Equivalence between exponential concentration in quantum machine learning kernels and barren plateaus in variational algorithms
Quantum Physics
2025-01-16 v3
Abstract
We formalize a rigorous connection between barren plateaus (BP) in variational quantum algorithms and exponential concentration of quantum kernels for machine learning. Our results imply that recently proposed strategies to build BP-free quantum circuits can be utilized to construct useful quantum kernels for machine learning. This is illustrated by a numerical example employing a provably BP-free quantum neural network to construct kernel matrices for classification datasets of increasing dimensionality without exponential concentration.
Cite
@article{arxiv.2501.07433,
title = {Equivalence between exponential concentration in quantum machine learning kernels and barren plateaus in variational algorithms},
author = {Pranav Kairon and Jonas Jäger and Roman V. Krems},
journal= {arXiv preprint arXiv:2501.07433},
year = {2025}
}