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arXiv:quant-ph/9807078

A Modification of Grover's Algorithm as a Fast Database Search

Douglas Alan Ross

Published Jul 28, 1998• 3 citations
arXivHTMLPDF

Abstract

A modification of Grover's algorithm is proposed, which can be used directly as a fast database search. An explicit two q-bit example is displayed in detail. We discuss the case where the database has multiple entries corresponding to the same target value.
DOI
10.48550/arxiv.quant-ph/9807078

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Grover's algorithm is normally presented as a method of searching a database, however it would be more accurately described as a method of identifying elements of an interval of the integers which satisfy some logical clause - an example might be identifying binary strings which correspond to the solutions of a Sudoku problem. In this paper we present the first method of performing a true database search using Grover's search algorithm, by first creating a mapping from a set of indices in the range 0:2^n-1 to a set of database elements, then applying the clause to these elements. We then demonstrate the feasibility of an attack against the Diffie-Hellman cryptosystem based on a Grover's search of a database of candidate solutions generated via the number field sieve algorithm.
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Grover's quantum search algorithm is considered as one of the milestone in the field of quantum computing. The algorithm can search for a single match in a database with NNN records in O(N)O(\sqrt{N})O(N​) assuming that the item must exist in the database with quadratic speedup over the best known classical algorithm. This review paper discusses the performance of Grover's algorithm in case of multiple matches where the problem is expected to be easier. Unfortunately, we will find that the algorithm will fail for M>3N/4M>3N/4M>3N/4, where MMM is the number of matches in the list.