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We propose a hybrid quantum-classical method to investigate the equilibriumphysics and the dynamics of strongly correlated fermionic models withspin-based quantum processors. Our proposal avoids the usual pitfalls offermion-to-spin mappings thanks to a slave-spin method which allows toapproximate the original Hamiltonian into a sum of self-correlatedfree-fermions and spin Hamiltonians. Taking as an example a Rydberg-basedanalog quantum processor to solve the interacting spin model, we avoid thechallenges of variational algorithms or Trotterization methods. We explore therobustness of the method to experimental imperfections by applying it to thehalf-filled, single-orbital Hubbard model on the square lattice in and out ofequilibrium. We show, through realistic numerical simulations of currentRydberg processors, that the method yields quantitatively viable results evenin the presence of imperfections: it allows to gain insights into equilibriumMott physics as well as the dynamics under interaction quenches. This methodthus paves the way to the investigation of physical regimes -- whetherout-of-equilibrium, doped, or multiorbital -- that are difficult to explorewith classical processors.

Hubbard physics with Rydberg atoms: using a quantum spin simulator to simulate strong fermionic correlations