Quantum search on structured problems

This paper shows how a basic property of unitary transformations can be used for meaningful computations. This approach immediately leads to search-type applications, where it improves the number of steps by a square-root - a simple minded search that takes N steps, can be improved to O(sqrt(N)) steps. The quantum search algorithm is one of several immediate consequences of this framework. Several novel search-related applications are presented.Comment: To be presented at the 1st NASA QCQC conference in Palm Springs, California, Feb. 17-20, '98. 12 pages, postscrip

From Schr\"odinger's Equation to the Quantum Search Algorithm

The quantum search algorithm is a technique for searching N possibilities in only sqrt(N) steps. Although the algorithm itself is widely known, not so well known is the series of steps that first led to it, these are quite different from any of the generally known forms of the algorithm. This paper describes these steps, which start by discretizing Schr\"odinger's equation. This paper also provides a self-contained introduction to the quantum search algorithm from a new perspective.Comment: Postscript file, 16 pages. This is a pedagogical article describing the invention of the quantum search algorithm. It appeared in the July, 2001 issue of American Journal of Physics (AJP

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 sqrt(N) queries. This paper shows that by replacing the selective inversions by selective phase shifts of Pi/3, the algorithm gets transformed into something similar to a classical search algorithm. Just like classical search algorithms this algorithm has a fixed point in state-space toward which it preferentially converges. In contrast, the original 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.Comment: 13 pages, 4 figure