How to Prepare a Quantum State?

Sublinar in an the number of points is due to this idea that i can prepare quantum state. Curam stands for quantom random access memory. So when you take all the point s and you compute just once the function saying, what is the distance between this and this? It goes away faster. Of course it's way more complicated. But yes, that's the idea. And you cannot be better than log for some reason.