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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The canonical basis of the quantum adjoint representation [PDF]
Journal of Combinatorial Algebra, 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 +9 more sources
Decomposition of the Adjoint Representation of the Small Quantum sl 2 [PDF]
Communications in Mathematical Physics, 1997 1.1. Given a finite type root datum and a primitive root of unity q = l √ 1, G. Lusztig has defined in [Lu] a remarkable finite dimensional Hopf algebra u over the cyclotomic field Q( l √ 1). It is called a restricted quantum universal enveloping algebra,
Viktor Ostrik
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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 $N_f$.
Georg Bergner +4 more
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Three-dimensional QCD in the adjoint representation and random matrix theory [PDF]
, 2000 In this paper we complete the derivations of finite volume partition functions for QCD using random matrix theories by calculating the effective low-energy partition function for three-dimensional QCD in the adjoint representation from a random matrix ...
U. Magnea
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Finite-temperature chiral transition in QCD with quarks in the fundamental and adjoint representation [PDF]
, 2005 We study the nature of the finite-temperature chiral transition in QCD with N_f light quarks in the fundamental and adjoint representation. Universality and renormalization-group (RG) arguments show that the possibility of having a continuous ...
Ettore Vicari +2 more
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A category for the adjoint representation [PDF]
, 2000 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
Ruth Stella Huerfano, Mikhail Khovanov
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Lie Supergroups Obtained from 3-Dimensional Lie Superalgebras Associated to the Adjoint Representation and Having a 2-Dimensional Derived Ideal [PDF]
International Journal of Mathematics and Mathematical Sciences, 2008 We give the explicit multiplication law of the Lie supergroups for which the base manifold is a 3-dimensional Lie group and whose underlying Lie superalgebra g=g0⊕g1 which satisfies g1=g0, g0 acts on g1 via the adjoint representation and g0 has a 2 ...
I. Hernández, R. Peniche
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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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, 2014 Let G be a p-adic Lie group and Ad be the adjoint representation of G on its Lie algebra. It was claimed in the literature that the kernel K of Ad always has an abelian open normal subgroup.
Helge Glöckner
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