Interaction graph engineering in trapped-ion quantum simulators with global drives

Trapped-ion quantum simulators have demonstrated a long history of studying the physics of interacting spin-lattice systems using globally addressed entangling operations, which are typically laser beams addressing the whole ion chain simultaneously. Here, we broaden and delimit the set of effective spin-spin interactions achievable using exclusively global driving fields. We find that new categories of interaction graphs become achievable with perfect or near-perfect theoretical fidelity by tailoring the coupling to each vibrational mode of the ion crystal, or by shaping the trapping potential to include specific anharmonic terms. We also derive a rigorous test to determine whether a desired interaction graph is accessible using only globally driven fields. These tools broaden the reach of trapped-ion quantum simulators so that they may more easily address open questions in materials science and quantum chemistry.