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Quantum Walks on Quantum Cellular Automata Lattices: Towards a New Model for Quantum Computation

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Cellular Automata (ACRI 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11115))

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Abstract

Many physical problems cannot be easily formulated as quantum circuits, which are a successful universal model for quantum computation. Because of this, new models that are closer to the structure of physical systems must be developed. Discrete and continuous quantum walks have been proven to be a universal quantum computation model, but building quantum computing systems based on their structure is not straightforward. Although classical cellular automata are models of universal classical computation, this is not the case for their quantum counterpart, which is limited by the no-coning theorem and the no-go lemma. Here we combine quantum walks, which reproduce unitary evolution in space with quantum cellular automata, which reproduce unitary evolution in time, to form a new model of quantum computation. Our results show that such a model is possible.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Democritus University of Thrace, 67100, Xanthi, Greece

    Ioannis G. Karafyllidis & Georgios Ch. Sirakoulis

Authors
  1. Ioannis G. Karafyllidis
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  2. Georgios Ch. Sirakoulis
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Corresponding author

Correspondence to Ioannis G. Karafyllidis .

Editor information

Editors and Affiliations

  1. University of Milano-Bicocca, Milan, Italy

    Giancarlo Mauri

  2. University of Perpignan, Perpignan, France

    Samira El Yacoubi

  3. University of Milano-Bicocca, Milan, Italy

    Alberto Dennunzio

  4. University of Tokyo, Tokyo, Japan

    Katsuhiro Nishinari

  5. University of Milano-Bicocca, Milan, Italy

    Luca Manzoni

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Karafyllidis, I.G., Sirakoulis, G.C. (2018). Quantum Walks on Quantum Cellular Automata Lattices: Towards a New Model for Quantum Computation. In: Mauri, G., El Yacoubi, S., Dennunzio, A., Nishinari, K., Manzoni, L. (eds) Cellular Automata. ACRI 2018. Lecture Notes in Computer Science(), vol 11115. Springer, Cham. https://doi.org/10.1007/978-3-319-99813-8_29

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  • DOI: https://doi.org/10.1007/978-3-319-99813-8_29

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-99812-1

  • Online ISBN: 978-3-319-99813-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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