TY - JOUR
T1 - Quantum walks on simplicial complexes
AU - Matsue, Kaname
AU - Ogurisu, Osamu
AU - Segawa, Etsuo
N1 - Funding Information:
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.
Publisher Copyright:
© 2016, Springer Science+Business Media New York.
PY - 2016/5/1
Y1 - 2016/5/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84957609309&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84957609309&partnerID=8YFLogxK
U2 - 10.1007/s11128-016-1247-6
DO - 10.1007/s11128-016-1247-6
M3 - Article
AN - SCOPUS:84957609309
SN - 1570-0755
VL - 15
SP - 1865
EP - 1896
JO - Quantum Information Processing
JF - Quantum Information Processing
IS - 5
ER -