Introduction to Quantum Walks

  • Renato Portugal
Part of the Quantum Science and Technology book series (QST)


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.


Quantum Walk Element Distinctness Problem Discrete-time Walk Classical Random Walk CO-OPERATION IN 
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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Renato Portugal
    • 1
  1. 1.Department of Computer ScienceNational Laboratory of Scientific Computing (LNCC)PetrópolisBrazil

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