  We propose a scheme for the construction of one-particle Green's function
(GF) of an interacting electronic system via statistical sampling on a quantum
computer. Although the non-unitarity of creation and annihilation operators for
the electronic spin orbitals prevents us from preparing specific states
selectively, probabilistic state preparation is demonstrated to be possible for
the qubits. We provide quantum circuits equipped with at most two ancillary
qubits for obtaining all the components of GF. We perform simulations of such
construction of GFs for LiH and H$_2$O molecules based on the unitary
coupled-cluster (UCC) method to demonstrate the validity of our scheme by
comparing the spectra exact within UCC and those from full configuration
interaction calculations. We also examine the accuracy of sampling method by
exploiting the Galitskii--Migdal formula, which gives the total energy only
from the GF.
