Rapid sampling though quantum computing

This paper extends the quantum search class o f algorithms to the multiple solution case. It is shown that, like the basic search algorithm, these too can be represented as a rotation in an appropriately defined two dimensional vector space. This yields new applications an algorithm is presented that can create an arbitrarily specified quantum superposition on a space o f size N in o(4r-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(,f-N) steps. A classical algorithm would need f2(N) steps. This research was supported in part by funding from the U. S. Army Research Office under contract no. DAAG55-98-C-0040. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed lbr profit or commercial advantage and that copies bear this notice and the lull citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. STOC 2000 Portland Oregon USA Copyright ACM 2000 1-58113-184-4/00/5...$5.00