Quantum simulation of the hexagonal Kitaev model with trapped ions

We present a detailed study of quantum simulations of coupled spin systems in surface-electrode (SE) ion-trap arrays, and illustrate our findings with a proposed implementation of the hexagonal Kitaev model (Kitaev A 2006 Ann. Phys. 321 2). The effective (pseudo) spin interactions making up such quantum simulators are found to be proportional to the dipole-dipole interaction between the trapped ions, and are mediated by motion that can be driven by state-dependent forces. The precise forms of the trapping potentials and the interactions are derived in the presence of an SE and a cover electrode. These results are the starting point to derive an optimized SE geometry for trapping ions in the desired honeycomb lattice of Kitaev's model, where we design the dipole-dipole interactions in a way that allows for coupling all three bond types of the model simultaneously, without the need for time discretization. Finally, we propose a simple wire structure that can be incorporated into a microfabricated chip to generate localized state-dependent forces which drive the couplings prescribed by this particular model; such a wire structure should be adaptable to many other situations.