Upperbounds on the probability of finding marked connected components using quantum walks

03/04/2019

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by   Adam Glos, et al.

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Finding a marked vertex in a graph can be a complicated task when using quantum walks. Recent results show that for two or more adjacent marked vertices search by quantum walk with Grover's coin may have no speed-up over classical exhaustive search. In this paper, we analyze the probability of finding a marked vertex and prove several upper bounds for various sets of marked vertices. All upper bounds are given in explicit form.