{"paper":{"title":"Quantum Chebyshev's Inequality and Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DS","stat.CO"],"primary_cat":"quant-ph","authors_text":"Fr\\'ed\\'eric Magniez, Yassine Hamoudi","submitted_at":"2018-07-17T14:09:38Z","abstract_excerpt":"In this paper we provide new quantum algorithms with polynomial speed-up for a range of problems for which no such results were known, or we improve previous algorithms. First, we consider the approximation of the frequency moments $F_k$ of order $k \\geq 3$ in the multi-pass streaming model with updates (turnstile model). We design a $P$-pass quantum streaming algorithm with memory $M$ satisfying a tradeoff of $P^2 M = \\tilde{O}(n^{1-2/k})$, whereas the best classical algorithm requires $P M = \\Theta(n^{1-2/k})$. Then, we study the problem of estimating the number $m$ of edges and the number $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.06456","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}