  Grover's algorithm is usually described in terms of the iteration of a
compound operator of the form $Q = - H I_{0} H I_{x_0}$. Although it is quite
straightforward to verify the algebra of the iteration, this gives little
insight into why the algorithm works. What is the significance of the compound
structure of $Q$? Why is there a minus sign? Later it was discovered that $H$
could be replaced by essentially any unitary $U$. What is the freedom involved
here? We give a description of Grover's algorithm which provides some
clarification of these questions.
