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Quantum Complexity of Boolean Matrix Multiplication and Related Problems

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Computing with New Resources

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8808))

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Abstract

This paper surveys the state of the art of research on quantum algorithms for problems related to matrix multiplication, such as triangle finding, Boolean matrix multiplication and Boolean product verification. The exposition highlights how simple tools from quantum computing, and in particular the technique known as quantum search, can be used in a multitude of situations to design quantum algorithms that outperform the best known classical algorithms. Some open problems in this area are also described.

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Authors and Affiliations

  1. Department of Computer Science Graduate, School of Information Science and Technology, The University of Tokyo, Tokyo, Japan

    François Le Gall

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  1. François Le Gall
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Correspondence to François Le Gall .

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Editors and Affiliations

  1. Department of Computer Science, The University of Auckland, Auckland, New Zealand

    Cristian S. Calude

  2. University of Latvia, Riga, Latvia

    Rūsiņš Freivalds

  3. School of Informatics, Kyoto University, Kyoto, Japan

    Iwama Kazuo

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Le Gall, F. (2014). Quantum Complexity of Boolean Matrix Multiplication and Related Problems. In: Calude, C., Freivalds, R., Kazuo, I. (eds) Computing with New Resources. Lecture Notes in Computer Science(), vol 8808. Springer, Cham. https://doi.org/10.1007/978-3-319-13350-8_13

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  • DOI: https://doi.org/10.1007/978-3-319-13350-8_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-13349-2

  • Online ISBN: 978-3-319-13350-8

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