  Quantum simulation using synthetic systems is a promising route to solve
outstanding quantum many-body problems in regimes where other approaches,
including numerical ones, fail. Many platforms are being developed towards this
goal, in particular based on trapped ions, superconducting circuits, neutral
atoms or molecules. All of which face two key challenges: (i) scaling up the
ensemble size, whilst retaining high quality control over the parameters and
(ii) certifying the outputs for these large systems. Here, we use programmable
arrays of individual atoms trapped in optical tweezers, with interactions
controlled by laser-excitation to Rydberg states to implement an iconic
many-body problem, the antiferromagnetic 2D transverse field Ising model. We
push this platform to an unprecedented regime with up to 196 atoms manipulated
with high fidelity. We probe the antiferromagnetic order by dynamically tuning
the parameters of the Hamiltonian. We illustrate the versatility of our
platform by exploring various system sizes on two qualitatively different
geometries, square and triangular arrays. We obtain good agreement with
numerical calculations up to a computationally feasible size (around 100
particles). This work demonstrates that our platform can be readily used to
address open questions in many-body physics.
