1998/05/27 by Gilles Brassard, Peter Hoyer, Alain Tapp · 2 citations
Physics and Astronomy · #quant-ph
paper · pdf · doi:10.1007/bfb0055105
published as 25th Intl. Colloquium on Automata, Languages, and Programming (ICALP), LNCS 1443, pp. 820-831, 1998 · 12 pages, LaTeX2e
arxiv created 1998/05/27 · arxiv updated 2017/01/03
We study some extensions of Grover's quantum searching algorithm. First, we generalize the Grover iteration in the light of a concept called amplitude amplification. Then, we show that the quadratic speedup obtained by the quantum searching algorithm over classical brute force can still be obtained for a large family of search problems for which good classical heuristics exist. Finally, as our main result, we combine ideas from Grover's and Shor's quantum algorithms to perform approximate counting, which can be seen as an amplitude estimation process.