Quantum-classical hybrid algorithm to construct quantum explicit model from quantum kernel method

Quantum machine learning is a promising field for quantum computers and various models have been explored. These models can be broadly categorized as either implicit models that leverage quantum kernel methods or explicit models, known as quantum circuit learning. Implicit models consistently achieve lower training errors than explicit models but face linear prediction time scaling with the training data size. In contrast, explicit models predict in constant time. Additionally, implicit models tend to overfit training datasets, which may result in weaker generalization compared to explicit models under certain conditions. However, explicit models' optimization faces inherent challenges due to the barren plateau phenomenon. In this study, we introduce a quantum-classical hybrid algorithm designed to systematically and efficiently convert an implicit model to an explicit model. This explicit model exhibits as high performance as the implicit model and can perform inference with a much smaller number of quantum circuit executions. In classification tasks using both MNISQ and VQE-generated datasets, we demonstrate that the explicit model we developed offers a generalization comparable to that of the implicit model but with reduced computational costs. These results suggest that our proposed algorithm not only reduces the prediction time of implicit models but also aids in constructing high-performance explicit models, especially in addressing challenges such as the barren plateau phenomenon.