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Quantum Hamiltonian Complexity

Final Report Summary - QHC (Quantum Hamiltonian Complexity)

Quantum computation, born about a quarter of a century ago, holds a promise for a technological
revolution, suggesting that quantum systems process information in ways that are very different (and
often unimaginably more efficient) than classical systems. Over the past decade, quantum
computation has changed its focus; whereas in its early days, its main focus was on achieving
progress 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 systems
are studied and manipulated with the aid of a computational perspective. The insights borrowed from computer science and
from 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 university
several 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 using
quantum algorithmic tools, new understanding regarding the robustness of multiparticle entanglement, and its limitations, and more.