Quantum kernels with Gaussian state encoding for machine learning

Kernel methods are powerful for machine learning, as they can represent data in feature spaces that similarities between samples may be faithfully captured. Recently, it is realized that quantum-enhanced machine learning is closely related to kernel methods, where the exponentially large Hilbert space can be a feature space more expressive than classical ones. Here we investigate quantum kernel methods of encoding data into continuous-variable quantum states, with two newly introduced quantum kernels named squeezing amplitude kernel and coherent phase kernel from Gaussian state encoding, in which data is encoded as either in the amplitude or the phase. The kernels can be calculated on a quantum computer and then are combined with classical machine learning, e.g. support vector machine, for training and predicting tasks. Their comparisons with other classical kernels are also addressed. Lastly, we briefly discuss the universal approximation property of continuous-variable quantum kernels. (c) 2022 Elsevier B.V. All rights reserved.