The role of gaps in digitized counterdiabatic QAOA for fully-connected spin models

TL;DR

This paper investigates how digitized-counterdiabatic corrections improve the convergence of QAOA in fully-connected spin models, showing that spectral gaps significantly influence algorithm performance.

Contribution

It applies digitized-counterdiabatic QAOA to fully-connected spin models and links its effectiveness to spectral properties, highlighting the importance of energy gaps.

Findings

Larger spectral gaps lead to better convergence.

Digitized-counterdiabatic corrections enhance QAOA performance.

Performance depends on spectral properties of the problem instances.

Abstract

Recently, digitized-counterdiabatic (CD) corrections to the quantum approximate optimization algorithm (QAOA) have been proposed, yielding faster convergence within the desired accuracy than standard QAOA. In this manuscript, we apply this approach to a fully-connected spin model with random couplings. We show that the performances of the algorithm are related to the spectral properties of the instances analyzed. In particular, the larger the gap between the ground state and the first excited states, the better the convergence to the exact solution.