Two Feasible Schemes for Preparing Cluster States with Ion-Trap Setup

We present two schemes for preparing cluster states with atomicqubits in an ion-trap system. In the first scheme an auxiliary atomic levelis needed. While in the second scheme an additional classical driven fieldis used, and the multi-ion cluster states can be generated by one step. Both the schemes are insensitive to thermal motion of the ions, all the facilities used in them are well within state of the art.