Exploring Ground States of Fermi-Hubbard Model on Honeycomb Lattices with Counterdiabaticity

TL;DR

This paper develops and tests variational quantum algorithms with counterdiabatic driving to efficiently find ground states of the Fermi-Hubbard model on honeycomb lattices, demonstrating improved performance over traditional methods.

Contribution

The authors introduce a novel variational quantum algorithm incorporating counterdiabatic interactions and compare its effectiveness with standard approaches on quantum circuits.

Findings

Counterdiabatic ansatz outperforms traditional variational ansatz.

Analysis of Trotter step number and duration to reduce errors.

Successful implementation on systems with up to 26 qubits.

Abstract

Exploring the ground state properties of many-body quantum systems conventionally involves adiabatic processes, alongside exact diagonalization, in the context of quantum annealing or adiabatic quantum computation. Shortcuts to adiabaticity by counter-diabatic driving serve to accelerate these processes by suppressing energy excitations. Motivated by this, we develop variational quantum algorithms incorporating the auxiliary counterdiabatic interactions, comparing them with digitized adiabatic algorithms. These algorithms are then implemented on gate-based quantum circuits to explore the ground states of the Fermi-Hubbard model on honeycomb lattices, utilizing systems with up to 26 qubits. The comparison reveals that the counter-diabatic inspired ansatz is superior to traditional Hamiltonian variational ansatz. Furthermore, the number and duration of Trotter steps are analyzed to understand and mitigate errors. Given the model's relevance to materials in condensed matter, our study paves the way for using variational quantum algorithms with counterdiabaticity to explore quantum materials in the noisy intermediate-scale quantum era.