Rapid sampling through quantum computing

The quantum search algorithm can be synthesized with almost any unitary operation, provided there is only a single solution. This paper extends the generalized quantum search algorithm to the situation with multiple solutions; this solves an open problem in quantum computing. It is shown that, like the basic generalized search algorithm, this too can be represented as a rotation in a two dimensional complex Hilbert space. This yields new applications - an algorithm is presented that can create an arbitrarily specified superposition on a space of size N in O(sqrt(N)) steps. By making a measurement on this superposition, it is possible to obtain a sample according to an arbitrarily specified classical probability distribution in O(sqrt(N)) steps. A classical algorithm would need at least O(N) steps