论文标题
分析拉达量量子步行
Analysis of Lackadaisical Quantum Walks
论文作者
论文摘要
缺乏的量子步行是通过向图中的每个顶点添加一个自环获得的懒惰随机行走的量子类似物。我们在分析上证明，缺乏的量子步行可以在任何常规的局部电弧传输图上找到一个独特的标记顶点，其成功概率恒定的概率比打击时间更快。该结果证明了以前的工作中的几个猜测和数值发现，包括猜想的猜想表明，缺乏的量子步行找到了一个独特的标记顶点，在圆环，循环，约翰逊图和其他类别的顶点传播图上具有恒定的成功概率。我们的证明建立并使用了缺乏量子量子步行与任何局部弧线传输图之间的量子插值步道之间的关系。
The lackadaisical quantum walk is a quantum analogue of the lazy random walk obtained by adding a self-loop to each vertex in the graph. We analytically prove that lackadaisical quantum walks can find a unique marked vertex on any regular locally arc-transitive graph with constant success probability quadratically faster than the hitting time. This result proves several speculations and numerical findings in previous work, including the conjectures that the lackadaisical quantum walk finds a unique marked vertex with constant success probability on the torus, cycle, Johnson graphs, and other classes of vertex-transitive graphs. Our proof establishes and uses a relationship between lackadaisical quantum walks and quantum interpolated walks for any locally arc-transitive graph.
