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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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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On the adjoint representation of a hopf algebra [PDF]
Proceedings of the Edinburgh Mathematical Society, 2019 We 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.
S. Kolb +3 more
semanticscholar +5 more sources
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
doaj +2 more sources
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
semanticscholar +1 more source
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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Worldline description of a bi-adjoint scalar and the zeroth copy
Journal of High Energy Physics, 2021 Bi-adjoint scalars are helpful in studying properties of color/kinematics duality and the double copy, which relates scattering amplitudes of gauge and gravity theories. Here we study bi-adjoint scalars from a worldline perspective.
Fiorenzo Bastianelli +2 more
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GMOR relation for a QCD-like theory from S-duality
Physics Letters B, 2022 Following [1] we study a QCD-like gauge theory using a non-supersymmetric setup in type IIB string theory. The setup includes an O3 plane and N D3 anti-branes and it realises a USp(2N) ‘electric’ gauge theory with four “quarks” in the two-index ...
Adi Armoni, Henry Harper-Gardner
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Spectrum and mass anomalous dimension of SU(2) gauge theories with fermions in the adjoint representation: from $N_f=1/2$ to $N_f=2$ [PDF]
, 2017 We summarize our results concerning the spectrum and mass anomalous dimension of SU(2) gauge theories with various numbers of fermions in the adjoint representation, where each Majorana fermion corresponds effectively to half a Dirac flavour $N_f$.
G. Bergner +4 more
semanticscholar +1 more source
The canonical basis of the quantum adjoint representation [PDF]
, 2016 We identify the canonical basis of the quantum adjoint representation of a quantized enveloping algebra with a basis that we defined before the theory of canonical bases was available.
G. Lusztig
semanticscholar +1 more source