  Trapped ions have emerged as one of the highest quality platforms for the
quantum simulation of interacting spin models of interest to various fields of
physics. In such simulators, two effective spins can be made to interact with
arbitrary strengths by coupling to the collective vibrational or phonon states
of ions, controlled by precisely tuned laser beams. However, the task of
determining laser control parameters required for a given spin-spin interaction
graph is a type of inverse problem, which can be highly mathematically complex.
In this paper, we adapt a modern machine learning technique developed for
similar inverse problems to the task of finding the laser control parameters
for a number of interaction graphs. We demonstrate that typical graphs, forming
regular lattices of interest to physicists, can easily be produced for up to 50
ions using a single GPU workstation. The scaling of the machine learning method
suggests that this can be expanded to hundreds of ions with moderate additional
computational effort.
