Excitation Gaps of Ground and Excited State Energy of the Fermi-Hubbard Model Using Variational Quantum Eigensolver

TL;DR

This paper demonstrates a novel quantum algorithm for calculating ground and excited state energies of small Hubbard models, providing insights into their phase diagrams and energy gaps using a hybrid variational approach.

Contribution

It introduces a new ansatz combining HVA and NPA for improved energy calculations on the Hubbard model with a hybrid optimization strategy.

Findings

Accurate energies for 4x1 and 2x2 Hubbard lattices obtained.

Phase diagrams of excitation gaps analyzed for various charge and spin states.

Hybrid optimization enhances convergence and accuracy.

Abstract

The Hubbard model is a challenging quantum many-body problem and serves as a benchmark for quantum computing research. Accurate computation of its ground and excited state energies is essential for understanding correlated electron systems. In this study, the ground, first, and second excited state energies of 4$\times$1 and 2$\times$2 Hubbard lattices are obtained using a newly designed ansatz circuit. The ansatz is constructed by combining concepts from the Hamiltonian Variational Ansatz (HVA) and the Number-Preserving Ansatz (NPA). A hybrid optimization strategy is applied, where COBYLA is used for coarse convergence and L-BFGS for fine-tuning. The resulting energies are evaluated, and the corresponding physical properties of the systems are analyzed through phase diagrams of the energy excitation gaps for different charge and spin configurations.