  Kernel methods have a wide spectrum of applications in machine learning.
Recently, a link between quantum computing and kernel theory has been formally
established, opening up opportunities for quantum techniques to enhance various
existing machine learning methods. We present a distance-based quantum
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 raise the kernel to an arbitrary power and to assign arbitrary
weights to each training data. Given a specific input state, our protocol
calculates the weighted power sum of fidelities of quantum data in quantum
parallel via a swap-test circuit followed by two single-qubit measurements,
requiring only a constant number of repetitions regardless of the number of
data. We also show that our classifier is equivalent to measuring the
expectation value of a Helstrom operator, from which the well-known optimal
quantum state discrimination can be derived. We demonstrate the
proof-of-principle via classical simulations with a realistic noise model and
experiments using the IBM quantum computer.
