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Braiding, Majorana fermions, Fibonacci particles and topological quantum computing

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Abstract

This paper is an introduction to relationships between topology, quantum computing, and the properties of Fermions. In particular, we study the remarkable unitary braid group representations associated with Majorana fermions.

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  • 03 October 2018

    The original version of this article contained error in the acknowledgement section.

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Acknowledgements

Much of this paper is based upon our joint work in the papers and books [1, 33, 34, 36,37,38, 40, 42,43,44, 49,50,51, 53, 54, 61,62,67]. We have woven this work into the present paper in a form that is coupled with recent and previous work on relations with logic and with Majorana fermions. This work was partially supported by the Laboratory of Topology and Dynamics, Novosibirsk State University (contract no. 14.Y26.31.0025 with the Ministry of Education and Science of the Russian Federation) and by the Simons Foundation Collaboration Grant, Award Number 426075.

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Authors and Affiliations

  1. Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL, USA

    Louis H. Kauffman

  2. Department of Computer Science and Electrical Engineering, University of Maryland Baltimore County, 1000 Hilltop Circle, Baltimore, MD, 21250, USA

    Samuel J. Lomonaco

  3. Department of Mechanics and Mathematics, Novosibirsk State University, Novosibirsk, Russia

    Louis H. Kauffman

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Kauffman, L.H., Lomonaco, S.J. Braiding, Majorana fermions, Fibonacci particles and topological quantum computing. Quantum Inf Process 17, 201 (2018). https://doi.org/10.1007/s11128-018-1959-x

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