An information-theoretic analysis of Grover's algorithm
Author
Arıkan, Erdal
Date
2003-06-07Source Title
IEEE International Symposium on Information Theory, 2003 - Proceedings
Publisher
IEEE
Pages
339 - 347
Language
English
Type
Conference PaperItem Usage Stats
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Abstract
Grover discovered a quantum algorithm for identifying a target element in an unstructured search universe of N items in approximately 1r/4VN queries to a quantum oracle. For classical search using a classical oracle, the search complexity is of order N /2 queries since on average half of the items must be searched. In work preceding Grover's, Bennett et al. had shown that no quantum algorithm can solve the search problem in fewer than D(VN) queries. Thus, Grover's algorithm has optimal order of complexity. Here, we present an informationtheoretic analysis of Grover's algorithm and show that the square-root speed-up by Grover's algorithm is the best possible by any algorithm using the same quantum oracle.
Keywords
Grover's algorithmQuantum search
Entropy
Information analysis
Algorithm design and analysis
Quantum computing
Physics computing
Performance gain
Computer errors
Error correction
Time measurement
Upper bound