We propose a hybrid quantum-classical simulator for non-equilibrium dynamics of strongly correlated quantum lattice models in the thermodynamic limit based on ideas from dynamical mean field theory (DMFT). Our scheme uses a digital quantum coprocessor to efficiently solve an impurity problem whose parameters are iterated to self-consistency via a classically computed feedback loop where quantum gate errors can be partly accounted for. Our results indicate that a hybrid scheme with near-future quantum devices has the potential to outperform purely classical non-equilibrium DMFT simulations.
Kreula, J. M., Clark, S. R., & Jaksch, D. (2016). Non-linear quantum-classical scheme to simulate non-equilibrium strongly correlated fermionic many-body dynamics. Scientific Reports, 6, . https://doi.org/10.1038/srep32940