Results 1 to 10 of about 110,884 (185)
Quantum Register Algebra: the mathematical language for quantum computing [PDF]
Quantum Information Processing, 2023 11 ...
J. Hrdina +7 more
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Algebraic quantum codes: linking quantum mechanics and discrete mathematics [PDF]
International Journal of Computer Mathematics: Computer Systems Theory, 2020 19 pages; written for both mathematicians and ...
Markus Grassl
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Quantum gravity observables: observation, algebras, and mathematical structure* [PDF]
Journal of Physics A: Mathematical and TheoreticalAbstract The questions of describing observables and observation in quantum gravity appear to be centrally important to its physics. A relational approach holds significant promise, and a classification of different types of relational observables (gravitationally dressed, field relational, and more general) is outlined.
Steven B. Giddings
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Hypercomplex Algebras and their application to the mathematical formulation of Quantum Theory [PDF]
, 2014 Quantum theory (QT), namely in terms of Schr dinger's 1926 wave functions in general requires complex numbers to be formulated. However, it soon turned out to even require some hypercomplex algebra. Incorporating Special Relativity leads to an equation (Dirac 1928) requiring pairwise anti-commuting coefficients, usually $4\times 4$ matrices. A unitary
Hertig, Torsten +2 more
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This paper, the fourth in a series, culminates the development of a novel paradigm termed **Transdimensional Mathematics**. This framework unifies continuous and discrete mathematical structures through the fundamental interaction of positive and negative spatial dimensions, with core relations such as $xX = a = \text{const.}$ describing an ...
Alaei jordehi, Mohammad Reza
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World Journal of Neuroscience, 2013 The thesis of this paper is that Information, Cognition and a Principle of Existence are intrinsically structured in the quantum model of reality. We reach such evidence by using the Clifford algebra. We analyze quantization in some traditional cases of quantum mechanics and, in particular in quantum harmonic oscillator, orbital angular momentum ...
Elio Conte
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This first applied-mathematics applications volume (Applied Mathematics Volume I) is structurally independent from the pure mathematics volume but conceptually based on the same integrated construction. The pure mathematics volume develops a law-space geometry and a principal-bundle-based generalized noncommutative Lie algebra that treat "laws ...
Gao, Zheng
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Quantum Computing Techniques for Numerical Linear Algebra in Computational Mathematics
Panamerican Mathematical JournalQuantum computing is a new and exciting area of computational mathematics that has the ability to solve very hard problems that traditional computing methods have not been able to solve for a long time. This abstract goes into detail about how quantum computing can be used in numerical linear algebra, which is an important part of computational ...
Sharada Narsingrao Ohatkar
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C*-Algebras and Mathematical Foundations of Quantum Statistical Mechanics [PDF]
, 2023 Jean-Bernard Bru +1 more
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Dyson--Schwinger Equations, Renormalization Conditions, and the Hopf Algebra of Perturbative Quantum Field Theory: An Advanced Mathematical and Physical Analysis [PDF]
This paper delves into the complex mathematical structures and physical applications underlying the work \textit{Dyson--Schwinger Equations, Renormalization Conditions, and the Hopf Algebra of Perturbative Quantum Field Theory} by Paul-Hermann Balduf.
Wen-Xiang Chen
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