Quantum Computation of Molecular Green's Functions in the Frequency Domain Using Multi-Controlled Gates

The Green's function provides fundamental information about the response properties and correlation effects of a physical system and has been a primary target in quantum simulation of many-body physics. Several protocols of computing Green's functions in the frequency domain on quantum computers have been proposed, but their experimental demonstrations are hindered by the lack of efficient implementation of multi-controlled gates present in these protocols. In this work, we employ a recently proposed hardware-efficient implementation of a Toffoli-class gate on fixed-frequency transmons to calculate frequency-domain Green's functions of diatomic molecules. We obtain quasiparticle spectra and correlation energies of the diatomic molecules from the computed frequency-domain Green's functions. Our work demonstrates practical usage of multi-controlled gates for simulating quantum many-body physics on near-term quantum hardware.