A fast scheme for one-step preparation of a highly entangled cluster state in the ion-trap system

We propose to implement a highly entangled cluster state (HECS) with only one step based on the resonant interactions among N two-level ions and two different standing-wave lasers with a phase difference of π/2. The time for preparation of the HECS is related only to the frequency of the vibrational mode ν (i.e. t=2π/ν). We can ensure that the preparation time is short enough by setting the larger vibrational mode frequency ν to neglect the effect of the decoherence of the qubits. During the process of preparing the HECS, the heating effect of the vibrational mode can be neglected and the initial qubits need only one evolution with the time interval t. The reduced operation steps and the shorter preparation time make the present scheme more feasible in experiments.