Entanglement generation in qubit-ADAPT-VQE through four-qubit algebraic classification

TL;DR

This paper investigates the ability of qubit-ADAPT-VQE, a variational quantum algorithm, to generate highly entangled ground states in four-qubit spin models, using algebraic classification to analyze entanglement classes.

Contribution

It introduces an algebraic classification method to evaluate qubit-ADAPT-VQE's performance on different entanglement classes, demonstrating its effectiveness in highly entangled states.

Findings

Accurately reaches ground states across all entanglement classes.

Demonstrates versatility of qubit-ADAPT-VQE in highly entangled systems.

Uses algebraic classification to identify entanglement classes.

Abstract

While variational quantum algorithms are among the most promising approaches for the noisy intermediate-scale quantum (NISQ) era, their scalability is often hindered by the barren plateau problem. Among the proposals that have demonstrated robustness against this issue, the ADAPT-VQE algorithm stands out for ground state estimation, primarily due to its iterative ansatz construction. Although ADAPT-VQE has been extensively benchmarked on molecular Hamiltonians, where the ground states typically exhibit low entanglement, its performance for highly entangled ground states remains largely unexplored. In this work, we explore a variant of this algorithm known as qubit-ADAPT-VQE, assessing its ability to achieve ground states with substantial entanglement in spin models. We focus on four-qubit systems and employ an algebraic entanglement classification to identify distinct entanglement classes among ground states, and consider a representative of each class as an initial state to evaluate the performance of the algorithm. Our findings highlight the versatility of qubit-ADAPT-VQE, demonstrating that it accurately reaches the ground state across all entanglement classes and initial energy values.