2017/07/01 by Matsue, Kaname, Ogurisu, Osamu, Segawa, Etsuo
#FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.1707.00156
In this paper, we propose an extension of quantum searches on graphs driven by quantum walks to simplicial complexes. To this end, we newly define a quantum walk on simplicial complex which is an alternative of preceding studies by authors. We show that the quantum search on the specific simplicial complex corresponding to the triangulation of n-dimensional unit square driven by this new simplicial quantum walk works well, namely, a marked simplex can be found with probability 1+o(1) with in a time O(√(N)), where N is the number of simplices with the dimension of marked simplex.