Quantum Kernel Methods for Supervised Machine Learning

Kernel methods are a subset of machine learning algorithms that learn patterns in the input data by using a positive-definite similarity measure between pairs of points. In this context, the output of such a similarity measure (or kernel function) corresponds to an inner product on vectors obtained through a feature map on the input data. A feature map itself, however, need not be explicitly computed. Kernel methods are especially elegant in the sense that any kernel function, as a black-box pairwise similarity measure, can be substituted into the algorithm in a modular way. Following the advance of quantum computing into the so-called noisy intermediate-scale (NISQ) era, several quantum circuits have been proposed as classically intractable kernels for supervised learning. While the utility of quantum kernels has been demonstrated for specifically structured data, open questions remain regarding their general role in machine learning. Operating within constraints of presently available quantum hardware, this work examines two promising avenues for NISQ-compatible applications. First, we consider hybrid multi-kernels consisting of quantum-quantum and quantum-classical combinations as a means of improving the classification performance of quantum support-vector machines. Next, by leveraging an existing method for non-Trotterized time evolution in quantum circuits, we employ a time-dependent quantum kernel to classify time series data in a novel application. Together, these results culminate in a roadmap for the continuing development of near-term quantum kernel methods.