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Yang–Baxterizations, Universal Quantum Gates and Hamiltonians

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Abstract

The unitary braiding operators describing topological entanglements can be viewed as universal quantum gates for quantum computation. With the help of the Brylinski’s theorem, the unitary solutions of the quantum Yang–Baxter equation can be also related to universal quantum gates. This paper derives the unitary solutions of the quantum Yang–Baxter equation via Yang–Baxterization from the solutions of the braid relation. We study Yang–Baxterizations of the non-standard and standard representations of the six-vertex model and the complete solutions of the non-vanishing eight-vertex model. We construct Hamiltonians responsible for the time-evolution of the unitary braiding operators which lead to the Schrödinger equations.

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Authors and Affiliations

  1. Institute of Theoretical Physics, Chinese Academy of Sciences, P. O. Box 2735, Beijing, 100080, P. R. China

    Yong Zhang

  2. Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 South Morgan Street, Chicago, IL, 60607-7045, USA

    Louis H. Kauffman

  3. Nankai Institute of Mathematics, Nankai University Tianjin, 300071, P. R. China

    Mo-Lin Ge

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  1. Yong Zhang
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  2. Louis H. Kauffman
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  3. Mo-Lin Ge
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Correspondence to Louis H. Kauffman.

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Zhang, Y., Kauffman, L.H. & Ge, ML. Yang–Baxterizations, Universal Quantum Gates and Hamiltonians. Quantum Inf Process 4, 159–197 (2005). https://doi.org/10.1007/s11128-005-7655-7

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  • DOI: https://doi.org/10.1007/s11128-005-7655-7

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