Machine learning for quantum models and quantum optimization for classical problems

This manuscript is divided in two parts. In the first one we explore different machine learning inspired techniques to reconstruct the topological phase diagram of a few variants of the Kitaev chain and the extended Hubbard model in 1D. By applying four algorithms to a dataset of correlation functions we show how reliable this methods can be at predicting unknown phases and transfer the knowledge of one model to the other allowing also for interpretability of the results. In the second part we study Bayesian optimization and use it to run the Quantum Approximate Optimization Algorithm on the neutral atom quantum computer of the company PASQAL to solve a classical combinatorial problem. We show that the fast convergence and resilience to noise of the algorithm makes it suitable for this type of platforms. We conclude with an analysis of a measurement-based quantum computation approach on neutral atoms with an estimation of resources needed to perform it.