 A geometrical approach to quantum holonomic computing algorithmsA.M. Samoilenko, Y.A. Prykarpatsky, Ufuk Taneri, A.K. Prykarpatsky and D.L. Blackmore Mathematics and Computers in Simulation (MATCOM), 2004, vol. 66, issue 1, 1-20 Abstract: The article continues a presentation of modern quantum mathematics backgrounds started in [Quantum Mathematics and its Applications. Part 1. Automatyka, vol. 6, AGH Publisher, Krakow, 2002, No. 1, pp. 234–2412; Quantum Mathematics: Holonomic Computing Algorithms and Their Applications. Part 2. Automatyka, vol. 7, No. 1, 2004]. A general approach to quantum holonomic computing based on geometric Lie-algebraic structures on Grassmann manifolds and related with them Lax type flows is proposed. Making use of the differential geometric techniques like momentum mapping reduction, central extension and connection theory on Stiefel bundles it is shown that the associated holonomy groups properly realizing quantum computations can be effectively found concerning diverse practical problems. Two examples demonstrating two-form curvature calculations important for describing the corresponding holonomy Lie algebra are presented in detail. Keywords: Quantum computers; Quantum algorithms; Dynamical systems; Grassmann manifolds; Symplectic structures; Connections; Holonomy groups; Lax type integrable flows (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:66:y:2004:i:1:p:1-20 DOI: 10.1016/j.matcom.2004.01.017 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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