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Probing the Kitaev honeycomb model on a neutral-atom quantum computer
Simon J. Evered, Marcin Kalinowski, Alexandra A. Geim, Tom Manovitz, Dolev Bluvstein, Sophie H. Li, Nishad Maskara, Hengyun Zhou, Sepehr Ebadi, Muqing Xu, Joseph Campo, Madelyn Cain, Stefan Ostermann, Susanne F. Yelin, Subir Sachdev, Markus Greiner, Vladan Vuletić, Mikhail D. Lukin
TL;DR
Beyond one dimension, local fermion operations such as nearest-neighbor hopping acquire macroscopic operator weight on qubits. The work implements a honeycomb-based fermion mapping with Floquet evolution and evaluates topological and exchange behavior, obtaining C=0 for the Abelian phase and C=1 for phase B.
Problem
Beyond one dimension, even simple local fermion operations such as nearest-neighbor hopping lead to macroscopic operator weight on the qubit side.
Method
The approach combines a honeycomb-based fermion-to-qubit mapping with measurement-based preparation, Floquet evolution using movable traps and tunable entangling gates, and error detection or postselection.
Results
The learned Hamiltonian gives C=0 for the Abelian phase and C=1 for phase B, while exchange and control protocols match expectations and improve with postselection.
Takeaways & Limitations
The mapping and Floquet circuit preserve topological order up to a small decay from gate errors and provide evidence for observing the fermion exchange phase.
Takeaways & Limitations
The Chern number is obtained from a learned Hamiltonian rather than individual snapshots, and the authors identify comparison with other extraction methods as future work.
Abstract
from arXiv · showhide
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.
METHODS
The experiment combines tunable entangling gates, atom rearrangement, measurement-based preparation, and postselection to simulate Kitaev-model fermions and characterize topological phases. These procedures preserve topological order while enabling fermion dynamics, Chern-number extraction, and exchange-statistics measurements.
- Tunable entangling gates: Tunable CPHASE gates are implemented with a cosine phase profile and calibrated by measuring the accumulated entangling phase.The normalized angle satisfies θ=1 for the CZ gate; calibration uses a two-atom benchmarking sequence and phase scans.
- Topological-state preparation: Measurement-based preparation uses ancillas, mid-circuit measurement, feedforward, and controlled-Y operations to create the target long-range-entangled topological state.The protocol first prepares a ZXXZ toric-code state, then extends operators to the honeycomb plaquettes.
- Error detection: Error detection is optional for the main results but consistently improves data quality through decoding and loss postselection.Acceptance fractions range from 3% to 25% for string observables, 1% to 7% for fermion-exchange color plots, and 2% to 5% for Fig. 5e.
- Floquet evolution: Floquet evolution transports one data-qubit sublattice between gates, applies basis-changing rotations, and implements periodic cylindrical boundary conditions.The same circuit structure supports different Floquet circuits by changing the CPHASE gates, while dynamical decoupling suppresses dephasing from motion.
- Topological characterization: The Floquet circuit preserves topological order up to gate-error decay, while the learned parent Hamiltonian yields C=0 for the Abelian phase and C=1 for phase B.For batch sizes above 200, the bootstrapped averaged Chern number is above 0.9 and approaches 1 with increasing batch size.
- Fermion dynamics: Large JZ suppresses particle-number-changing components, making the shortest particle-conserving Floquet circuit depth-6; exchange experiments observe the expected fermion hops and improve with postselection.The exchange protocol moves fermions from sites A and D to B and C, while the encoded hopping reproduces the Fermi-Hubbard model when particle number is conserved.