利用量子游走寻找图的结构异常
Finding structural anomalies in graphs by means of quantum walks
摘要：
我们探讨了使用量子游走图上找到结构异常，如额外的边缘或循环，在一个图的可能性。我们把注意力集中在星形图上，它的边缘就像从中心枢纽出来的辐条。如果有$N$辐条，我们表明，量子行走可以找到一个额外的边缘连接两个辐条或辐条上的循环在$O(\sqrt{N})$步骤。我们最初发现，如果所有的辐条都有循环，除了一个，行走将无法找到没有循环的辐条，但如果我们选择粒子从没有循环的顶点反射的相位，这可以被修复。因此，在某些情况下，量子游走可以用来发现图中的结构异常。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
