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We report on a quantum-classical simulation of the single-band Hubbard modelusing two-site dynamical mean-field theory (DMFT). Our approach uses IBM'ssuperconducting qubit chip to compute the zero-temperature impurity Green'sfunction in the time domain and a classical computer to fit the measuredGreen's functions and extract their frequency domain parameters. We find thatthe quantum circuit synthesis (Trotter) and hardware errors lead to incorrectfrequency estimates, and subsequently to an inaccurate quasiparticle weightwhen calculated from the frequency derivative of the self-energy. These errorsproduce incorrect hybridization parameters that prevent the DMFT algorithm fromconverging to the correct self-consistent solution. To avoid this pitfall, wecompute the quasiparticle weight by integrating the quasiparticle peaks in thespectral function. This method is much less sensitive to Trotter errors andallows the algorithm to converge to self-consistency for a half-filled Mottinsulating system after applying quantum error mitigation techniques to thequantum simulation data.

Quantum-classical simulation of two-site dynamical mean-field theory on noisy quantum hardware