Quantum classical algorithm for solving the Hubbard model via the dynamical mean-field theory.

We study a proof-of-principle example of the hybrid quantum-classical simulation of the single-band Hubbard model in the thermodynamic limit. The Dynamical Mean Field theory approach maps the Hubbard model to an effective impurity model subject to self-consistency conditions. Using a quantum computer, we compute the zero-temperature retarded impurity Green's function in the time domain and apply classical methods for self-consistency. We then use Quantum Machine learning to train a parameterized circuit to distinguish between metal and Mott insulators to capture the Mott transition. This work provides an exciting application of small-scale quantum devices feasible with near-future technology.

A.B. is supported by NSF DMR-1728457. J. M. and K.-M.T. are supported by DoE DE-SC0017861. K.-M. T. is partially supported by NSF OAC-1931445.