Abstract
Quantum simulations of many-body systems are among the most promising applications of quantum computers. In particular, models based on strongly-correlated fermions are central to our understanding of quantum chemistry and materials problems, and can lead to exotic, topological phases of matter. However, due to the non-local nature of fermions, such models 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, realize subsequent fermionic evolution through Floquet engineering with tunable entangling gates 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 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 and study 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.
*DOE Quantum Systems Accelerator Center, DARPA ONISQ program, DARPA IMPAQT program, DARPA MeasQuIT program, Center for Ultracold Atoms (an NSF Physics Frontiers Center), the National Science Foundation, IARPA and the Army Research Office under the Entangled Logical Qubits program, Wellcome Leap Foundation under the Quantum for Bio program, QuEra Computing, the National Defense Science and Engineering Graduate (NDSEG) fellowship, the Harvard Quantum Initiative Postdoctoral Fellowship in Science and Engineering, the Fannie and John Hertz Foundation, the Department of Energy Computational Science Graduate Fellowship.
