符号图上匹配的量子搜索
Quantum search of matching on signed graphs
摘要：
我们构造了一个由量子行走驱动的带符号边的量子搜索模型。这种量子行走的时间演化算子提供了一个加权邻接矩阵，该矩阵由对每个边的符号分配引起。这个符号可以被认为是所谓的边着色。作为应用，在完全图的任意边着色下，我们考虑了从完全图的边集中量子搜索着色边的问题。我们发现，这种量子行走发现一个彩色边缘的时间复杂度内的$O(n^{\frac{2-α}{2}})$概率$1-o(1)$，而相应的随机游走线图上找到它们的时间复杂度内的$O(n^{2-α})$，如果我们设置的边缘数的匹配由$O(n^α)$为$0 \le α\le 1$。
英文摘要：
We construct a quantum searching model of a signed edge driven by a quantum walk. The time evolution operator of this quantum walk provides a weighted adjacency matrix induced by the assignment of sign to each edge. This sign can be regarded as so called the edge coloring. Then as an application, under an arbitrary edge coloring which gives a matching on a complete graph, we consider a quantum search of a colored edge from the edge set of a complete graph. We show that this quantum walk finds a colored edge within the time complexity of $O(n^{\frac{2-α}{2}})$ with probability $1-o(1)$ while the corresponding random walk on the line graph finds them within the time complexity of $O(n^{2-α})$ if we set the number of the edges of the matching by $O(n^α)$ for $0 \le α\le 1$.
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。
