A Quantum Algorithm for Finding k-Minima
| 言語 | 英語 |
|---|---|
| 種類 | 国際会議等の予稿 |
| 著者 | Kohei Miyamoto，Masakazu Iwamura，Koichi Kise |
| 論文名 | A Quantum Algorithm for Finding k-Minima |
| 論文誌名 | Proc. 19th Asian Quantum Information Science Conference (AQIS2019) |
| ページ数 | 4 |
| 発表場所 | Seoul, Korea |
| 査読の有無 | 有 |
| 発表の種類 | ポスター発表 |
| 年月 | 2019年8月 |
| 分野 | 量子コンピューティング, 最近傍探索 |
| キー | Miyamoto2019_AQISb (id=1681) |
要約
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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