Quantum Algorithms for Unsupervised Machine Learning and Neural Networks

TL;DR

This thesis explores how quantum algorithms can enhance unsupervised machine learning and neural networks, proposing new quantum methods that are faster than classical counterparts and testing them on real quantum hardware.

Contribution

It introduces novel quantum algorithms for unsupervised learning, neural networks, and quantum data analysis, with practical implementations on current quantum computers.

Findings

Quantum algorithms outperform classical ones in speed.

Simulations show comparable learning accuracy.

Real quantum experiments validate the proposed methods.

Abstract

In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then describe more precisely how to link them through linear algebra: we introduce quantum algorithms to efficiently solve tasks such as matrix product or distance estimation. These results are then used to develop new quantum algorithms for unsupervised machine learning, such as k-means and spectral clustering. This allows us to define many fundamental procedures, in particular in vector and graph analysis. We will also present new quantum algorithms for neural networks, or deep learning. For this, we introduce an algorithm to perform a quantum convolution product on images, as well as a new way to perform a fast tomography on quantum states. We prove that these quantum algorithms are faster versions of equivalent classical algorithms, but exhibit random effects due to the quantum nature of the computation. Many simulations have been carried out to study these effects and measure their learning accuracy on real data. Finally, we will present a quantum orthogonal neural network circuit adapted to the currently available small and imperfect quantum computers. This allows us to perform real experiments to test our theory.