The paper explores the application of quantum computing to machine learning, focusing on two novel methods that leverage the large dimensionality of quantum Hilbert space to enhance classification tasks. The first method, the quantum variational classifier, uses a variational quantum circuit to classify training data, similar to conventional support vector machines (SVMs). The second method, the quantum kernel estimator, directly estimates the kernel function and optimizes the classifier. Both methods aim to exploit the quantum state space as a feature space to achieve computational speed-ups. The authors experimentally implement these methods on a superconducting quantum processor, demonstrating high classification success rates even in the presence of noise. The paper discusses the theoretical underpinnings of these methods, including the relationship between quantum variational classifiers and SVMs, and highlights the potential for quantum advantage in applications beyond binary classification.The paper explores the application of quantum computing to machine learning, focusing on two novel methods that leverage the large dimensionality of quantum Hilbert space to enhance classification tasks. The first method, the quantum variational classifier, uses a variational quantum circuit to classify training data, similar to conventional support vector machines (SVMs). The second method, the quantum kernel estimator, directly estimates the kernel function and optimizes the classifier. Both methods aim to exploit the quantum state space as a feature space to achieve computational speed-ups. The authors experimentally implement these methods on a superconducting quantum processor, demonstrating high classification success rates even in the presence of noise. The paper discusses the theoretical underpinnings of these methods, including the relationship between quantum variational classifiers and SVMs, and highlights the potential for quantum advantage in applications beyond binary classification.