Engineering quantum simulation Halmiltonian in a trapped ion quantum computer

A quantum simulator based on trapped ion chains may seem a natural fit for studying spin dynamics in a 1D system. However, despite the all-to-all connectivity of two qubit gates in a long ion chain, tailoring interactions for long-range or higher dimensional connectivity remains a challenge. Here we explore different ways to implement more flexible interactions in a ion chain and compare their efficiency and fidelity when applied for certain higher dimensional models