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arXiv · 1707.00156

Quantum Search on Simplicial Complexes

Kaname Matsue·Osamu Ogurisu·Etsuo Segawa
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Abstract

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.

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Kaname Matsue, Osamu Ogurisu, Etsuo Segawa. 2017-12-05. Quantum Search on Simplicial Complexes. https://arxiv.org/abs/1707.00156

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