Quantum simulations of many-body systems are among the most promising applications of quantum computers. Fermionic models are especially important due to their central role in understanding phenomena across natural sciences, but are challenging to simulate with qubit devices. Here we realize a digital quantum simulation architecture for two-dimensional fermionic systems based on reconfigurable atom arrays. We utilize a fermion-to-qubit mapping based on Kitaev's model on a honeycomb lattice, in which fermionic statistics are encoded using long-range entangled states. We prepare these states efficiently using measurement and feedforward, and realize subsequent fermionic evolution through Floquet engineering with tunable entangling gates interspersed with atom rearrangement. Leveraging this fermion description of the Kitaev spin model, we efficiently prepare topological states across its complex phase diagram and verify the non-Abelian spin liquid phase by evaluating an odd Chern number. We further explore this two-dimensional fermion system by realizing tunable strong interactions and studying dynamics of the Fermi-Hubbard model on a square lattice. These results pave the way for digital quantum simulations of complex fermionic systems for materials science, chemistry, and high-energy physics.
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