  Motivated by far-reaching applications ranging from quantum simulations of
complex processes in physics and chemistry to quantum information processing, a
broad effort is currently underway to build large-scale programmable quantum
systems. Such systems provide unique insights into strongly correlated quantum
matter, while at the same time enabling new methods for computation and
metrology. Here, we demonstrate a programmable quantum simulator based on
deterministically prepared two-dimensional arrays of neutral atoms, featuring
strong interactions controlled via coherent atomic excitation into Rydberg
states. Using this approach, we realize a quantum spin model with tunable
interactions for system sizes ranging from 64 to 256 qubits. We benchmark the
system by creating and characterizing high-fidelity antiferromagnetically
ordered states, and demonstrate the universal properties of an Ising quantum
phase transition in (2+1) dimensions. We then create and study several new
quantum phases that arise from the interplay between interactions and coherent
laser excitation, experimentally map the phase diagram, and investigate the
role of quantum fluctuations. Offering a new lens into the study of complex
quantum matter, these observations pave the way for investigations of exotic
quantum phases, non-equilibrium entanglement dynamics, and hardware-efficient
realization of quantum algorithms.
