Quantum Annealing for the Fermi-Hubbard Model

Recently, a compact fermion to qubit encoding for the Fermi-Hubbard model (FHM) on a square lattice was proposed [1]. The encoding uses at most terms of Pauli weight-3 with an additional feature of low qubit to fermionic mode ratio. Studying a 2D square lattice, we propose a quantum annealing protocol using this compact encoding to access the Fermi-Hubbard model ground state. We show with numerical simulation that for both interacting 2D spinless and spinful systems we are able to achieve low energy states for reasonable total annealing times. This setup provides a promising path for future analog quantum computing platforms to simulate FHMs.

[1] Derby, Klassen, Bausch, Cubitt, Phys. Rev. B 104, 035118