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A Grover-based quantum search of optimal order for an unknown number of marked elements

Christof Zalka
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Abstract

We want to find a marked element out of a black box containing N elements. When the number of marked elements is known this can be done elegantly with Grover's algorithm, a variant of which even gives a correct result with certainty. On the other hand, when the number of marked elements is not known the problem becomes more difficult. For every prescribed success probability I give an algorithm consisting of several runs of Grover's algorithm that matches a recent bound by Buhrman and de Wolf on the order of the number of queries to the black box. The improvement in the order over a previously known algorithm is small and the number of queries can clearly still be reduced by a constant factor.

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Christof Zalka. 1999-02-12. A Grover-based quantum search of optimal order for an unknown number of marked elements. https://arxiv.org/abs/quant-ph/9902049

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