49 research outputs found
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