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We provide a classification of all dynamical Lie algebras generated by 2-local spin interactions on undirected graphs.
F. Albertini and D. D’Alessandro, Notions of controllability for quantum mechanical systems, in Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228) , Vol. 2 (2001) pp. 1589–1594 vol.2
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R. D. Somma, Quantum computation, complexity, and many-body physics, arXiv preprint quant-ph/0512209 (2005)
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R. Somma, H. Barnum, G. Ortiz, and E. Knill, Efficient solvability of Hamiltonians and limits on the power of some quantum computational models, Phys. Rev. Lett. 97
2006
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R. Zeier and T. Schulte-Herbrüggen, Symmetry principles in quantum systems theory, Journal of mathematical physics 52
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V. Galitski, Quantum-to-classical correspondence and hubbard-stratonovich dynamical systems: A lie-algebraic approach, Phys. Rev. A 84
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A. W. Knapp, Lie Groups Beyond an Introduction , Vol. 140 (Springer Science & Business Media, 2013)
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Z. Zimborás, R. Zeier, T. Schulte-Herbrüggen, and D. Burgarth, Symmetry criteria for quantum simulability of effective interactions, Physical Review A 92
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J. R. McClean, S. Boixo, V. N. Smelyanskiy, R. Babbush, and H. Neven, Barren plateaus in quantum neural network training landscapes, Nature Communications 9
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A. Chapman and S. T. Flammia, Characterization of solvable spin models via graph invariants, Quantum 4
2020
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D. d’Alessandro, Introduction to quantum control and dynamics , 2nd ed. (Chapman and hall/CRC, 2021)
2021
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C. Ortiz Marrero, M. Kieferová, and N. Wiebe, Entanglement-Induced Barren Plateaus, PRX Quantum 2
2021
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D’Alessandro, Domenico and Hartwig, Jonas T, Dynamical decomposition of bilinear control systems subject to symmetries, Journal of Dynamical and Control Systems 27
2021
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S. Moudgalya and O. I. Motrunich, Hilbert space fragmentation and commutant algebras, Phys. Rev. X 12
2022
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M. Larocca, N. Ju, D. García-Martín, P. J. Coles, and M. Cerezo, Theory of overparametrization in quantum neural networks, Nature Computational Science 3
2023
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2023
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M. Ragone, B. N. Bakalov, F. Sauvage, A. F. Kemper, C. Ortiz Marrero, M. Larocca, and M. Cerezo, A Lie algebraic theory of barren plateaus for deep parametrized quantum circuits, Nature Communications 15
2024
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E. Fontana, D. Herman, S. Chakrabarti, N. Kumar, R. Yalovetzky, J. Heredge, S. H. Sureshbabu, and M. Pistoia, Characterizing barren plateaus in quantum ansätze with the adjoint representation, Nature Communications 15
2024
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2023
Cited alongside, same era.
M. Cerezo, M. Larocca, D. García-Martín, N. L. Diaz, P. Braccia, E. Fontana, M. S. Rudolph, P. Bermejo, A. Ijaz, S. Thanasilp, E. R. Anschuetz, and Z. Holmes, Does provable absence of barren plateaus imply classical simulability? or, why we need to rethink variational quantum computing, arXiv preprint 2312.09121 (2023)
2023
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2024
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2024
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