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QI: Fachverband Quanteninformation
QI 29: Quantum Information: Concepts and Methods I
QI 29.7: Vortrag
Donnerstag, 13. März 2025, 12:45–13:00, HS IV
Symmetry analysis of Two-Local Quantum Spin Dynamics — •Roberto Gargiulo1,2 and Robert Zeier1 — 1Forschungszentrum Jülich GmbH, Peter Grünberg Institute, Quantum Control (PGI-8), 52425 Jülich, Germany — 2University of Cologne, Institute for theoretical physics (THP), 50937 Cologne, Germany
Fundamental tools in the study of dynamics of quantum systems are Lie groups and Lie algebras, which have various applications: In the context of quantum control a Lie-theoretic approach can provide answers to reachability and simulability. In addition to reachability, the knowledge of the Lie algebras corresponding to the given ansätze is necessary for understanding optimization problems in variational quantum algorithms. In many-body systems, these tools lead to a systematic description of physical models based on dynamical properties and in special cases to classical simulability.
We build upon recent work (see [1, 2, 3]), by providing a structured study and classification of Lie algebras obtained by interactions of pairs of qubits with given graph connectivity. Specifically, we consider certain sums of Pauli strings as generators, whereas previous work mainly focused on dynamics generated by single Pauli strings.
- [1] Sujay Kazi et al. arXiv: 2410.05187 [quant-ph]
- [2] Gerard Aguilar et al. arXiv: 2408.00081 [quant-ph]
- [3] Efekan Kökcü et al. arXiv: 2409.19797 [quant-ph]
Keywords: Symmetries; Variational Quantum Algorithms; Lie Algebra; Quantum Control; Classical Simulability