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

The Fermi-Hubbard model represents one of the benchmarks for testing quantum computational methods for condensed matter. Here, the authors are able to reproduce qualitative properties of the model on 1 x 8 and 2 x 4 lattices, by running a VQE-based algorithm on a superconducting quantum processor. 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 x 8 and 2 x 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.

Automated summary

The authors successfully reproduced qualitative properties of the Fermi-Hubbard model using a VQE-based algorithm on a superconducting quantum processor, and employed various error-mitigation techniques to demonstrate the effectiveness of the algorithm.