Green's functions of molecules using a quantum computer

Given the recent rapid development of techniques for quantum computation of electronic structures[1],
we propose an algorithm for the construction of one-particle Green's function (GF) of an interacting electronic system via
statistical sampling on a quantum computer for quantum chemistry.[2]
By avoiding the difficulty coming from the non-unitarity of creation and annihilation operators for the electronic spin orbitals,
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 H2O molecules based on the unitary coupled-cluster (UCC) method and compare the quasiparticle and satellite spectra exact within UCC and those from full configuration interaction calculations.

[1] Peruzzo et al., Nat. Comm. 5, 4213 (2014); O'Malley et el., Phys. Rev. X 6, 031007 (2016); Hempel et al., Phys. Rev. X 8, 031022 (2018)
[2] Kosugi and Matsushita, arXiv:1908.03902 (2019)