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 a 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 on \(n+1\) vertices we consider a quantum search of a colored edge from the edge set of the complete graph. We show that this quantum walk finds a colored edge within the time complexity of \(O(n^{\frac{2-\alpha }{2}})\) with probability \(1-o(1)\), while the corresponding random walk on the line graph finds them within the time complexity of \(O(n^{2-\alpha })\) if we set the number of the edges of the matching by \(t=O(n^{\alpha })\) for \(0 \le \alpha \le 1\) red with \(t \le \frac{n}{2}\).

我们构造了一个由量子游动驱动的有符号边的量子搜索模型。这个量子游走的时间演化算子提供了一个加权邻接矩阵，该矩阵是通过将符号分配给每个边而产生的。该标志可以被认为是所谓的边缘着色。然后作为一个应用程序，在任意边缘着色下，该着色在\（n + 1 \）个顶点上的完整图上给出匹配，我们考虑从完整图的边缘集对彩色边缘进行量子搜索。我们证明了这种量子行走在概率为\（1-o（1）\）的\（O（n ^ {\ frac {2- \ alpha} {2}}）\）的时间复杂度内找到了一个有色边，而线图上的相应随机游动在\（O（n ^ {2- \ alpha}）\）的时间复杂度内找到它们如果我们设置匹配的边缘的数量由\（T = O（N ^ {\阿尔法}）\）为\（0 \文件\阿尔法\文件1 \）红色\（T \文件\压裂{ n} {2} \）。