Quantum Algorithm for k-distinctness with Prior Knowledge on the Input

Details Quantum Algorithm for k-distinctness with Prior Knowledge on the Input Quantum Algorithm for k-distinctness with Prior Knowledge on the Input

2011-08-15

arxiv.org/abs/1108.3022v1

Physics

Quantum Physics

21 pages

Scientific paper

It is known that the dual of the general adversary bound can be used to build quantum query algorithms with optimal complexity. Despite this result, not many quantum algorithms have been designed this way. This paper shows another example of such algorithm. We use the learning graph technique from arXiv:1105.4024 to give a quantum algorithm for $k$-distinctness problem that runs in $o(n^{3/4})$ queries, for a fixed $k$, given some prior knowledge on the structure of the input. The best known quantum algorithm for the unconditional problem uses $O(n^{k/(k+1)})$ queries.

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