論文の言語 英語 Kohei Miyamoto, Masakazu Iwamura and Koichi Kise A Quantum Algorithm for Finding k-Minima Proc. 19th Asian Quantum Information Science Conference (AQIS2019) 有 ポスター発表 2019年8月 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.
• 注記
Full version of the paper is available at https://arxiv.org/abs/1907.03315
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• BibTeX用エントリー
@InProceedings{Miyamoto2019,
author =	{Kohei Miyamoto and Masakazu Iwamura and Koichi Kise},
title =	{A Quantum Algorithm for Finding k-Minima},
booktitle =	{Proc. 19th Asian Quantum Information Science Conference (AQIS2019)},
year =	2019,
month =	aug
}