The characteristic of Quantum Kernel in initial learning process

Outgoing inspection of the production line is very important for many manufacturing companies. In recent years, two class classification of good and defective products must be carried out efficiently as the number of small-quantity, high-mix products have been increasing. The support vector machine with kernel method (kernel learning) is the most popular method in two class classification used in factories. Quantum kernel learning is one of the most promising applications of quantum technology. In this study, we propose an analysis method that allows us to know the difference between classical and quantum machine learning by plotting false positive rate (FPR) and true positive rate (TPR) on Receiver Operating Characteristic (ROC) space. Quantum machine learning uses quantum data with feature maps. We compared quantum and classical data using a small-sized existing datasets. First, it was not possible to confirm that the quantum data incorporating quantum entanglement could achieve the effect in this study. Next, when we examined the learning process of quantum data with Pauli feature map and classical data, we observed differences in the initial learning process. Based on these results, in contrast to the commonly used ROC curve, we plotted the FPR and TPR separately on the ROC space according to the training size. Plotting on ROC space in this experiment shows that quantum kernel learning is a method to reduce only FPR from high FPR and TPR. We found that the kernel learning process using quantum data is different from one using classical data.