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

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

Quantum computers can search rapidly by using almost any transformation

A quantum computer has a clear advantage over a classical computer for exhaustive search. The quantum mechanical algorithm for exhaustive search was originally derived by using subtle properties of a particular quantum mechanical operation called the Walsh-Hadamard (W-H) transform. This paper shows that this algorithm can be implemented by replacing the W-H transform by almost any quantum mechanical operation. This leads to several new applications where it improves the number of steps by a square-root. It also broadens the scope for implementation since it demonstrates quantum mechanical algorithms that can readily adapt to available technology.Comment: This paper is an adapted version of quant-ph/9711043. It has been modified to make it more readable for physicists. 9 pages, postscrip