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 wave function that is first expressed as a linear–linear
combination of state vectors. The real-time evolution and the Green’s
function are obtained by combining the dynamics of the individual
state vectors in a linear combination. The use of the adaptive protocol
enables us to generate compact ansatzes on-the-fly while running the
simulation. In order to improve the convergence of spectral features,
Padé approximants are applied to obtain the Fourier transform
of the Green’s function. We demonstrate the evaluation of the
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.