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Where can quantum kernel methods make a big difference?

The classification problem is a core problem of supervised learning, which is widely present in our life. As a class of algorithms for pattern analysis, Kernel methods have been widely and effectively applied to classification problems. However, when very complex patterns are encountered, the existing kernel methods are powerless. Recent studies have shown that quantum kernel methods can effectively handle some classification problems of complex patterns that classical kernel methods cannot handle. However, this does not mean that quantum kernel methods are better than classical kernel methods in all cases. It is still unclear under what circumstances quantum kernel methods can realize their great potential. In this paper, by exploring and summarizing the essential differences between quantum kernel functions and classical kernel functions, we propose a criterion based on inter-class and intra-class distance and geometric properties to determine under what circumstances quantum kernel methods will be superior. We validate our method with toy examples and multiple real datasets from Qiskit and Kaggle. The experiments show that our method can be used as a valid determination method.

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