We show that a parametrized quantum neural network can be used to build a nonparametric quantum kernel for machine learning that inherits the concentration properties of the neural network cost function. This construction establishes a rigorous connection between barren plateaus (BPs) in variational quantum algorithms and exponential concentration of quantum kernels for machine learning. Our results imply that recently proposed algorithms for building BP-free quantum circuits can be utilized to construct useful quantum kernels for machine learning with unknown inductive bias. This is illustrated by a numerical example employing a provably BP-free quantum neural network to construct kernel matrices for multiple classification datasets of increasing dimensionality.

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• Machine learning
• Quantum circuits
• Quantum computation