Generalization of Grovers Algorithm to Multiobject Search in Quantum Computing, Part II: General Unitary Transformations

There are major advantages in a newer version of Grovers quantum algorithm utilizing a general unitary transformation in the search of a single object in a large unsorted database. In this paper, we generalize this algorithm to multiobject search. We show the techniques to achieve the reduction of the problem to one on an invariant subspace of dimension just equal to two.