用量子行走或量子行走穿越迷宫来寻找路径
Finding paths with quantum walks or quantum walking through a maze
摘要：
我们表明，它是可能的，使用量子行走找到一条路径，从一个标记的顶点到另一个。在链中连接的$M$星的特定情况下，可以以$O(M\sqrt{N})$步骤找到从第一个星到最后一个星的路径，其中$N$是每个星的辐条的数量。首先，我们提供了一个分析结果表明，通过在一个相位调制的高度叠加的初始状态，我们可以找到路径在$O(M\sqrt{N}\log M)$步骤。接下来，我们提高了这种效率，表明恢复的路径也可以进行一系列的连续搜索时，我们开始在最后一个已知的位置和搜索下一个连接的$O(\sqrt{N})$步骤导致的整体效率的$O(M\sqrt{N})$。对于这个结果，我们使用的解析解，可以得到一个环的明星的两倍链的长度。
英文摘要：
We show that it is possible to use a quantum walk to find a path from one marked vertex to another. In the specific case of $M$ stars connected in a chain, one can find the path from the first star to the last one in $O(M\sqrt{N})$ steps, where $N$ is the number of spokes of each star. First we provide an analytical result showing that by starting in a phase-modulated highly superposed initial state we can find the path in $O(M\sqrt{N}\log M)$ steps. Next, we improve this efficiency by showing that the recovery of the path can also be performed by a series of successive searches when we start at the last known position and search for the next connection in $O(\sqrt{N})$ steps leading to the overall efficiency of $O(M\sqrt{N})$. For this result we use the analytical solution that can be obtained for a ring of stars of double the length of the chain.
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。
