We present the quantum algorithm for the Longest Trail Problem. The problem is to search the longest edge-simple path for a graph with $n$ vertexes and $m$ edges. Here edge-simple means no edge occurs in the path twice, but vertexes can occur several times. The running time of our algorithm is $O^*(1.728^m)$.

翻译：我们为最长期的轨迹问题展示量子算法。 问题在于要搜索最长的边缘简单路径, 以使用 $n 的顶端和 $ $ 的边缘。 这里的边缘简单意味着路径不会出现两次边缘, 但顶端可以发生几次。 我们的算法运行时间是 $@( 1. 728) $ 。