LAUSR

We propose a scheme for the construction of the one-particle Green's function (GF) of an interacting electronic system via statistical sampling on a quantum computer. Although the nonunitarity 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 the GF. We perform simulations of such construction of GFs for LiH and ${\mathrm{H}}_{2}\mathrm{O}$ molecules based on the unitary coupled-cluster (UCC) method to demonstrate the validity of our scheme by comparing the quasiparticle and satellite spectra exact within the UCC method and those from full configuration-interaction calculations. We also examine the accuracy of the sampling method by exploiting the Galitskii-Migdal formula, which gives the total energy only from the GF.