Kernel methods in Quantum Machine Learning

Daniel T. Chang

Quantum kernel methods, i.e., kernel methods with quantum kernels, offer distinct advantages as a hybrid quantum-classical approach to quantum machine learning (QML), including applicability to Noisy Intermediate-Scale Quantum (NISQ) devices and usage for solving all types of machine learning problems. Kernel methods rely on the notion of similarity between points in a higher (possibly infinite) dimensional feature space. For machine learning, the notion of similarity assumes that points close in the feature space should be close in the machine learning task space. In this paper, we discuss the use of variational quantum kernels with task-specific quantum metric learning to generate optimal quantum embeddings (a.k.a. quantum feature encodings) that are specific to machine learning tasks. Such task-specific optimal quantum embeddings, implicitly supporting feature selection, are valuable not only to quantum kernel methods in improving the latter's performance, but they can also be valuable to non-kernel QML methods based on parameterized quantum circuits (PQCs) as pretrained embeddings and for transfer learning. This further demonstrates the quantum utility, and quantum advantage (with classically-intractable quantum embeddings), of quantum kernel methods.

Nikhil Gupta, Mr. VIGNESHWAR RANGINI, Mr. Bhushan +1 more

Daniel T. Chang

Quantum machine learning (QML) is the use of quantum computing for the computation of machine learning algorithms. With the prevalence and importance of classical data, a hybrid quantum-classical approach to QML is called for. Parameterized Quantum Circuits (PQCs), and particularly Quantum Kernel PQCs, are generally used in the hybrid approach to QML. In this paper we discuss some important aspects of PQCs with quantum kernels including PQCs, quantum kernels, quantum kernels with quantum advantage, and the trainability of quantum kernels. We conclude that quantum kernels with hybrid kernel methods, a.k.a. quantum kernel methods, offer distinct advantages as a hybrid approach to QML. Not only do they apply to Noisy Intermediate-Scale Quantum (NISQ) devices, but they also can be used to solve all types of machine learning problems including regression, classification, clustering, and dimension reduction. Furthermore, beyond quantum utility, quantum advantage can be attained if the quantum kernels, i.e., the quantum feature encodings, are classically intractable.

Michael Brooks

Bhanu Chander

The basic idea of artificial intelligence and machine learning is that machines have the talent to learn from data, previous experience, and perform the work in future consequences. In the era of the digitalized world which holds big data has long-established machine learning methods consistently with requisite high-quality computational resources in numerous useful and realistic tasks. At the same time, quantum machine learning methods work exponentially faster than their counterparts by making use of quantum mechanics. Through taking advantage of quantum effects such as interference or entanglement, quantum computers can proficiently explain selected issues that are supposed to be tough for traditional machines. Quantum computing is unexpectedly related to that of kernel methods in machine learning. Hence, this chapter provides quantum computation, advance of QML techniques, QML kernel space and optimization, and future work of QML.