Quantum simulation of the hexagonal Kitaev model with trapped ions

Abstract

We present a detailed study of quantum simulations of coupled spin systems in\nsurface-electrode ion-trap arrays, and illustrate our findings with a proposed\nimplementation of the hexagonal Kitaev model [A. Kitaev, Annals of Physics\n321,2 (2006)]. The effective (pseudo)spin interactions making up such quantum\nsimulators are found to be proportional to the dipole-dipole interaction\nbetween the trapped ions, and are mediated by motion which can be driven by\nstate-dependent forces. The precise forms of the trapping potentials and the\ninteractions are derived in the presence of a surface electrode and a cover\nelectrode. These results are the starting point to derive an optimized\nsurface-electrode geometry for trapping ions in the desired honeycomb lattice\nof Kitaev's model, where we design the dipole-dipole interactions in a way that\nallows for coupling all three bond types of the model simultaneously, without\nthe need for time discretization. Finally we propose a simple wire structure\nthat can be incorporated in a microfabricated chip to generate localized\nstate-dependent forces which drive the couplings prescribed by this particular\nmodel; such a wire structure should be adaptable to many other situations.\n