Quantum Information Processing

, Volume 15, Issue 5, pp 1865–1896 | Cite as

Quantum walks on simplicial complexes



We construct a new type of quantum walks on simplicial complexes as a natural extension of the well-known Szegedy walk on graphs. One can numerically observe that our proposing quantum walks possess linear spreading and localization as in the case of the Grover walk on lattices. Moreover, our numerical simulation suggests that localization of our quantum walks reflects not only topological but also geometric structures. On the other hand, our proposing quantum walk contains an intrinsic problem concerning exhibition of non-trivial behavior, which is not seen in typical quantum walks such as Grover walks on graphs.


Quantum walk Simplicial complexes Tethered and movable quantum walks 



KM was partially supported by Coop with Math Program, a commissioned project by MEXT, Japan. OO was partially supported by JSPS KAKENHI Grant Number 24540208. ES was partially supported by JSPS Grant-in-Aid for Young Scientists (B) (No. 25800088). Finally, we would like to thank the referees for their careful reading of this paper and for helpful suggestions about construction and discussion of this paper.


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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.The Institute of Statistical MathematicsTachikawaJapan
  2. 2.Division of Mathematical and Physical SciencesKanazawa UniversityKanazawaJapan
  3. 3.Graduate school of Information SciencesTohoku UniversityAobaJapan

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