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Quantum Walk Based Search Algorithms

  • Conference paper
Theory and Applications of Models of Computation (TAMC 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4978))

Abstract

In this survey paper we give an intuitive treatment of the discrete time quantization of classical Markov chains. Grover search and the quantum walk based search algorithms of Ambainis, Szegedy and Magniez et al. will be stated as quantum analogues of classical search procedures. We present a rather detailed description of a somewhat simplified version of the MNRS algorithm. Finally, in the query complexity model, we show how quantum walks can be applied to the following search problems: Element Distinctness, Matrix Product Verification, Restricted Range Associativity, Triangle, and Group Commutativity.

Research supported by the European Commission IST Integrated Project Qubit Applications (QAP) 015848, and by the ANR Blanc AlgoQP grant of the French Research Ministry.

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Author information

Authors and Affiliations

  1. CNRS–LRI, Université Paris–Sud, 91405, Orsay, France

    Miklos Santha

  2. Centre for Quantum Technologies, Nat. Univ. of Singapore, Singapore, 117543

    Miklos Santha

Authors
  1. Miklos Santha
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Editor information

Manindra Agrawal Dingzhu Du Zhenhua Duan Angsheng Li

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Santha, M. (2008). Quantum Walk Based Search Algorithms. In: Agrawal, M., Du, D., Duan, Z., Li, A. (eds) Theory and Applications of Models of Computation. TAMC 2008. Lecture Notes in Computer Science, vol 4978. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79228-4_3

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  • DOI: https://doi.org/10.1007/978-3-540-79228-4_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-79227-7

  • Online ISBN: 978-3-540-79228-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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