Results 1 to 10 of about 1,431,594 (178)
Characterizing barren plateaus in quantum ansätze with the adjoint representation [PDF]
Nature Communications, 2023 Variational quantum algorithms, a popular heuristic for near-term quantum computers, utilize parameterized quantum circuits which naturally express Lie groups.
Enrico Fontana +7 more
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On the adjoint representation of a hopf algebra [PDF]
Proceedings of the Edinburgh Mathematical Society, 2020 AbstractWe consider the adjoint representation of a Hopf algebra $H$ focusing on the locally finite part, $H_{{\textrm ad\,fin}}$, defined as the sum of all finite-dimensional subrepresentations. For virtually cocommutative $H$ (i.e., $H$ is finitely generated as module over a cocommutative Hopf subalgebra), we show that $H_{{\textrm ad\,fin}}$ is a ...
Kolb S, Lorenz M, Nguyen B, Yammine R
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A Category for the Adjoint Representation [PDF]
Journal of Algebra, 2001 We construct an abelian category C and exact functors in C which on the Grothendieck group descend to the action of a simply-laced quantum group in its adjoint representation. The braid group action in the adjoint representation lifts to an action in the derived category of C.
Huerfano, Ruth Stella, Khovanov, Mikhail
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Exterior Powers of the Adjoint Representation
Canadian Journal of Mathematics, 1997 AbstractExterior powers of the adjoint representation of a complex semisimple Lie algebra are decomposed into irreducible representations, to varying degrees of satisfaction.
Mark Reeder
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Co-Adjoint representation and controllability
Proyecciones (Antofagasta), 2018 Let ? an invariant control system over Lie group G The existence of a nontrivial simplectic orbit of G is analysed, so that the Hamiltonian system equivalent to ? via the co-adjoint representation, has a vector called simplectic. This allows the construction of a strictly increasing function over the positive trajectories of ?, determining sufficient ...
Víctor Ayala, Luis B. Vergara
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When ancient numerical demons meet physics-informed machine learning: adjoint-based gradients for implicit differentiable modeling [PDF]
Hydrology and Earth System SciencesRecent advances in differentiable modeling, a genre of physics-informed machine learning that trains neural networks (NNs) together with process-based equations, have shown promise in enhancing hydrological models' accuracy, interpretability, and ...
Y. Song +7 more
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Torus knots in adjoint representation and Vogel’s universality
European Physical Journal C: Particles and FieldsVogel’s universality gives a unified description of the adjoint sector of representation theory for simple Lie algebras in terms of three parameters $$\alpha ,\beta ,\gamma $$ α , β , γ , which are homogeneous coordinates of Vogel’s plane.
Liudmila Bishler, Andrei Mironov
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A representation for an adjoint operator
Journal of Numerical Analysis and Approximation Theory, 1975 Not available.
Stephen P. Travis
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Three-dimensional lattice SU(Nc) gauge theories with multiflavor scalar fields in the adjoint representation [PDF]
Physical review B, 2021 We consider three-dimensional lattice SU(Nc) gauge theories with multiflavor (Nf > 1) scalar fields in the adjoint representation. We investigate their phase diagram, identify the different Higgs phases with their gauge-symmetry pattern, and determine ...
C. Bonati +3 more
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Useful relations among the generators in the defining and adjoint representations of SU(N)
SciPost Physics Lecture Notes, 2021 There are numerous relations among the generators in the defining and adjoint representations of SU(N). These include Casimir operators, formulae for traces of products of generators, etc.
Howard E. Haber
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