Quantum Semi-Supervised Kernel Learning

TL;DR

This paper introduces a quantum algorithm for semi-supervised kernel support vector machines that leverages quantum computing to efficiently handle large datasets with limited labels, maintaining computational speedups.

Contribution

It extends the quantum LS-SVM algorithm to incorporate semi-supervised learning, enabling efficient training with both labeled and unlabeled data.

Findings

The quantum semi-supervised algorithm retains the same speedup as fully-supervised quantum LS-SVM.

Theoretical analysis confirms the algorithm's computational complexity benefits.

The approach leverages quantum sample-based Hamiltonian simulation for semi-supervised learning.

Abstract

Quantum computing leverages quantum effects to build algorithms that are faster then their classical variants. In machine learning, for a given model architecture, the speed of training the model is typically determined by the size of the training dataset. Thus, quantum machine learning methods have the potential to facilitate learning using extremely large datasets. While the availability of data for training machine learning models is steadily increasing, oftentimes it is much easier to collect feature vectors that to obtain the corresponding labels. One of the approaches for addressing this issue is to use semi-supervised learning, which leverages not only the labeled samples, but also unlabeled feature vectors. Here, we present a quantum machine learning algorithm for training Semi-Supervised Kernel Support Vector Machines. The algorithm uses recent advances in quantum sample-based Hamiltonian simulation to extend the existing Quantum LS-SVM algorithm to handle the semi-supervised term in the loss. Through a theoretical study of the algorithm's computational complexity, we show that it maintains the same speedup as the fully-supervised Quantum LS-SVM.