{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:TEV6TYGSPHO4OGIIOHGZB2WXI5","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"206951161609554b0ec04ea63d6822395f0e4d056dd0afb3c3f9e3c51a8a2cb3","cross_cats_sorted":["cs.CC","cs.DS","stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-07-17T14:09:38Z","title_canon_sha256":"c725c8ff7b0faa124c9f815f6f821dd9881d06973fe17ce4c98f302445f541f4"},"schema_version":"1.0","source":{"id":"1807.06456","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.06456","created_at":"2026-05-17T23:41:25Z"},{"alias_kind":"arxiv_version","alias_value":"1807.06456v3","created_at":"2026-05-17T23:41:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.06456","created_at":"2026-05-17T23:41:25Z"},{"alias_kind":"pith_short_12","alias_value":"TEV6TYGSPHO4","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"TEV6TYGSPHO4OGII","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"TEV6TYGS","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:2fe806594ae35578cf6def0b0c489229634e665598a19cd5c22ea0da4c565c4c","target":"graph","created_at":"2026-05-17T23:41:25Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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 $","authors_text":"Fr\\'ed\\'eric Magniez, Yassine Hamoudi","cross_cats":["cs.CC","cs.DS","stat.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-07-17T14:09:38Z","title":"Quantum Chebyshev's Inequality and Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.06456","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:39055ad3a8634990fab761c0dc00a12baab6f5b404341c931467d33697e5b8c6","target":"record","created_at":"2026-05-17T23:41:25Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"206951161609554b0ec04ea63d6822395f0e4d056dd0afb3c3f9e3c51a8a2cb3","cross_cats_sorted":["cs.CC","cs.DS","stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-07-17T14:09:38Z","title_canon_sha256":"c725c8ff7b0faa124c9f815f6f821dd9881d06973fe17ce4c98f302445f541f4"},"schema_version":"1.0","source":{"id":"1807.06456","kind":"arxiv","version":3}},"canonical_sha256":"992be9e0d279ddc7190871cd90ead7475926d39109830f9ac5f4040a71b69546","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"992be9e0d279ddc7190871cd90ead7475926d39109830f9ac5f4040a71b69546","first_computed_at":"2026-05-17T23:41:25.056178Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:25.056178Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jVsMX1g1JjTVT1GVqi8T3oZHRHVxOZjMkknbtzzq49XLEwb6I4V9U6zOXceXfNQ/hCNXEhCUUgx89Ft6n1G9Aw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:25.057122Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.06456","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:39055ad3a8634990fab761c0dc00a12baab6f5b404341c931467d33697e5b8c6","sha256:2fe806594ae35578cf6def0b0c489229634e665598a19cd5c22ea0da4c565c4c"],"state_sha256":"cc6b283f4dafbf7946a270e38770d8b735f6568a0cbb5c0bca88df6c50d1aec1"}