A fast quantum mechanical algorithm for database search
Abstract
Imagine a phone directory containing N names arranged in completely random order. In order to find someone's phone number with a 50% probability, any classical algorithm (whether deterministic or probabilistic) will need to look at a minimum of N/2 names. Quantum mechanical systems can be in a superposition of states and simultaneously examine multiple names. By properly adjusting the phases of various operations, successful computations reinforce each other while others interfere randomly. As a result, the desired phone number can be obtained in only O(sqrt(N)) steps. The algorithm is within a small constant factor of the fastest possible quantum mechanical algorithm.
Cite
@article{arxiv.quant-ph/9605043,
title = {A fast quantum mechanical algorithm for database search},
author = {Lov K. Grover},
journal= {arXiv preprint arXiv:quant-ph/9605043},
year = {2008}
}
Comments
8 pages, single postscript file. This is an updated version of a paper that was originally presented at STOC 1996. The algorithm is the same; however, the proof has been simplified by using a new interpretation termed "inversion about average." Also a few recently discovered insights have been added. Journal Ref.: Proceedings, 28th Annual ACM Symposium on the Theory of Computing (STOC), May 1996, pages 212-219