Quantum Walks On Graphs

  • Aharonov D
  • Ambainis A
  • Kempe J
 et al. 
  • 121


    Mendeley users who have this article in their library.
  • 316


    Citations of this article.


We set the ground for a theory of quantum walks on graphs- the generalization of random walks on finite graphs to the quantum world. Such quantum walks do not converge to any stationary distribution, as they are unitary and reversible. However, by suitably relaxing the definition, we can obtain a measure of how fast the quantum walk spreads or how confined the quantum walk stays in a small neighborhood. We give definitions of mixing time, filling time, dispersion time. We show that in all these measures, the quantum walk on the cycle is almost quadratically faster then its classical correspondent. On the other hand, we give a lower bound on the possible speed up by quantum walks for general graphs, showing that quantum walks can be at most polynomially faster than their classical counterparts.

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document


  • Dorit Aharonov

  • Andris Ambainis

  • Julia Kempe

  • Umesh Vazirani

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free