发现星图中的结构异常：一般方法
Finding structural anomalies in star graphs: A general approach
摘要：
我们开发了一个一般的理论，在星图上的量子行走搜索。一个星图有N条边，每条边都与一个中心顶点相连。一个图G附着在这些边中的一条上，我们想知道它附着在哪条边上。这是通过量子漫步来实现的，量子漫步是随机漫步的一种。这个遍历包含O（\sqrt{N}）步，这表示相对于经典搜索的加速，经典搜索需要O（N）步。整个图，星加G，被分成两部分，我们发现，量子加速发生，与这两部分相关的本征值在N到无穷大的极限必须是相同的。我们的理论告诉我们应该如何选择行走的初始状态，以及为了找到G，行走必须走多少步。
英文摘要：
We develop a general theory for a quantum-walk search on a star graph. A star graph has N edges each of which is attached to a central vertex. A graph G is attached to one of these edges, and we would like to find out to which edge it is attached. This is done by means of a quantum walk, a quantum version of a random walk. This walk contains O(\sqrt{N}) steps, which represents a speedup over a classical search, which would require O(N) steps. The overall graph, star plus G, is divided into two parts, and we find that for a quantum speedup to occur, the eigenvalues associated with these two parts in the N goes to infinity limit must be the same. Our theory tells us how the initial state of the walk should be chosen, and how many steps the walk must make in order to find G.
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