Observing ground-state properties of the Fermi-Hubbard model using a scalable algorithm on a quantum computer

Stasja Stanisic, Jan Lukas Bosse, Filippo Maria Gambetta, Raul A. Santos, Wojciech Mruczkiewicz, Thomas E. O’Brien, Eric Ostby and Ashley Montanaro ()
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Stasja Stanisic: Phasecraft Ltd.
Jan Lukas Bosse: Phasecraft Ltd.
Filippo Maria Gambetta: Phasecraft Ltd.
Raul A. Santos: Phasecraft Ltd.
Wojciech Mruczkiewicz: Google Quantum AI
Thomas E. O’Brien: Google Quantum AI
Eric Ostby: Google Quantum AI
Ashley Montanaro: Phasecraft Ltd.

Nature Communications, 2022, vol. 13, issue 1, 1-11

Abstract: Abstract The famous, yet unsolved, Fermi-Hubbard model for strongly-correlated electronic systems is a prominent target for quantum computers. However, accurately representing the Fermi-Hubbard ground state for large instances may be beyond the reach of near-term quantum hardware. Here we show experimentally that an efficient, low-depth variational quantum algorithm with few parameters can reproduce important qualitative features of medium-size instances of the Fermi-Hubbard model. We address 1 × 8 and 2 × 4 instances on 16 qubits on a superconducting quantum processor, substantially larger than previous work based on less scalable compression techniques, and going beyond the family of 1D Fermi-Hubbard instances, which are solvable classically. Consistent with predictions for the ground state, we observe the onset of the metal-insulator transition and Friedel oscillations in 1D, and antiferromagnetic order in both 1D and 2D. We use a variety of error-mitigation techniques, including symmetries of the Fermi-Hubbard model and a recently developed technique tailored to simulating fermionic systems. We also introduce a new variational optimisation algorithm based on iterative Bayesian updates of a local surrogate model.

Date: 2022
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DOI: 10.1038/s41467-022-33335-4

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