Two-dimensional ion crystals in radio-frequency traps for quantum simulation

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 two-dimensional (2D) ion crystal confined in a radio-frequency (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.