The theory of the quantum kernel-based binary classifier

Abstract

Binary classification is a fundamental problem in machine learning. Recent development of quantum similarity-based binary classifiers and kernel method that exploit quantum interference and feature quantum Hilbert space opened up tremendous opportunities for quantum-enhanced machine learning. To lay the fundamental ground for its further advancement, this work extends the general theory of quantum kernel-based classifiers. Existing quantum kernel-based classifiers are compared and the connection among them is analyzed. Focusing on the squared overlap between quantum states as a similarity measure, the essential and minimal ingredients for the quantum binary classification are examined. The classifier is also extended concerning various aspects, such as data type, measurement, and ensemble learning. The validity of the Hilbert-Schmidt inner product, which becomes the squared overlap for pure states, as a positive definite and symmetric kernel is explicitly shown, thereby connecting the quantum binary classifier and kernel methods.

16 pages, 3 figures

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Cited by in corpus (21)

• Noisy intermediate-scale quantum (NISQ) algorithms
• Universal expressiveness of variational quantum classifiers and quantum kernels for support vector machines
• Universal Approximation Property of Quantum Machine Learning Models in Quantum-Enhanced Feature Spaces
• Linear-depth quantum circuits for multiqubit controlled gates
• Variational Quantum Approximate Support Vector Machine with Inference Transfer
• Quantum readout error mitigation via deep learning
• Noisy Quantum Kernel Machines
• Numerical evidence against advantage with quantum fidelity kernels on classical data
• Compact quantum kernel-based binary classifier
• Approximate complex amplitude encoding algorithm and its application to data classification problems
• Supervised Learning with Quantum Measurements
• Kernel-based quantum regressor models learn non-Markovianity
• A Multi-Class SWAP-Test Classifier
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• Variable Hyperparameterized Gaussian Kernel using Displaced Squeezed Vacuum State
• Quadratic speed-ups in quantum kernelized binary classification
• Multi-channel convolutional neural quantum embedding
• Classification using a two-qubit quantum chip