  The computational difficulty of solving fully quantum many-body spin problems
is a significant obstacle to understanding the behavior of strongly correlated
quantum matter. Experimental ion-trap quantum simulation is a promising
approach for studying these lattice spin models, but has so far been limited to
one-dimensional systems. This work argues that such quantum simulation
techniques are extendable to a 2D ion crystal confined in a radiofrequency (rf)
trap. Using appropriately chosen parameters, driven ion motion due to the rf
fields can be made small and will not limit the types of quantum spin models
that can be experimentally encoded. The rf-driven motion is calculated to
modestly reduce the stability region of a 2D crystal and must be considered
when designing the 2D trap. The system will be scalable to 100+ quantum
particles, far beyond the realm of classical intractability, while maintaining
the traditional ion-trap strengths of individual-ion control, long quantum
coherence times, and site-resolved projective spin measurements.
