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Quantum Walks and Search Algorithms pp 17–37Cite as

Introduction to Quantum Walks

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Part of the book series: Quantum Science and Technology ((QST))

Abstract

Quantum walks play an important role in the development of quantum algorithms. Algorithms based on quantum walks generally use a technique called amplitude amplification, which was introduced in Grover’s algorithm. This technique differs from the ones used in algebraic algorithms, in which the Fourier transform plays the main role. However, it is possible to go beyond Grover’s algorithm in terms of efficiency. The best algorithm to solve the element distinctness problem is based on quantum walks. This problem consists in determining whether there are repeated elements in a set of elements. When Grover’s algorithm is used, the solution is less efficient.

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Notes

  1. 1.

    http://qubit.lncc.br/qwalk

  2. 2.

    http://www.math.wvu.edu/~gould

  3. 3.

    http://cpc.cs.qub.ac.uk/summaries/AEAX_v1_0.html

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Authors and Affiliations

  1. Department of Computer Science, National Laboratory of Scientific Computing (LNCC), Petrópolis, RJ, Brazil

    Renato Portugal

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  1. Renato Portugal
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Portugal, R. (2013). Introduction to Quantum Walks. In: Quantum Walks and Search Algorithms. Quantum Science and Technology. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6336-8_3

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  • DOI: https://doi.org/10.1007/978-1-4614-6336-8_3

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-6335-1

  • Online ISBN: 978-1-4614-6336-8

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