Results 1 to 10 of about 1,498,972 (229)
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
doaj +5 more sources
The canonical basis of the quantum adjoint representation [PDF]
arXiv, 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
arxiv +11 more sources
Decomposition of the Adjoint Representation of the Small Quantum sl 2 [PDF]
Communications in Mathematical Physics, 1997 Given a finite type root datum and a primitive root of unity $q=\sqrt[l]{1}$, G.~Lusztig has defined in [Lu] a remarkable finite dimensional Hopf algebra $\fu$ over the cyclotomic field ${\Bbb Q}(\sqrt[l]{1})$. In this note we study the adjoint representation $\ad$ of $\fu$ in the simplest case of the root datum $sl_2$.
Viktor Ostrik
semanticscholar +7 more sources
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 ...
Stefan Kolb +3 more
openaire +5 more sources
Adjoints and low-rank covariance representation [PDF]
Nonlinear Processes in Geophysics, 2001 Abstract. Quantitative measures of the uncertainty of Earth system estimates can be as important as the estimates themselves. Direct calculation of second moments of estimation errors, as described by the covariance matrix, is impractical when the number of degrees of freedom of the system state is large and the sources of uncertainty are not ...
Michael K. Tippett, Stephen E. Cohn
openalex +9 more sources
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
semanticscholar +5 more sources
A Category for the Adjoint Representation
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.
Ruth Stella Huerfano, Mikhail Khovanov
openalex +5 more sources
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
openalex +3 more sources
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
openalex +3 more sources
A representation for an adjoint operator
Journal of Numerical Analysis and Approximation Theory, 1975 Not available.
Stephen P. Travis
doaj +3 more sources