  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 $O(\sqrt{N})$, where $N$ is the
number of simplices with the dimension of marked simplex.
