Compressed variational quantum eigensolver for the Fermi-Hubbard model

TL;DR

This paper introduces a method to compress the variational quantum eigensolver for the Fermi-Hubbard model, enabling the study of larger instances on current quantum hardware with improved accuracy.

Contribution

A novel compression technique for the variational quantum eigensolver applied to the Fermi-Hubbard model, facilitating larger problem sizes on existing quantum hardware.

Findings

Successfully implemented on superconducting hardware for a 2x1 Hubbard model

Achieved relatively high accuracy in finding the ground state

Demonstrated potential for scaling to larger instances

Abstract

The Fermi-Hubbard model is a plausible target to be solved by a quantum computer using the variational quantum eigensolver algorithm. However, problem sizes beyond the reach of classical exact diagonalisation are also beyond the reach of current quantum computing hardware. Here we use a simple method which compresses the first nontrivial subcase of the Hubbard model -- with one spin-up and one spin-down fermion -- enabling larger instances to be addressed using current quantum computing hardware. We implement this method on a superconducting quantum hardware platform for the case of the $2 \times 1$ Hubbard model, including error-mitigation techniques, and show that the ground state is found with relatively high accuracy.