  We explore quantum search from the geometric viewpoint of a complex
projective space $CP$, a space of rays. First, we show that the optimal quantum
search can be geometrically identified with the shortest path along the
geodesic joining a target state, an element of the computational basis, and
such an initial state as overlaps equally, up to phases, with all the elements
of the computational basis. Second, we calculate the entanglement through the
algorithm for any number of qubits $n$ as the minimum Fubini-Study distance to
the submanifold formed by separable states in Segre embedding, and find that
entanglement is used almost maximally for large $n$. The computational time
seems to be optimized by the dynamics as the geodesic, running across entangled
states away from the submanifold of separable states, rather than the amount of
entanglement itself.
