Expanding the set of native ion-ion interaction graphs for quantum simulation

Trapped-ion quantum simulators generate pair-wise interactions by using spin-dependent optical dipole forces to couple to the motional modes of the ion crystal. While it is common for trapped-ion quantum simulations to host fully-connected interactions which decay algebraically with distance, such interactions are not a fundamental limitation of trapped-ion simulations. Here, we show a suite of achievable interaction graphs in both 1D and 2D which may be generated either by selective coupling to specific vibrational modes or by arranging the ions to be equally-spaced along the trap axis. To this end, we investigate a monolithic trap design that allows for a much more expansive set of 1D and 2D interaction graphs compared to traditional ion-trap quantum simulation approaches.