Importance of Kernel Bandwidth in Quantum Machine Learning
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Quantum kernel methods are considered a promising avenue for applying quantum computers to machine learning problems. However, recent results overlook the central role hyperparameters play in determining the performance of machine learning methods. In this work we show how optimizing the bandwidth of a quantum kernel can improve the performance of the kernel method from a random guess to being competitive with the best classical methods. Without hyperparameter optimization, kernel values decrease exponentially with qubit count, which is the cause behind recent observations that the performance of quantum kernel methods decreases with qubit count. We reproduce these negative results and show, through extensive numerical experiments using multiple quantum kernels and classical datasets, that if the kernel bandwidth is optimized, the performance instead improves with growing qubit count. We draw a connection between the bandwidth of classical and quantum kernels and show analogous behavior in both cases.
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