Quantum Algorithms to Determine Spin-Resolved Exchange-Correlation Potential for Strongly Correlated Materials

TL;DR

This paper introduces a quantum algorithmic framework using variational quantum eigensolvers to accurately determine spin-resolved exchange-correlation potentials in strongly correlated lattice systems, aiding the development of better density functional approximations.

Contribution

It presents a novel quantum algorithmic approach to compute spin-resolved XC potentials for strongly correlated materials, validated on Hubbard models with high fidelity.

Findings

High-fidelity reproduction of ground-state energies and densities.

Accurate construction of magnetic and non-magnetic XC potentials.

Empirical scaling relation for computational complexity.

Abstract

Accurate exchange-correlation (XC) potentials are essential for density functional theory, yet reliable approximations remain challenging for strongly correlated systems. In this work, we present a quantum algorithmic framework to determine spin-resolved XC potentials using a variational quantum eigensolver. Using the Hubbard model as a prototypical strongly correlated lattice system, we prepare ground states in fixed spin sectors through a Hamiltonian variational ansatz combined with a continuation strategy that gradually increases the interaction strength. From the resulting many-body ground states, we extract the XC energy and compute the corresponding spin-resolved XC potentials via finite differences. The accuracy of the approach is benchmarked against exact diagonalization for one- and two-dimensional Hubbard systems of various lattice sizes. We demonstrate that the variational ansatz reproduces the ground-state energies and densities with high fidelity, enabling accurate construction of both magnetic and non-magnetic XC potentials. We analyzed the dependence of the XC potentials on the interaction strength, charge, spin densities, and magnetization. We also present an empirical complexity scaling relation for the computational cost of the method at a fixed fidelity. These results illustrate how quantum simulations can be used to construct spin-resolved XC functionals for correlated lattice models, providing a potential pathway for improving density functional approximations in strongly correlated materials.