Construction of Green's functions on a quantum computer: applications to molecular systems

Understand

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.