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Towards an optimal swap gate

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Abstract

We present a novel approach that generalizes the well- known quantum SWAP gate to higher dimensions and construct a regular quantum gate composed entirely in terms of the generalized CNOT gate that cyclically permutes the states of \(d\) qudits for \(d\) prime. We also investigate the case for \(d\) other than prime. A key feature of the construction design relates to the periodicity evaluation for a family of linear recurrences which we achieve by exploiting generating functions and their factorization over the complex reals.

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Acknowledgments

The authors would like to thank Matthew G. Parker, Gary McGuire and Rüdiger Schack for helpful comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics and Physics, Nottingham Trent University, Nottingham, NG11 8NS, United Kingdom

    Colin Wilmott

  2. Faculty of Informatics, Masaryk University, Šumavská 416/15, 602 00 , Brno, Czech Republic

    Colin Wilmott

  3. Department of Mathematics, Royal Holloway, University of London, Egham, Surrey, TW20 0EX, United Kingdom

    Peter R. Wild

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  1. Colin Wilmott
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  2. Peter R. Wild
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Correspondence to Colin Wilmott.

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Wilmott, C., Wild, P.R. Towards an optimal swap gate. Quantum Inf Process 13, 1467–1482 (2014). https://doi.org/10.1007/s11128-014-0741-y

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  • DOI: https://doi.org/10.1007/s11128-014-0741-y

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