www.fgks.org   »   [go: up one dir, main page]

Grover's algorithm: Difference between revisions

Content deleted Content added
Citation bot (talk | contribs)
Alter: title, template type. Add: arxiv, doi, page, issue, volume, journal. Removed parameters. Some additions/deletions were parameter name changes. | Use this bot. Report bugs. | #UCB_CommandLine
Line 1:
{{Short description|Quantum search algorithm
}}
{{Use American English|date=January 2019}}In [[quantum computing]], '''Grover's algorithm''', also known as the '''quantum search algorithm''', refers tois a [[quantum algorithm]] for unstructured search that finds [[with high probability]] the unique input to a [[black box]] function that produces a particular output value, using just <math>O(\sqrt{N})</math> evaluations of the function, where <math>N</math> is the size of the function's [[domain of a function|domain]]. It was devised by [[Lov Grover]] in 1996.<ref>{{Cite book|last=Grover|first=Lov K.|title=Proceedings of the twenty-eighth annual ACM symposium on Theory of computing - STOC '96 |chapter=A fast quantum mechanical algorithm for database search |date=1996-07-01|chapter-url=https://doi.org/10.1145/237814.237866|location=Philadelphia, Pennsylvania, USA|publisher=Association for Computing Machinery|pages=212–219|doi=10.1145/237814.237866|arxiv=quant-ph/9605043|bibcode=1996quant.ph..5043G|isbn=978-0-89791-785-8|s2cid=207198067}}</ref>
 
The analogous problem in classical computation cannot be solved in fewer than <math>O(N)</math> evaluations (because, on average, one has to check half of the domain to get a 50% chance of finding the right input). [[Charles H. Bennett (physicist)|Charles H. Bennett]], Ethan Bernstein, [[Gilles Brassard]], and [[Umesh Vazirani]] proved that any quantum solution to the problem needs to evaluate the function <math>\Omega(\sqrt{N})</math> times, so Grover's algorithm is [[Asymptotically optimal algorithm|asymptotically optimal]].<ref name=bennett_1997>{{cite journal