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QI: Fachverband Quanteninformation

QI 1: Quantum Foundations

QI 1.3: Vortrag

Montag, 18. März 2024, 10:15–10:30, HFT-FT 101

Towards exact factorization of quantum dynamics via Lie algebras — •David Edward Bruschi¹, André Xuereb², and Robert Zeier³ — ¹Institue for Quantum Computing Analytics (PGI-12), Forschunsgzentrum Jülich, Jülich, Germany — ²Department of Physics, University of Malta, Malta — ³Quantum Control (PGI-8), Forschungszentrum Jülich, Jülich, Germany

Determining exactly the dynamics of a physical system is the paramount goal of any branch of physics. Quantum dynamics are characterized by the non-commutativity of operators, which implies that the dynamics usually cannot be tackled analytically and require ad-hoc solutions or numerical approaches. A priori knowledge on the ability to obtain exact results would be of great advantage for many tasks of modern interest, such as quantum computing, quantum simulation and quantum annealing.

In this work we lay the foundations for an approach to determine the dimensionality of a Hamiltonian Lie algebra by appropriately characterizing its generating terms. This requires us to develop a new tool to construct sequences of operators that determine the final dimension of the algebra itself. Our work is exact and fully general, therefore providing statements on the ultimate ability to exactly control the dynamics or simulate specific classes of physical systems. This work has important implications not only for theoretical physics, but it also aids our understanding of the structure of the Hilbert space, as well as Lie algebras.

Keywords: Quantum dynamics; Lie algebras; Quantum Simulations