Spatial search on Sierpinski carpet using quantum walk

Shu Tamegai, Shohei Watabe, Tetsuro Nikuni

Published 2018-04-18Version 1

We investigate a spatial search problem on a fractal lattice using the quantum walk. A recent study made a conjecture that the behavior of the search on a fractal lattice is determined by the spectral dimension not by the fractal dimension. However, this conjecture has so far only been discussed in connection with two- and three-dimensional Sierpinski gaskets. We tackle this problem for the two-dimensional Sierpinski carpet, and show that our simulation result supports the conjecture.