Quantum Counting

@misc{citeulike:1418099, 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.}, author = {Brassard, Gilles and Hoyer, Peter and Tapp, Alain }, citeulike-article-id = {1418099}, eprint = {quant-ph/9805082}, keywords = {algorithms, quantum}, month = {May}, posted-at = {2007-06-28 02:19:35}, priority = {4}, title = {Quantum Counting}, url = {http://arxiv.org/abs/quant-ph/9805082}, year = {1998} }

TY - ELEC ID - citeulike:1418099 L3 - citeulike-article-id:1418099 TI - Quantum Counting N2 - 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. KW - algorithms KW - quantum AU - Brassard, Gilles AU - Hoyer, Peter AU - Tapp, Alain PY - 1998/May/27/ UR - http://arxiv.org/abs/quant-ph/9805082 ER -