Investigating innovative approaches to analog computing by harnessing the emerging dynamics of quantum systems represents an exciting and modern frontier. This endeavor holds the potential to transform domains such as optimization, machine learning, and simulations by addressing complex problems that classical computers struggle to solve. It introduces a new computational paradigm applicable to fields like optimization, artificial intelligence, and scientific simulations, offering the promise of improving the efficiency and effectiveness of solving intricate real-world challenges. During this theoretical internship, the Master's student will learn, generalize, and apply methods developed in recent and promising works to explore innovative and advanced strategies for utilizing the intricacies of quantum systems. The goal is to develop emergent computational capabilities, particularly aimed at solving optimization problems and tackling interdisciplinary challenges. The internship’s theoretical research will involve both analytical and numerical methods, with a focus on the quantum many-body physics of state-of-the-art quantum platforms, including superconducting quantum circuits and other quantum systems. This is an internship proposal that can continue into a PhD thesis.