Quantum walks on simplicial complexes
Mathematical Physics
2015-08-05 v2 Geometric Topology
math.MP
Quantum Physics
Abstract
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 reflect not only topological but also geometric structures. On the other hand, our proposing quantum walk contains an intrinsic problem concerning exhibition of nontrivial behavior, which is not seen in typical quantum walks such as Grover walks on graphs.
Cite
@article{arxiv.1507.01194,
title = {Quantum walks on simplicial complexes},
author = {Kaname Matsue and Osamu Ogurisu and Etsuo Segawa},
journal= {arXiv preprint arXiv:1507.01194},
year = {2015}
}
Comments
36 pages. We found a mistake in Lemma 2.6 in the first version. In the current version we modify it