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

## TL;DR

This paper presents a quantum computing scheme for constructing one-particle Green's functions of molecular systems, enabling spectral analysis and energy calculations with probabilistic state preparation and quantum circuits.

## Contribution

It introduces a novel quantum algorithm for Green's function construction using minimal ancillary qubits and demonstrates its effectiveness through molecular simulations.

## Key findings

- Successfully simulated GFs for LiH and H2O molecules.
- Achieved accurate spectral results compared to exact UCC and FCI calculations.
- Validated sampling method via Galitskii--Migdal energy estimates.

## Abstract

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.