  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.
