Quantum technologies exploit non-classical properties such as quantum superposition and entanglement to devise techniques for imaging, sensing, secure communication, and computing. An important goal of our research is to come up with new ideas how to use synthetic quantum system as physical simulation devices to explore quantum many-body phenomena. This requires the development of methods for benchmarking these devices using tools from quantum information theory and machine learning. Specifically, we develop methods for efficiently characterizing quantum states from measurements, for example quantifying their entanglement, and for simulating quantum many-body physics on classical computers, thereby pushing the limits of numerical methods.