We study a proof-of-principle example of the recently proposed hybrid quantum-classical simulation of strongly correlated fermion models in the thermodynamic limit. In a "two-site" dynamical mean-field theory (DMFT) approach we reduce the Hubbard model to an effective impurity model subject to self-consistency conditions. The resulting minimal two-site representation of the non-linear hybrid setup involves four qubits implementing the impurity problem, plus an ancilla qubit on which all measurements are performed. We outline a possible implementation with superconducting circuits feasible with near-future technology.
Kreula, J. M., García-Álvarez, L., Lamata, L., Clark, S. R., Solano, E., & Jaksch, D. (2016). Few-qubit quantum-classical simulation of strongly correlated lattice fermions. EPJ Quantum Technology, 3(1), . https://doi.org/10.1140/epjqt/s40507-016-0049-1