Quantum-classical simulation of two-site dynamical mean-field theory on
  noisy quantum hardware
We report on a quantum-classical simulation of the single-band Hubbard model
using two-site dynamical mean-field theory (DMFT). Our approach uses IBM's
superconducting qubit chip to compute the zero-temperature impurity Green's
function in the time domain and a classical computer to fit the measured
Green's functions and extract their frequency domain parameters. We find that
the quantum circuit synthesis (Trotter) and hardware errors lead to incorrect
frequency estimates, and subsequently to an inaccurate quasiparticle weight
when calculated from the frequency derivative of the self-energy. These errors
produce incorrect hybridization parameters that prevent the DMFT algorithm from
converging to the correct self-consistent solution. To avoid this pitfall, we
compute the quasiparticle weight by integrating the quasiparticle peaks in the
spectral function. This method is much less sensitive to Trotter errors and
allows the algorithm to converge to self-consistency for a half-filled Mott
insulating system after applying quantum error mitigation techniques to the
quantum simulation data.
Trevor Keen Thomas Maier Steven Johnston Pavel Lougovski