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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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Hypercomplex Algebras and their application to the mathematical formulation of Quantum Theory
, 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
Torsten Hertig +2 more
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Quantum Register Algebra: the mathematical language for quantum computing
Quantum Information Processing, 2023 11 ...
Jaroslav Hrdina +7 more
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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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Book Review: Lie Algebras and Quantum Mechanics and Vector Bundles in Mathematical Physics [PDF]
Bulletin of the American Mathematical Society, 1973 Paul R. Chernoff, Jerrold E. Marsden
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Perturbative Algebraic Quantum Field Theory [PDF]
, 2015 These notes are based on the course given by Klaus Fredenhagen at the Les Houches Winter School in Mathematical Physics (January 29 - February 3, 2012) and the course "QFT for mathematicians" given by Katarzyna Rejzner in Hamburg for the Research Training Group 1670 (February 6 -11, 2012).
Thomas Strobl, Damien Calaque
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Separability and distillability in composite quantum systems -a primer- [PDF]
, 2000 Quantum mechanics is already 100 years old, but remains alive and full of challenging open problems. On one hand, the problems encountered at the frontiers of modern theoretical physics like Quantum Gravity, String Theories, etc.
A. Sanpera +17 more
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, 2002 In this paper we explore the boundary between biology and the study of formal systems (logic). In the end, we arrive at a summary formalism, a chapter in "boundary mathematics" where there are not only containers but also extainers >
Kauffman, Louis H.
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Complexity vs Energy: Theory of Computation and Theoretical Physics [PDF]
, 2013 This paper is a survey dedicated to the analogy between the notions of {\it complexity} in theoretical computer science and {\it energy} in physics. This analogy is not metaphorical: I describe three precise mathematical contexts, suggested recently, in ...
Manin, Yuri I.
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The sl(n)-WZNW Fusion Ring: a combinatorial construction and a realisation as quotient of quantum cohomology [PDF]
, 2010 A simple, combinatorial construction of the sl(n)-WZNW fusion ring, also known as Verlinde algebra, is given. As a byproduct of the construction one obtains an isomorphism between the fusion ring and a particular quotient of the small quantum cohomology ...
Baxter +46 more
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