  A large qubit capacity and an individual readout capability are two crucial
requirements for large-scale quantum computing and simulation. As one of the
leading physical platforms for quantum information processing, the ion trap has
achieved quantum simulation of tens of ions with site-resolved readout in 1D
Paul trap, and that of hundreds of ions with global observables in 2D Penning
trap. However, integrating these two features into a single system is still
very challenging. Here we report the stable trapping of 512 ions in a 2D Wigner
crystal and the sideband cooling of their transverse motion. We demonstrate the
quantum simulation of long-range quantum Ising models with tunable coupling
strengths and patterns, with or without frustration, using 300 ions. Enabled by
the site resolution in the single-shot measurement, we observe rich spatial
correlation patterns in the quasi-adiabatically prepared ground states, which
allows us to verify quantum simulation results by comparing with the calculated
collective phonon modes and with classical simulated annealing. We further
probe the quench dynamics of the Ising model in a transverse field to
demonstrate quantum sampling tasks. Our work paves the way for simulating
classically intractable quantum dynamics and for running NISQ algorithms using
2D ion trap quantum simulators.
