  The Fermi-Hubbard model (FHM) on a two dimensional square lattice has long
been an important testbed and target for simulating fermionic Hamiltonians on
quantum hardware. We present an alternative for quantum simulation of FHMs
based on an adiabatic protocol that could be an attractive target for next
generations of quantum annealers. Our results rely on a recently introduced
low-weight encoding that allows the FHM to be expressed in terms of Pauli
operators with locality of at most three. We theoretically and numerically
determine promising quantum annealing setups for both interacting 2D spinless
and spinful systems, that enable to reach near the ground state solution with
high fidelity for systems as big as $6\times 6$ (spinless) and $4\times 3$
(spinful). Moreover, we demonstrate the scaling properties of the minimal gap
and analyze robustness of the protocol against control noise. Additionally, we
identify and discuss basic experimental requirements to construct near term
annealing hardware tailored to simulate these problems. Finally, we perform a
detailed resource estimation for the introduced adiabatic protocol, and discuss
pros and cons of this approach relative to gate-based approaches for near-term
platforms.
