Quadratic speed-ups in quantum kernelized binary classification

Abstract: Classification is at the core of data-driven prediction and decision-making, representing a fundamental task in supervised machine learning. Recently, several quantum machine learning algorithms that use quantum kernels as a measure of similarities between data have emerged to perform binary classification on datasets encoded as quantum states. The potential advantages of quantum kernels arise from the ability of quantum computers to construct kernels that are more effective than their classical counterparts in capturing patterns in data or computing kernels more efficiently. However, existing quantum kernel-based classification algorithms do not harness the capability of having data samples in quantum superposition for additional enhancements. In this work, we demonstrate how such capability can be leveraged in quantum kernelized binary classifiers (QKCs) through Quantum Amplitude Estimation (QAE) for quadratic speed-up. Additionally, we propose new quantum circuits for the QKCs in which the number of qubits is reduced by one, and the circuit depth is reduced linearly with respect to the number of sample data. We verify the quadratic speed-up over previous methods through numerical simulations on the Iris dataset.