  Many-body Green's functions encode all the properties and excitations of
interacting electrons. While these are challenging to be evaluated accurately
on a classical computer, recent efforts have been directed towards finding
quantum algorithms that may provide a quantum advantage for this task,
exploiting architectures that will become available in the near future. In this
work we introduce a novel near-term quantum algorithm for computing
one-particle Green's functions via their Lehmann representation. The method is
based on a generalization of the quantum equation of motion algorithm that
gives access to the charged excitations of the system. We demonstrate the
validity of the present proposal by computing the Green's function of a
two-site Fermi-Hubbard model on a IBM quantum processor.
