Optimal quantum kernels for small data classification

While quantum machine learning (ML) has been proposed to be one of the most promising applications of quantum computing, how to build quantum ML models that outperform classical ML remains a major open question. Here, we demonstrate an algorithm for constructing quantum kernels for support vector machines that adapts quantum gate sequences to data. The algorithm includes three essential ingredients: greedy search in the space of quantum circuits, Bayesian information criterion as circuit selection metric and Bayesian optimization of the parameters of the optimal quantum circuit identified. The performance of the resulting quantum models for classification problems with a small number of training points significantly exceeds that of optimized classical models with conventional kernels. In addition, we illustrate the possibility of mapping quantum circuits onto molecular fingerprints and show that performant quantum kernels can be isolated in the resulting chemical space. This suggests that methods developed for optimization and interpolation of molecular properties across chemical spaces can be used for building quantum circuits for quantum machine learning with enhanced performance.