Quantum Search on Simplicial Complexes

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.

Published in "Quantum Studies: Mathematics and Foundations"

References in corpus (11)

• Exploring Topological Phases With Quantum Walks
• Faster quantum walk algorithm for the two dimensional spatial search
• Topological phases and delocalization of quantum walks in random environments
• Quantum walk-based search and centrality
• Perfect state transfer by means of discrete-time quantum walk search algorithms on highly symmetric graphs
• Edge-state enhanced transport in a 2-dimensional quantum walk
• Quantum walk based search algorithms
• Spatial quantum search in a triangular network
• Quantum walks induced by Dirichlet random walks on infinite trees
• A Characterization of the Graphs to Induce Periodic Grover Walk
• Up and down grover walks on simplicial complexes