Quantum many-body dynamics for combinatorial optimisation and machine learning
The goal of this thesis is to explore and qualify the use of N-body quantum dynamics to solve hard industrial problems and machine learning tasks. As a collaboration between industrial and academic partners, this thesis explores the capabilities of a neutral atom device in tackling real-world problems. First, we look at combinatorial optimisation problems and showcase how neutral atoms can naturally encode a famous combinatorial optimisation problem called the Maximum Independent Set on Unit-Disk graphs. These problems appear in industrial challenges such as Smart-Charging of electric vehicles. The goal is to understand why and how we can expect a quantum approach to solve this problem more efficiently than classical method and our proposed algorithms are tested on real hardware using a dataset from EDF, the French Electrical company. We furthermore explore the use of 3D neutral atoms to tackle problems that are out of reach of classical approximation methods. Finally, we try to improve our intuition on the types of instances for which a quantum approach can(not) yield better results than classical methods.
In the second part of this thesis, we explore the use of quantum dynamics in the field of machine learning. In addition of being a great chain of buzzwords, Quantum Machine Learning (QML) has been increasingly investigated in the past years. In this part, we propose and implement a quantum protocol for machine learning on datasets of graphs, and show promising results regarding the complexity of the associated feature space. Finally, we explore the expressivity of quantum machine learning models and showcase examples where classical methods can efficiently approximate quantum machine learning models.