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Quantum Algorithms for Finding Constant-Sized Sub-hypergraphs

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Computing and Combinatorics (COCOON 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8591))

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Abstract

We develop a general framework to construct quantum algorithms that detect if a 3-uniform hypergraph given as input contains a sub-hypergraph isomorphic to a prespecified constant-sized hypergraph. This framework is based on the concept of nested quantum walks recently proposed by Jeffery, Kothari and Magniez, and extends the methodology designed by Lee, Magniez and Santha for similar problems over graphs. As applications, we obtain a quantum algorithm for finding a 4-clique in a 3-uniform hypergraph on n vertices with query complexity O(n 1.883), and a quantum algorithm for determining if a ternary operator over a set of size n is associative with query complexity O(n 2.113).

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Author information

Authors and Affiliations

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

    François Le Gall

  2. Graduate School of Informatics, Nagoya University, Japan

    Harumichi Nishimura

  3. NTT Communication Science Laboratories, NTT Corporation, Japan

    Seiichiro Tani

Authors
  1. François Le Gall
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  2. Harumichi Nishimura
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  3. Seiichiro Tani
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Georgia State University, 34 Peachtree Street, Suite 1410, 30303, Atlanta, GA, USA

    Zhipeng Cai

  2. Department of Computer Science, Georgia State University, 34 Peachtree Street, Suite 1443, 30303, Atlanta, GA, USA

    Alex Zelikovsky

  3. Department of Computer Science, Georgia State University, 34 Peachtree Street, Suite 1449, 30303, Atlanta, GA, USA

    Anu Bourgeois

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© 2014 Springer International Publishing Switzerland

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Le Gall, F., Nishimura, H., Tani, S. (2014). Quantum Algorithms for Finding Constant-Sized Sub-hypergraphs. In: Cai, Z., Zelikovsky, A., Bourgeois, A. (eds) Computing and Combinatorics. COCOON 2014. Lecture Notes in Computer Science, vol 8591. Springer, Cham. https://doi.org/10.1007/978-3-319-08783-2_37

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  • DOI: https://doi.org/10.1007/978-3-319-08783-2_37

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08782-5

  • Online ISBN: 978-3-319-08783-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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