A Framework to Study the Relationship Between Classical Data and Quantum Characteristics in Quantum Machine Learning

Quantum Machine Learning (QML) holds the promise of improving conventional machine learning, but the conditions under which an advantage can be obtained are still unclear. Although many studies have been conducted in the literature, there is no conclusive evidence that allows us to determine which types of classical datasets or which problem complexities benefit from the use of quantum techniques. Moreover, there have been contradicting findings when dealing with small or unbalanced datasets. In order to systematically approach this challenge and clarify the need for quantum properties in specific tasks, we propose the adoption of a framework capable of exploring the solution space of quantum feature maps and providing solid evidence of their potential advantages. Our framework comprises three main components: (a) the construction of datasets designed to highlight the specific characteristics that are expected to be relevant in quantum machine learning tasks; (b) the definition of metrics that serve as proxies for quantum kernels with desirable properties; and (c) an evolutionary-guided search for quantum feature maps maximizing those metrics. When using this framework with sensible parameter choices, we obtain results suggesting that some previous studies may have reported overfitted outcomes. This shows that justifying the need for quantum mechanical properties might be beyond the actual scope of conventional classical tasks, since there is no clear quantum feature that contributes to the gain shown by some of the QML techniques most commonly applied in the literature.