Hybrid model of the kernel method for quantum computers

TL;DR

This paper introduces a hybrid quantum-classical kernel method for machine learning, demonstrating its effectiveness in classifying points relative to a circle with high accuracy, and adapting kernel methods for quantum processing constraints.

Contribution

It proposes a novel hybrid quantum-classical kernel learning model and develops a quantum algorithm for internal product calculations within quantum Hilbert spaces.

Findings

Achieved 99% accuracy in classifying points inside or outside a circle.

Successfully implemented quantum internal product calculations.

Demonstrated the feasibility of quantum-enhanced kernel methods.

Abstract

The field of quantum machine learning is a promising way to lead to a revolution in intelligent data processing methods. In this way, a hybrid learning method based on classic kernel methods is proposed. This proposal also requires the development of a quantum algorithm for the calculation of internal products between vectors of continuous values. In order for this to be possible, it was necessary to make adaptations to the classic kernel method, since it is necessary to consider the limitations imposed by the Hilbert space of the quantum processor. As a test case, we applied this new algorithm to learn to classify whether new points generated randomly, in a finite square located under a plane, were found inside or outside a circle located inside this square. It was found that the algorithm was able to correctly detect new points in 99% of the samples tested, with a small difference due to considering the radius slightly larger than the ideal. However, the kernel method was able to perform classifications correctly, as well as the internal product algorithm successfully performed the internal product calculations using quantum resources. Thus, the present work represents a contribution to the area, proposing a new model of machine learning accessible to both physicists and computer scientists.