Many body Green's function using variational dynamics

We present a method to compute many-body real-time Green's function using adaptive variational quantum dynamics simulation. The real-time Green's function involves the time evolution of a quantum state with one additional electron w.r.t. the ground state wavefunction. Simulation of such a non-normal quantum state is achieved by expressing it as a linear combination of multiple branch states. The real-time evolution and Green's function are obtained by combining the dynamics of the individual branch states. In order to minimize the error of a convergent Fourier transform of the Green's function using finite time simulation, we use the Padé approximation of the real-time data. We apply our method to the Hubbard model at half-filling and find very good agreement with exact results. As a part of error mitigation, we develop a resolution-enhancing method that we successfully apply to noisy data.