Equivalence between exponential concentration in quantum machine learning kernels and barren plateaus in variational algorithms
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| Format: | Preprint |
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2025
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| _version_ | 1866913177150685184 |
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| author | Kairon, Pranav Jäger, Jonas Krems, Roman V. |
| author_facet | Kairon, Pranav Jäger, Jonas Krems, Roman V. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07433 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equivalence between exponential concentration in quantum machine learning kernels and barren plateaus in variational algorithms Kairon, Pranav Jäger, Jonas Krems, Roman V. Quantum Physics 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. |
| title | Equivalence between exponential concentration in quantum machine learning kernels and barren plateaus in variational algorithms |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2501.07433 |