Quantum-classical simulation of two-site dynamical mean-field theory on noisy quantum hardware

TL;DR

This paper demonstrates a hybrid quantum-classical approach to simulate the two-site dynamical mean-field theory for the Hubbard model on noisy quantum hardware, highlighting error impacts and mitigation strategies for accurate results.

Contribution

It introduces a method combining quantum hardware and classical fitting to perform DMFT, addressing hardware errors and proposing a robust way to compute quasiparticle weight.

Findings

Quantum hardware errors affect frequency estimates and quasiparticle weights.

Error mitigation enables convergence to self-consistent solutions.

Spectral peak integration improves robustness against Trotter errors.

Abstract

We report on a quantum-classical simulation of the single-band Hubbard model using two-site dynamical mean-field theory (DMFT). Our approach uses IBM's superconducting qubit chip to compute the zero-temperature impurity Green's function in the time domain and a classical computer to fit the measured Green's functions and extract their frequency domain parameters. We find that the quantum circuit synthesis (Trotter) and hardware errors lead to incorrect frequency estimates, and subsequently to an inaccurate quasiparticle weight when calculated from the frequency derivative of the self-energy. These errors produce incorrect hybridization parameters that prevent the DMFT algorithm from converging to the correct self-consistent solution. To avoid this pitfall, we compute the quasiparticle weight by integrating the quasiparticle peaks in the spectral function. This method is much less sensitive to Trotter errors and allows the algorithm to converge to self-consistency for a half-filled Mott insulating system after applying quantum error mitigation techniques to the quantum simulation data.