Results 51 to 60 of about 47,626 (83)

Quantum Register Algebra: the mathematical language for quantum computing

Quantum Information Processing, 2022
We present Quantum Register Algebra (QRA) as an efficient tool for quantum computing. We show the direct link between QRA and Dirac formalism. We present Geometric Algebra Algorithms Optimizer (GAALOP) implementation of our approach.
J. Hrdina, D. Hildenbrand, Aleš Návrat, Christian Steinmetz, R. Alves, C. Lavor, Petr Vašík, I. Eryganov   +7 more
semanticscholar   +1 more source

Non-standard quantum algebra Uh(sl(2,R))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {U}_h (\mathfrak {sl}

Quantum Information Processing
We discuss the application of the Jordanian quantum algebra Uh(sl(2,R))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek ...
A. Ballesteros, J. Relancio, L. Santamar'ia-Sanz   +2 more
semanticscholar   +1 more source

Local Quantum Mechanical Prediction of the Singlet State Using Geometric Algebra

Journal of Quantum Information Science
We deduce the quantum mechanical prediction of $-{\bf a}\cdot{\bf b}$ for the singlet spin state employing local measurement functions following Bell's approach. This result represents the quantum mechanical expectation value for the joint measurement of
C. Diether
semanticscholar   +1 more source

Sequential Quantum Measurements and the Instrumental Group Algebra

Quantum Reports
Many of the most fundamental observables—position, momentum, phase point, and spin direction—cannot be measured by an instrument that obeys the orthogonal projection postulate.
Christopher S. Jackson
semanticscholar   +1 more source

Action of the Witt algebra on categorified quantum groups

Quantum Topology
We construct an action of the positive Witt algebra on the categorified quantum group associated to a simply-laced Lie algebra. In the type-A case, we show that this action induces an action of the positive Witt algebra on \mathfrak{gl}_{n ...
Jernej Grlj, A. Lauda
semanticscholar   +1 more source

Accelerating Large-Scale Linear Algebra Using Variational Quantum Imaginary Time Evolution

International Conference on Quantum Computing and Engineering
The solution of large sparse linear systems via factorization methods such as LU or Cholesky decomposition, can be computationally expensive due to the introduction of non-zero elements, or “fill-in.” Graph partitioning can be used to reduce the “fill-in,
Willie Aboumrad, Daiwei Zhu, Claudio Girotto, François-Henry Rouet, Jezer Jojo, R. Lucas, Jay Pathak, Ananth Kaushik, Martin Roetteler   +8 more
semanticscholar   +1 more source

RLL-Realization of two-parameter quantum affine algebra in type Cn(1)

Journal of Algebra and its Applications
We establish an explicit correspondence between the Drinfeld current algebra presentation for the two-parameter quantum affine algebra $U_{r, s}(\mathrm{C}_n^{(1)})$ and the $R$-matrix realization \'a la Faddeev, Reshetikhin and Takhtajan.
Xin Zhong, Naihong Hu, Naihuan Jing
semanticscholar   +1 more source

Branching rules for level-zero extremal weight modules from Uq(

Journal of Algebra
In this paper, we study the structure of a $U_q(\widehat{\mathfrak{sl}}_n)$-module $\Psi_{\varepsilon}^* V(\lambda)$, where $V(\lambda)$ is the extremal weight module of level-zero dominant weight $\lambda$ over the quantum affine algebra $U_q(\widehat ...
Shutaro Nakaoka
semanticscholar   +1 more source

Covariant decomposable maps on C*-algebras and quantum dynamics

Linear Algebra and its Applications
We characterize covariant positive decomposable maps between unital C*-algebras in terms of a dilation theorem, which generalizes a seminal result by H. Scutaru from Rep. Math. Phys. 16 (1):79-87, 1979.
Krzysztof Szczygielski
semanticscholar   +1 more source

Weyl, Demazure and fusion modules for the current algebra of sl r+1

, 2006
Vyjayanthi Chari, S. Loktev
semanticscholar   +1 more source