Fast generation of cluster states in a linear ion trap

We propose a practical scheme to generate cluster states by simultaneously accomplishing two-qubit conditional gating on an array of equidistant ions by using transverse modes. Our operation is robust to heating and insensitive to Lamb--Dicke parameter. Meanwhile, as it is carried out in a geometric quantum computing fashion, our scheme enables the fast and high-fidelity generation of cluster states. The experimental feasibility is discussed with sophisticated ion trap techniques.