and the success probability of the CPF gate. The required operations for Grover search are very close to the capabilities of current ion-trap techniques.