Quantum walks on graphs

D. Aharonov, A. Ambainis, Julia Kempe, U. Vazirani

Research output: Contribution to journalConference article

Abstract

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.

Original languageEnglish (US)
Pages (from-to)50-59
Number of pages10
JournalConference Proceedings of the Annual ACM Symposium on Theory of Computing
StatePublished - Jan 1 2001
Event33rd Annual ACM Symposium on Theory of Computing - Creta, Greece
Duration: Jul 6 2001Jul 8 2001

ASJC Scopus subject areas

  • Software

Cite this

Aharonov, D., Ambainis, A., Kempe, J., & Vazirani, U. (2001). Quantum walks on graphs. Conference Proceedings of the Annual ACM Symposium on Theory of Computing, 50-59.

Quantum walks on graphs. / Aharonov, D.; Ambainis, A.; Kempe, Julia; Vazirani, U.

In: Conference Proceedings of the Annual ACM Symposium on Theory of Computing, 01.01.2001, p. 50-59.

Research output: Contribution to journalConference article

Aharonov, D, Ambainis, A, Kempe, J & Vazirani, U 2001, 'Quantum walks on graphs', Conference Proceedings of the Annual ACM Symposium on Theory of Computing, pp. 50-59.
Aharonov D, Ambainis A, Kempe J, Vazirani U. Quantum walks on graphs. Conference Proceedings of the Annual ACM Symposium on Theory of Computing. 2001 Jan 1;50-59.
Aharonov, D. ; Ambainis, A. ; Kempe, Julia ; Vazirani, U. / Quantum walks on graphs. In: Conference Proceedings of the Annual ACM Symposium on Theory of Computing. 2001 ; pp. 50-59.
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