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Optimal Parallel Quantum Query Algorithms

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Book cover Algorithms - ESA 2014 (ESA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8737))

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Abstract

We study the complexity of quantum query algorithms that make p queries in parallel in each timestep. We show tight bounds for a number of problems, specifically Θ((n/p)2/3) p-parallel queries for element distinctness and Θ((n/p)k/(k + 1)) for k-sum. Our upper bounds are obtained by parallelized quantum walk algorithms, and our lower bounds are based on a relatively small modification of the adversary lower bound method, combined with recent results of Belovs et al. on learning graphs. We also prove some general bounds, in particular that quantum and classical p-parallel complexity are polynomially related for all total functions f when p is small compared to f’s block sensitivity.

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Author information

Authors and Affiliations

  1. IQC, University of Waterloo, Canada

    Stacey Jeffery

  2. CNRS, LIAFA, Univ Paris Diderot, Sorbonne Paris-Cité, 75205, Paris, France

    Frederic Magniez

  3. CWI and University of Amsterdam, The Netherlands

    Ronald de Wolf

Authors
  1. Stacey Jeffery
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  2. Frederic Magniez
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  3. Ronald de Wolf
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Editor information

Editors and Affiliations

  1. Massachusetts Institute of Technology, Cambridge, MA, USA

    Andreas S. Schulz

  2. Karlsruhe Institute of Technology (KIT), Kaiserstruhe 12, 76131, Karlsruhe, Germany

    Dorothea Wagner

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Jeffery, S., Magniez, F., de Wolf, R. (2014). Optimal Parallel Quantum Query Algorithms. In: Schulz, A.S., Wagner, D. (eds) Algorithms - ESA 2014. ESA 2014. Lecture Notes in Computer Science, vol 8737. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44777-2_49

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  • DOI: https://doi.org/10.1007/978-3-662-44777-2_49

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44776-5

  • Online ISBN: 978-3-662-44777-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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