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Quantum walk search may exhibit phenomena beyond the intuition from aconventional random walk theory. One of such examples is exceptionalconfiguration phenomenon -- it appears that it may be much harder to find anyof two or more marked vertices, that if only one of them is marked. In thispaper, we analyze the probability of finding any of marked vertices in suchscenarios and prove upper bounds for various sets of marked vertices. We applythe upper bounds to large collection of graphs and show that the quantum searchmay be slow even when taking real-world networks.

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