  We propose a hybrid quantum-classical method to investigate the equilibrium
physics and the dynamics of strongly correlated fermionic models with
spin-based quantum processors. Our proposal avoids the usual pitfalls of
fermion-to-spin mappings thanks to a slave-spin method which allows to
approximate the original Hamiltonian into a sum of self-correlated
free-fermions and spin Hamiltonians. Taking as an example a Rydberg-based
analog quantum processor to solve the interacting spin model, we avoid the
challenges of variational algorithms or Trotterization methods. We explore the
robustness of the method to experimental imperfections by applying it to the
half-filled, single-orbital Hubbard model on the square lattice in and out of
equilibrium. We show, through realistic numerical simulations of current
Rydberg processors, that the method yields quantitatively viable results even
in the presence of imperfections: it allows to gain insights into equilibrium
Mott physics as well as the dynamics under interaction quenches. This method
thus paves the way to the investigation of physical regimes -- whether
out-of-equilibrium, doped, or multiorbital -- that are difficult to explore
with classical processors.
