Results 1 to 10 of about 95 (95)
Quantum Register Algebra: the mathematical language for quantum computing
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 ...
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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
Hertig, Torsten +2 more
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Quantum gravity observables: observation, algebras, and mathematical structure*
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.
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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 ...
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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 P. R. Chernoff, J. E. Marsden
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MATHEMATICAL FUNDAMENTALS OF ALGEBRAIC LATTICIES AND THEIR APPLICATION IN QUANTUM CRYPTOLOGY
The ongoing development of quantum computers threatens state-of-the-art public key cryptographic schemes, such as discrete logarithm factorization key generation schemes, digital signatures, and elliptic curve cryptography. It is necessary to develop new cryptographic algorithms capable of resisting the attacks of quantum computers.
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Algebras, Representations and Quantum Mechanics(6) Approaches from mathematical science and quantum information, Chaos and Nonlinear Dynamics in Quantum-Mechanical and Macroscopic Systems)可積分性という概念は古典力学では明確に定義されているが,量子力学における対応概念は不明瞭である.また,古典力学との対応を求めず,量子力学のハイゼンベルグ方程式を解くという目的に限定しても,作用角変数に匹敵するような強力かつ柔軟な方法論の構築が望ましい.本講演ではこれらの問題点を指摘し,解決の糸口を代数の表現論による多様体上の量子力学の定式化に探ってみた. この論文は国立情報学研究所の電子図書館事業により電子化されました。
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Applications of the product formula for the universal R-matrix of quantum affine algebra to mathematical physics博士学位論文 (Thesis(doctor))
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Structure of bicentralizer algebras and inclusions of type III factors (Mathematical aspects of quantum fields and related topics)We investigate the structure of the relative bicentralizer algebra B(N ⊂ M, φ) for inclusions of von Neumann algebras with normal expectation where N is a type Ill₁ subfactor and φ ∈ N* is a faithful state. We first construct a canonical flow β[φ] : R*₊ ↷ B(N C M, ip) on the relative bicentralizer algebra and we show that the W*-dynamical system (B(N ⊂
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