Quantum simulations of many-body systems are among the most promising applications of quantum computers¹. In particular, models based on strongly correlated fermions are central to our understanding of quantum chemistry and materials problems², and can lead to exotic, topological phases of matter^3,4. However, owing to the non-local nature of fermions, such models are challenging to simulate with qubit devices⁵. Here we realize a digital quantum simulation architecture for two-dimensional fermionic systems based on reconfigurable atom arrays⁶. We utilize a fermion-to-qubit mapping based on Kitaev's model on a honeycomb lattice³, in which fermionic statistics are encoded using long-range entangled states⁷. We prepare these states efficiently using measurement⁸ and feedforward⁹, realize subsequent fermionic evolution through Floquet engineering^10,11 with tunable entangling gates¹² interspersed with atom rearrangement, and improve results with built-in error detection. Leveraging this fermion description of the Kitaev spin model, we efficiently prepare topological states across its complex phase diagram¹³ and verify the non-Abelian spin-liquid phase³ by evaluating an odd Chern number^14,15. We further explore this two-dimensional fermion system by realizing tunable dynamics and directly probing fermion exchange statistics. Finally, we simulate strong interactions and study the 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, chemistry¹⁶ and high-energy physics¹⁷.

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