Variational counterdiabatic driving of the Hubbard model for ground-state preparation

TL;DR

This paper applies a variational counterdiabatic protocol to the one-dimensional Hubbard model, enabling faster ground-state preparation by approximating the auxiliary gauge potential with nested commutators and an efficient algorithm.

Contribution

It introduces an exact algorithm for evaluating the variational counterdiabatic Hamiltonian in many-body systems, specifically applied to the Hubbard model.

Findings

The variational CD protocol effectively suppresses excitations in the Hubbard model.

The algorithm reduces computational complexity for nested commutators.

Results show potential for fast ground-state preparation in many-body quantum systems.

Abstract

Counterdiabatic (CD) protocols enable fast driving of quantum states by invoking an auxiliary adiabatic gauge potential (AGP) that suppresses transitions to excited states throughout the driving process. Usually, the full spectrum of the original unassisted Hamiltonian is a prerequisite for constructing the exact AGP, which implies that CD protocols are extremely difficult for many-body systems. Here, we apply a variational CD protocol recently proposed by P. W. Claeys et al. [Phys. Rev. Lett. 123, 090602 (2019)] to a two-component fermionic Hubbard model in one spatial dimension. This protocol engages an approximated AGP expressed as a series of nested commutators. We show that the optimal variational parameters in the approximated AGP satisfy a set of linear equations whose coefficients are given by the squared Frobenius norms of these commutators. We devise an exact algorithm that escapes the formidable iterative matrix-vector multiplications and evaluates the nested commutators and the CD Hamiltonian in analytic representations. We then examine the CD driving of the one-dimensional Hubbard model up to $L = 14$ sites with driving order $l \leqslant 3$. Our results demonstrate the usefulness of the variational CD protocol to the Hubbard model and permit a possible route towards fast ground-state preparation for many-body systems.