Strategies for solving the Fermi-Hubbard model on near-term quantum computers

TL;DR

This paper analyzes and optimizes variational quantum algorithms for solving the Fermi-Hubbard model, demonstrating that low-depth circuits can potentially outperform classical methods on near-term quantum hardware.

Contribution

It introduces a more efficient variational ansatz and provides a detailed complexity analysis, showing feasibility for near-term quantum computers to solve larger Hubbard model instances.

Findings

Depth complexities are significantly lower than previous work.

Numerical experiments suggest high-fidelity ground state solutions with low circuit depth.

Realistic noise effects still allow for potential quantum advantage.

Abstract

The Fermi-Hubbard model is of fundamental importance in condensed-matter physics, yet is extremely challenging to solve numerically. Finding the ground state of the Hubbard model using variational methods has been predicted to be one of the first applications of near-term quantum computers. Here we carry out a detailed analysis and optimisation of the complexity of variational quantum algorithms for finding the ground state of the Hubbard model, including costs associated with mapping to a real-world hardware platform. The depth complexities we find are substantially lower than previous work. We performed extensive numerical experiments for systems with up to 12 sites. The results suggest that the variational ans\"atze we used -- an efficient variant of the Hamiltonian Variational ansatz and a novel generalisation thereof -- will be able to find the ground state of the Hubbard model with high fidelity in relatively low quantum circuit depth. Our experiments include the effect of realistic measurements and depolarising noise. If our numerical results on small lattice sizes are representative of the somewhat larger lattices accessible to near-term quantum hardware, they suggest that optimising over quantum circuits with a gate depth less than a thousand could be sufficient to solve instances of the Hubbard model beyond the capacity of classical exact diagonalisation.