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We present several applications of quantum amplitude ampliication to nding claws and collisions in ordered or unordered functions. Our algorithms generalize those of Brassard, HHyer, and Tapp, and imply an O(N 3=4 log N) quantum upper bound for the element distinctness problem in the comparison complexity model (contrasting with (N log N) classical… (More)

Previous studies has shown that for a weighted undirected graph having n vertices and m edges, a minimal weight spanning tree can be found with O * √ mn calls to the weight oracle. The present note shows that a given spanning tree can be verified to be a minimal weight spanning tree with only O n calls to the weight oracle and O n + √ m log n total work.

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