  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 a Bayesian algorithm for constructing quantum kernels for support
vector machines that adapts quantum gate sequences to data. The algorithm
increases the complexity of quantum circuits incrementally by appending quantum
gates selected with Bayesian information criterion as circuit selection metric
and Bayesian optimization of the parameters of the locally optimal quantum
circuits identified. The goal is to build quantum kernels for SVM that can
solve classification problems with as little training data as possible. The
performance of the resulting quantum models for the classification problems
considered here significantly exceeds that of optimized classical models with
conventional kernels.
