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. 4 Author to whom any correspondence should be addressed. New Journal of Physics 13 (2011) 115011 1367-2630/11/115011+23$33.00 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft