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arXiv · 2501.07433

Equivalence between exponential concentration in quantum machine learning kernels and barren plateaus in variational algorithms

Pranav Kairon·Jonas Jäger·Roman V. Krems
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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.

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Pranav Kairon, Jonas Jäger, Roman V. Krems. 2025-01-13. Equivalence between exponential concentration in quantum machine learning kernels and barren plateaus in variational algorithms. https://doi.org/10.1103/6hbr-kj64

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