Recently, Ambainis gave an O(N^(2/3))-query quantum walk algorithm for

element distinctness, and more generally, an O(N^(L/(L+1)))-query algorithm for

finding L equal numbers. We point out that this algorithm actually solves a

much more general problem, the problem of finding a subset of size L that

satisfies any given property. We review the algorithm and give a considerably

simplified analysis of its query complexity. We present several applications,

including two algorithms for the problem of finding an L-clique in an N-vertex

graph. One of these algorithms uses O(N^(2L/(L+1))) edge queries, and the other

uses \tilde{O}(N^((5L-2)/(2L+4))), which is an improvement for L <= 5. The

latter algorithm generalizes a recent result of Magniez, Santha, and Szegedy,

who considered the case L=3 (finding a triangle). We also pose two open

problems regarding continuous time quantum walk and lower bounds.