A quantum algorithm is exact if it always produces the correct answer, on any input. Coming up with exact quantum algorithms that substantially outperform the best classical algorithm has been a quite challenging task. In this paper, we present two new exact quantum algorithms for natural problems: - for the problem EXACT_k^n in which we have to determine whether the sequence of input bits x_1, ..., x_n contains exactly k values x_i=1; - for the problem THRESHOLD_k^n in which we have to determine if at least k of n input bits are equal to 1.
@InProceedings{ambainis_et_al:LIPIcs.TQC.2013.263, author = {Ambainis, Andris and Iraids, Janis and Smotrovs, Juris}, title = {{Exact Quantum Query Complexity of EXACT and THRESHOLD}}, booktitle = {8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)}, pages = {263--269}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-55-2}, ISSN = {1868-8969}, year = {2013}, volume = {22}, editor = {Severini, Simone and Brandao, Fernando}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2013.263}, URN = {urn:nbn:de:0030-drops-43261}, doi = {10.4230/LIPIcs.TQC.2013.263}, annote = {Keywords: Quantum query algorithms, Complexity of Boolean functions} }
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