Importance of Kernel Bandwidth in Quantum Machine Learning

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, including quantum. In this work, we show how optimizing the bandwidth of a quantum kernel can improve the performance of the kernel method from random guess to being competitive with the best classical methods. We show that without hyperparameter optimization, kernel bandwidth reduces exponentially with qubit count. We identify this to be the cause behind recent observation that the performance of quantum kernel methods decreases with qubit count. We reproduce these negative results and show that if kernel bandwidth is optimized, the performance improves with growing qubit count, leading to the opposite conclusion about the possibility of quantum advantage. We provide numerical evidence of improved performance with increasing number of qubits using multiple quantum kernels and classical datasets.