  It has been shown in recent years that quantum information has a topological
nature (\cite{AC}, \cite{Co}, \cite{Co2}). In \cite{V}, Vicary undergoes the
study of quantum algorithms using this new topological approach. The advantage
of this new formalism is that it allows new proofs of correctness of the
algorithms such as Deutsch-Jozsa, hidden subgroup and single-shot Grover
algorithms. It also provide more clear insight to the generalizations of these
algorithms. In this paper, we consider (multi-step) Grover algorithm from this
new perspective.
