If I remember from when I worked on this, Grover allows searching N=2^n items with complexity O(sqrt(N)). Even if init was O(log N), this would be much smaller

If I remember from when I worked on this, Grover allows searching N=2^n items with complexity O(sqrt(N)). Even if init was O(log N), this would be much smaller than O(sqrt(N)) for large N, so can be (almost) ignored.