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.