Quantum kernels with squeezed-state encoding for machine learning

Abstract

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 machine learning enhanced by quantum computing is closely related to kernel methods, where the exponentially large Hilbert space turns to be a feature space more expressive than classical ones. In this paper, we generalize quantum kernel methods by encoding data into continuous-variable quantum states, which can benefit from the infinite-dimensional Hilbert space of continuous variables. Specially, we propose squeezed-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 discuss physical implementations of squeezed-state encoding for machine learning in quantum platforms such as trapped ions.