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Detail of Publication

Text Language English
Authors Kohei Miyamoto, Masakazu Iwamura and Koichi Kise
Title A Quantum Algorithm for Finding k-Minima
Journal Proc. 19th Asian Quantum Information Science Conference (AQIS2019)
Number of Pages 4 pages
Reviewed or not Reviewed
Presentation type Poster
Month & Year August 2019
Abstract We propose a new \textit{finding $k$-minima} algorithm and prove that the query complexity is $\mathcal{O}(\sqrt{kN})$, where $N$ is the number of data indices. The primary difficulty of the problem is that it requires to return $k$ answers. For the problem, an extension of the Amplitude Amplification (we call it \textit{searching all marked $k$ indices} algorithm) finds all $k$ data with the query complexity of $\mathcal{O}(\sqrt{kN})$ if an appropriate threshold is given. We give a quantum algorithm that searches a good threshold with the complexity of $\mathcal{O}(\sqrt{N}\log{k})$. In addition, we briefly prove the query complexity of the \textit{searching all marked $k$-indices} algorithm, which is not well discussed so far. Our algorithm can be directly adapted to distance-related problems like $k$-Nearest Neighbor Search, clustering and classification.
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