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

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.

arXiv comment6 pages, 2 figures

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• The Variational Quantum Eigensolver: a review of methods and best practices
• A variational quantum eigensolver for dynamic correlation functions
• Self-Consistent Determination of Single-Impurity Anderson Model Using Hybrid Quantum-Classical Approach on a Spin Quantum Simulator
• Computation of Green's function by local variational quantum compilation
• Super-resolution of Green's functions on noisy quantum computers
• Near-term quantum algorithm for computing molecular and materials properties based on recursive variational series methods