Final Report Summary - QHC (Quantum Hamiltonian Complexity) Quantum computation, born about a quarter of a century ago, holds a promise for a technologicalrevolution, suggesting that quantum systems process information in ways that are very different (andoften unimaginably more efficient) than classical systems. Over the past decade, quantumcomputation has changed its focus; whereas in its early days, its main focus was on achievingprogress on tasks interesting mostly for computer scientists, in particular building quantum computers and finding quantum algorithms, it is now being understood that an equally important contribution of the area lies in its implication on our understanding and manipulating of physics itself. Over the past decade or more a new field was created, called quantum Hamiltonian complexity, in which physical systemsare studied and manipulated with the aid of a computational perspective. The insights borrowed from computer science andfrom information theory applied to the study of many body quantum systems have led to profound new insights on physics. Supported by the "Quantum Hamiltonian complexity" grant, the PI Dorit Aharonov,one of the founders of the new field, advanced together with her group at the Hebrew universityseveral central directions in this area. Those include the understanding of how the highly complex quantum correlations coined quantum entanglement can be classified and presented classically, and what is the complexity of doing this, in various cases; What tools can be used to test and verify quantum systems performing highly complex quantum evolutions; better understanding of the local versus global nature of quantum entanglement; new insights into quantum cryptography related to quantum entanglement; exciting new relations and ideas of how to improve precision measurements usingquantum algorithmic tools, new understanding regarding the robustness of multiparticle entanglement, and its limitations, and more.