Quantum simulation of the hexagonal Kitaev model with trapped ions

Roman Schmied,Dietrich Leibfried,Janus H Wesenberg

doi:10.1088/1367-2630/13/11/115011

Roman Schmied, Dietrich Leibfried + Show 1 more

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https://doi.org/10.1088/1367-2630/13/11/115011

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Abstract

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.

Highlights

Ion trap systems have proven to perform well for implementing the basic elements of traditional quantum computing, where evolution is described in terms of discrete gate operations, which can be implemented step by step as intermediate states are irrelevant
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
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

Summary

Introduction

Ion trap systems have proven to perform well for implementing the basic elements of traditional quantum computing, where evolution is described in terms of discrete gate operations, which can be implemented step by step as intermediate states are irrelevant. While the initial proposal for quantum computing with trapped ions relied on a number of sequential steps to mediate effective qubit interactions [1], other approaches [2,3,4,5,6,7,8,9,10] achieve interaction between the internal states of the ions via constant Hamiltonians and allow the development of quantum simulators based on trapped ions [7, 8, 11,12,13,14,15] In such simulators, interactions between trapped ions are dominated by the Coulomb potential. Appendix A gives a summary of the used coordinate systems

Electrostatics in the presence of conducting planes

Spin–spin interactions between trapped ions

Kitaev model

Conclusions