How significant are the known collision and element distinctness quantum algorithms

Quantum search is a technique for searching N possibilities for a desired target in O(rootN) steps. It has been applied in the design of quantum algorithms for several structured problems. Many of these algorithms require significant amount of quantum hardware. In this paper we propose the criterion that an algorithm which requires O(S) hardware should be considered significant if it produces a speedup of better than O(rootS) over a simple quantum search algorithm. This is because a speedup of O(rootS) can be trivially obtained by dividing the search space into S separate parts and handing the problem to S independent processors that do a quantum search (in this paper we drop all logarithmic factors when discussing time/space complexity). Known algorithms for collision and element distinctness exactly saturate the criterion.