  We propose a new method for generating programmable interactions in one- and
two-dimensional trapped-ion quantum simulators. Here we consider the use of
optical tweezers to engineer the sound-wave spectrum of trapped ion crystals.
We show that this approach allows us to tune the interactions and connectivity
of the ion qubits beyond the power-law interactions accessible in current
setups. We demonstrate the experimental feasibility of our proposal using
realistic tweezer settings and experimentally relevant trap parameters to
generate the optimal tweezer patterns to create target spin-spin interaction
patterns in both one- and two-dimensional crystals. Our approach will advance
quantum simulation in trapped-ion platforms as it allows them to realize a
broader family of quantum spin Hamiltonians.
