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Abstract: We consider the problem of search of an unstructured list for a markedelement, when one is given advice as to where this element might be located, inthe form of a probability distribution. The goal is to minimise the expectednumber of queries to the list made to find the marked element, with respect tothis distribution. We present a quantum algorithm which solves this problemusing an optimal number of queries, up to a constant factor. For somedistributions on the input, such as certain power law distributions, thealgorithm can achieve exponential speed-ups over the best possible classicalalgorithm. We also give an efficient quantum algorithm for a variant of thistask where the distribution is not known in advance, but must be queried at anadditional cost. The algorithms are based on the use of Grover-s quantum searchalgorithm and amplitude amplification as subroutines.

Author: Ashley Montanaro

Source: https://arxiv.org/

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