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We investigate the behavior of coherence in scattering quantum walk search oncomplete graph under the condition that the total number of vertices of thegraph is greatly larger than the marked number of vertices we are searching, $N\gg v$. We find that the consumption of coherence represents the increase ofthe success probability for the searching,also the consumption of coherence isrelated to the efficiency of the algorithm represented by oracle queries.If nocoherence is consumed, the efficiency of the algorithm will be the same as theclassical blind search, implying that coherence is responsible for the speed upin this quantum algorithm over its classical counterpart. In case the initialstate is incoherent, still $N \gg v$ is assumed,the probability of success forsearching will not change with time, indicating that this quantum searchalgorithm loses its power.We then conclude that the coherence plays anessential role and is responsible for the speed up in this quantum algorithm.

Coherence as resource in scattering quantum walk search on complete graph