Simulating fermion dynamics and topological matter with reconfigurable atom arrays*

Quantum computers have the potential to fundamentally advance our ability to simulate strongly correlated many-body quantum systems. Fermionic models, in particular, are central to our understanding of quantum chemistry and materials science. However, such models are challenging to simulate with quantum computers, owing to the non-local nature of fermions. Here we report on the realization of digital quantum simulations of fermionic systems based on reconfigurable atom arrays. We use a fermion-to-qubit mapping based on Kitaev's model on a honeycomb lattice, in which fermionic statistics are encoded with long-range entangled states. We prepare these states efficiently using measurement and feedforward, and realize subsequent evolution through Floquet engineering with tunable entangling gates interspersed with atom rearrangement. Leveraging the fermion description of Kitaev's 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 dynamics and directly probing fermion exchange statistics. Finally, we simulate strong interactions to study dynamics of the Fermi-Hubbard model on a square lattice. These results pave the way for digital quantum simulations of complex fermionic systems relevant for materials science, chemistry, and high-energy physics.