Calculating the Green's function of two-site Fermionic Hubbard model in a photonic system

TL;DR

This paper demonstrates a photonic quantum system that calculates the Green's function of a two-site Fermionic Hubbard model, showcasing a new approach for studying complex many-body systems with high precision.

Contribution

It introduces a programmable photonic quantum circuit and experimental method to compute Green's functions for strongly-correlated models, advancing quantum simulation techniques.

Findings

Successfully calculated the Green's function spectral features.

Achieved high agreement with exact theoretical results.

Demonstrated the potential of photonic systems for complex quantum simulations.

Abstract

The Green's function has been an indispensable tool to study many-body systems that remain one of the biggest challenges in modern quantum physics for decades. The complicated calculation of Green's function impedes the research of many-body systems. The appearance of the noisy intermediate-scale quantum devices and quantum-classical hybrid algorithm inspire a new method to calculate Green's function. Here we design a programmable quantum circuit for photons with utilizing the polarization and the path degrees of freedom to construct a highly-precise variational quantum state of a photon, and first report the experimental realization for calculating the Green's function of the two-site Fermionic Hubbard model, a prototypical model for strongly-correlated materials, in photonic systems. We run the variational quantum eigensolver to obtain the ground state and excited states of the model, and then evaluate the transition amplitudes among the eigenstates. The experimental results present the spectral function of Green's function, which agrees well with the exact results. Our demonstration provides the further possibility of the photonic system in quantum simulation and applications in solving complicated problems in many-body systems, biological science, and so on.