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.

5 pages, 4 figures

References in corpus (9)

• Quantum algorithm for solving linear systems of equations
• Quantum computing with trapped ions
• The effect of data encoding on the expressive power of variational quantum machine learning models
• Data re-uploading for a universal quantum classifier
• Quantum Data Fitting
• Quantum-enhanced machine learning
• Supervised quantum machine learning models are kernel methods
• Universal Approximation Property of Quantum Machine Learning Models in Quantum-Enhanced Feature Spaces
• Protocol for implementing quantum nonparametric learning with trapped ions

Cited by in corpus (5)

• Continuous-variable quantum kernel method on a programmable photonic quantum processor
• Optimal Qubit Mapping Search for Encoding Classical Data into Matrix Product State Representation with Minimal Loss
• Variable Hyperparameterized Gaussian Kernel using Displaced Squeezed Vacuum State
• Quantum fidelity kernel with a trapped-ion simulation platform
• Towards Continuous-variable Quantum Neural Networks for Biomedical Imaging