A different kind of quantum search

The quantum search algorithm consists of an alternating sequence of selective inversions and diffusion type operations, as a result of which it can find a target state in an unsorted database of size N in only √ N queries. This paper shows that by replacing the selective inversions by selective phase shifts of π3 , the algorithm gets transformed into something similar to a classical search algorithm. Just like classical search algorithms the algorithm has a fixed point in state-space toward which it preferentially converges. In contrast, the quantum search algorithm moves uniformly in a two-dimensional state space. This feature leads to robust search algorithms and also to conceptually new schemes for error correction.