Abstract
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.
Supported in part by Canada's NSERC, Québec's fcar and the Canada Council.
Supported in part by the esprit Long Term Research Programme of the EU under project number 20244 (alcom-it). Research carried out while this author was at the Université de Montréal.
Supported in part by postgraduate fellowships from fcar and nserc.
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Brassard, G., HØyer, P., Tapp, A. (1998). Quantum counting. In: Larsen, K.G., Skyum, S., Winskel, G. (eds) Automata, Languages and Programming. ICALP 1998. Lecture Notes in Computer Science, vol 1443. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055105
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DOI: https://doi.org/10.1007/BFb0055105
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