Quantum classifier with tailored quantum kernel

TL;DR

This paper introduces a quantum classifier that uses a customizable quantum kernel based on state fidelity, enabling efficient quantum data classification with potential advantages over classical methods.

Contribution

The paper proposes a systematic way to tailor quantum kernels for classification, including a protocol for weighted fidelity calculations and demonstrations on simulators and real quantum hardware.

Findings

Quantum kernel can be systematically tailored with a quantum circuit.

The classifier requires only a constant number of repetitions regardless of data size.

Experimental validation conducted on IBM quantum hardware.

Abstract

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.