Eigenstate solutions of the Fermi-Hubbard model via symmetry-enhanced variational quantum eigensolver

TL;DR

This paper introduces a symmetry-enhanced variational quantum eigensolver that efficiently computes eigenstates of the Fermi-Hubbard model, significantly improving accuracy for ground and excited states by incorporating symmetries into quantum circuits and loss functions.

Contribution

The study develops a symmetry-aware VQE approach that effectively handles degeneracies and excited states in Hubbard models, outperforming traditional methods.

Findings

Enhanced accuracy in eigenstate calculations with symmetry incorporation

Significant improvement in excited state determination

Effective handling of degenerate states using penalty terms

Abstract

The Variational Quantum Eigensolver (VQE), as a hybrid quantum-classical algorithm, is an important tool for effective quantum computing in the current noisy intermediate-scale quantum (NISQ) era. However, the traditional hardware-efficient ansatz without taking into account symmetries requires more computational resources to explore the unnecessary regions in the Hilbert space. The conventional Subspace-Search VQE (SSVQE) algorithm, which can calculate excited states, is also unable to effectively handle degenerate states since the loss function only contains the expectation value of the Hamiltonian. In this study, the energy eigenstates of the one-dimensional Fermi-Hubbard model with two lattice sites and the two-dimensional Hubbard model with four lattice sites are calculated. By incorporating symmetries into the quantum circuits and loss function, we find that both the ground state and excited state calculations are improved greatly compared to the case without symmetries. The enhancement in excited state calculations is particularly significant. This is because quantum circuits that conserve the particle number are used, and appropriate penalty terms are added to the loss function, enabling the optimization process to correctly identify degenerate states. The results are verified through repeated simulations.