Finding structural anomalies in graphs by means of quantum walks

Autor: Edgar Feldman, Daniel Reitzner, Hai-Woong Lee, Hongjun Zheng, Mark Hillery, Vladimír Bužek
Rok vydání: 2010
Předmět:
DOI: 10.48550/arxiv.1009.0482
Popis: We explore the possibility of using quantum walks on graphs to find structural anomalies, such as extra edges or loops, on a graph. We focus our attention on star graphs, whose edges are like spokes coming out of a central hub. If there are $N$ spokes, we show that a quantum walk can find an extra edge connecting two of the spokes or a spoke with a loop on it in $O(\sqrt{N})$ steps. We initially find that if all of the spokes have loops except one, the walk will not find the spoke without a loop, but this can be fixed if we choose the phase with which the particle is reflected from the vertex without the loop. Consequently, quantum walks can, under some circumstances, be used to find structural anomalies in graphs.
Databáze: OpenAIRE