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An Application of the Deutsch-Jozsa Algorithm to Formal Languages and the Word Problem in Groups

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Theory of Quantum Computation, Communication, and Cryptography (TQC 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5106))

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Abstract

We adapt the Deutsch-Jozsa algorithm to the context of formal language theory. Specifically, we use the algorithm to distinguish between trivial and nontrivial words in groups given by finite presentations, under the promise that a word is of a certain type. This is done by extending the original algorithm to functions of arbitrary length binary output, with the introduction of a more general concept of parity. We provide examples in which properties of the algorithm allow to reduce the number of oracle queries with respect to the deterministic classical case. This has some consequences for the word problem in groups with a particular kind of presentation.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Newcastle upon Tyne, United Kingdom

    Michael Batty, Andrew J. Duncan & Sarah Rees

  2. Information Engineering Department, University of Siena, Italy

    Andrea Casaccino

  3. Institute for Quantum Computing and Department of Combinatorics and Optimization, University of Waterloo, Canada

    Simone Severini

Authors
  1. Michael Batty
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  2. Andrea Casaccino
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  3. Andrew J. Duncan
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  4. Sarah Rees
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  5. Simone Severini
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Editor information

Editors and Affiliations

  1. NTT Communication Science Laboratories, 3-1, Morinosato Wakamiya, Atsugi-shi, 243-0198, Kanagawa Pref., Japan

    Yasuhito Kawano

  2. Institute for Quantum Computing, University of Waterloo, N2L 3G1, Waterloo, ON, Canada

    Michele Mosca

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© 2008 Springer-Verlag Berlin Heidelberg

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Batty, M., Casaccino, A., Duncan, A.J., Rees, S., Severini, S. (2008). An Application of the Deutsch-Jozsa Algorithm to Formal Languages and the Word Problem in Groups. In: Kawano, Y., Mosca, M. (eds) Theory of Quantum Computation, Communication, and Cryptography. TQC 2008. Lecture Notes in Computer Science, vol 5106. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89304-2_6

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  • DOI: https://doi.org/10.1007/978-3-540-89304-2_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-89303-5

  • Online ISBN: 978-3-540-89304-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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