Quantum simulation of the hexagonal Kitaev model with trapped ions

TL;DR

This paper proposes a method for simulating the hexagonal Kitaev model using trapped ions in surface-electrode arrays, detailing the design of ion traps and interactions to realize the model's complex couplings.

Contribution

It introduces an optimized surface-electrode geometry and a wire structure for implementing the Kitaev model with trapped ions, enabling all three bond types simultaneously without time discretization.

Findings

Derived trapping potentials and interactions in surface-electrode setups.

Designed a honeycomb lattice with controllable dipole-dipole interactions.

Proposed a microfabricated wire structure for localized state-dependent forces.

Abstract

We present a detailed study of quantum simulations of coupled spin systems in surface-electrode ion-trap arrays, and illustrate our findings with a proposed implementation of the hexagonal Kitaev model [A. Kitaev, Annals of Physics 321,2 (2006)]. 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 which can be driven by state-dependent forces. The precise forms of the trapping potentials and the interactions are derived in the presence of a surface electrode and a cover electrode. These results are the starting point to derive an optimized surface-electrode 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 in 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.