Studies of the Fermi-Hubbard Model Using Quantum Computing

TL;DR

This paper demonstrates a quantum computing approach to estimate ground state energies of small Fermi-Hubbard lattices, showing high accuracy and scalability potential beyond classical computational limits.

Contribution

It introduces a scalable quantum algorithm for calculating ground state energies of Fermi-Hubbard models on small lattices, achieving high accuracy compared to true energies.

Findings

Accurate energy calculations within 0.60% for 1x4 lattice without Coulomb repulsion.

Within 1.50% accuracy for 2x2 lattice with Coulomb repulsion.

Within 0.18% accuracy for 2x4 lattice without Coulomb repulsion.

Abstract

The use of quantum computers to calculate the ground state (lowest) energies of a spin lattice of electrons described by the Fermi-Hubbard model of great importance in condensed matter physics has been studied. The ability of quantum bits (qubits) to be in a superposition state allows quantum computers to perform certain calculations that are not possible with even the most powerful classical (digital) computers. This work has established a method for calculating the ground state energies of small lattices which should be scalable to larger lattices that cannot be calculated by classical computers. Half-filled lattices of sizes 1x4, 2x2, 2x4, and 3x4 were studied. The calculated energies for the 1x4 and 2x2 lattices without Coulomb repulsion between the electrons and for the 1x4 lattice with Coulomb repulsion agrees with the true energies to within 0.60%, while for the 2x2 lattice with Coulomb repulsion the agreement is within 1.50% For the 2x4 lattice, the true energy without Coulomb repulsion was found to agree within 0.18%.