Bonn 2025 – scientific programme

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QI: Fachverband Quanteninformation

QI 35: Quantum Information: Concepts and Methods II

QI 35.6: Talk

Thursday, March 13, 2025, 15:45–16:00, HS IV

Deciding finiteness of Hamiltonian algebras — •David Edward Bruschi — Institute for Quantum Computing Analytics (PGI-12), 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 build on our approach previously introduced to determine the dimensionality of a Hamiltonian Lie algebra by appropriately characterizing its generating terms. In the original exact and fully general approach, we started to develop new tools to determine the final dimension of the algebra itself. We here extend the initial proposal by including a time-independent free Hamiltonian drift term, which improves the original proposal by allowing to tackle all bosonic Hamiltonians.

We are able to provide statements on the ultimate ability to exactly control the dynamics or simulate specific classes of physical systems of coupled quantum harmonic oscillators. 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; Factorization; Lie algebra