  We present a method to compute the many-body real-time Green's function using
an adaptive variational quantum dynamics simulation approach. The real-time
Green's function involves the time evolution of a quantum state with one
additional electron with respect to the ground state wavefunction that is first
expressed as a linear combination of state vectors. The real-time evolution and
Green's function is obtained by combining the dynamics of the individual
statevectors in the linear combination. The use of the adaptive protocol
enables us to generate compact ans\"atze on-the-fly while running the
simulation.
  In order to improve the convergence of spectral features
  Pad\'e approximants are applied to obtain the Fourier transform of Green's
function. We demonstrate the evaluation of Green's function on an IBM Q quantum
computer. As a part of our error mitigation strategy, we develop a
resolution-enhancing method that we successfully apply on the noisy data from
the real quantum hardware.
