Quantum optimization and machine learning: variational algorithms and applications

Abstract

This research project aims to investigate the potential and applications of quantum algorithms in optimization and machine learning, with a focus on open quantum systems and the integration with classical machine learning techniques to improve the performance of these algorithms. In addition, the project also aims to study simple quantum machine learning problems considering open quantum systems. The research will explore specific case studies to demonstrate the advantages and challenges associated with this hybrid approach. First, the project will analyze several algorithms, in particular QAOA and FALQON, examining the properties and limitations of these algorithms. Next, the research will investigate the combination of classical machine learning techniques, such as Support Vector Machines and neural networks, with quantum algorithms, in order to improve the efficiency and accuracy of quantum methods. Finally, the project will explore a series of case studies that illustrate the practical application of variational algorithms and hybrid techniques, particularly in the area of logistics and finance. These case studies will allow us to evaluate the effectiveness of the proposed approaches, especially in open quantum systems, and to identify possible challenges and opportunities for future research. (AU)