Quantum classifier with tailored quantum kernel

Kernel methods have broad applications in machine learning. Recently, a link between quantum computing and kernel theory has been formally established, opening up opportunities for quantum enhancements in various machine learning methods. We present a distance-based quantum binary classifier whose kernel is based on the quantum state fidelity between training and test data. The quantum kernel can be tailored systematically with a quantum circuit to assign an exponent to the kernel and assign weights to training data. Our classifier calculates the weighted power sum of fidelities of quantum data in parallel via a swap-test circuit and two single-qubit measurements, requiring only a constant number of repetitions regardless of the number of data. Furthermore, our classifier is equivalent to measuring the expectation value of a Helstrom operator, from which the optimal quantum state discrimination can be derived. We demonstrate the proof-of-principle via classical simulations with a realistic noise model and experiments using an IBM quantum computer.