N-body interactions between trapped ion spins

We present new techniques to realize quantum gates and simulations using ion-phonon interactions. We describe a single-step protocol to generate N-body entangling interactions between trapped atomic ion qubits using spin-dependent squeezing; we analyze the effect of multiple motional modes and present recent experimental results. This technique can potentially improve the expression of quantum processes beyond the native Mølmer-Sørensen Interaction on currently available trapped-ion quantum processors.