Quantum classifier with tailored quantum kernel

Carsten Blank,Daniel K Park,June-Koo Kevin Rhee,Francesco Petruccione

doi:10.1038/s41534-020-0272-6

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 performance of our classifier via classical simulations with a realistic noise model and proof-of-principle experiments using the IBM quantum cloud platform.

Highlights

Advances in quantum information science and machine learning have led to the natural emergence of quantum machine learning, a field that bridges the two, aiming to revolutionize information technology[1,2,3,4,5]
We propose a distance-based quantum classifier whose kernel is based on the quantum state fidelity, thereby enabling the use of a quantum feature map to the full extent
We show that the Quantum kernel based on state fidelity In order to take the full advantage of the quantum feature maps[8,9] in the full range of machine-learning applications, it is desirable to construct a kernel based on the quantum state fidelity, rather than considering only a real part of the quantum state overlap as done in ref

Summary

INTRODUCTION

Advances in quantum information science and machine learning have led to the natural emergence of quantum machine learning, a field that bridges the two, aiming to revolutionize information technology[1,2,3,4,5]. The swap-test classifier can be implemented without relying on the specific initial state by using a method based on quantum forking[12,13] at the cost of increasing the number of qubits In this case, the training data, corresponding labels, and the test data are provided on separate registers as. The controlled-swap gate exchanges the training data and the test data, and the classification is completed with the expectation value measurement of a two-qubit observable on the ancilla and the label qubits. We omit the parameter θ and write ~x 1⁄4 x~ðθÞ when the meaning is clear The classification for this trivial example requires quantum state fidelity rather than the real component of the inner product as the distance measure, verifying the advantage of the proposed method. This error can be circumvented since the classification only depends on the sign of the measurement outcome as shown in Eq (7), as long as npj Quantum Information (2020) 41

Blank et al 4

DISCUSSION

Findings

METHODS