Variational algorithms for quantum machine learning

In recent years, we have observed a new revolution in computer science, driven by the increasing availability of computational power and data. This historic event has seen the capillary diffusion of what is commonly known as artificial intelligence (AI). In particular, we have seen a rapid improvement of large language models that now can interact with people on a level that appeared impossible just a few years ago. Despite this newly found focus on AI and computer science, the technical difficulties that limit the increase in computational power are increasing, and the prediction described by Moore's law no longer holds. For this reason physicists, computer scientists, mathematicians, and engineers are studying another computational paradigm called quantum computing. Similar to the rise of large language models, quantum computing has gained significant attention in the last ten years due to the development of initial quantum hardware and its rapid advancements. The quantum computing paradigm offers a fundamentally different set of tools with respect to what is called classical computation. Quantum properties and effects like superposition, entanglement, and interference give us the ability to solve problems that we could not approach classically. In this thesis, we explore the intersection between artificial intelligence and quantum computing from an experimental point of view. We researched quantum AI models, utilizing both the classical and quantum paradigms using variational architectures. This thesis is organized as follows: part 1 contains an introduction to quantum computation, starting from the postulate of quantum mechanics, through an introduction to QML and finally the state of the art. Part 2 contains the description of the research we performed. It's divided into two main chapters containing fundamentally different approaches to quantum computing. Each chapter contains section illustrating our research on that approach.