{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:CQVRYISCZUHIEFH72I3BGH3MWX","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":"51da373f3c366e7f959809a496fdd89ecbf60159a041db40293ce1cbf2ff7753","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-09-23T17:27:24Z","title_canon_sha256":"54c87c71e4f98c80d72697a1fcf412cfaf3db16b25319d799262a36898d56465"},"schema_version":"1.0","source":{"id":"1109.5135","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5135","created_at":"2026-05-18T03:46:31Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5135v3","created_at":"2026-05-18T03:46:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5135","created_at":"2026-05-18T03:46:31Z"},{"alias_kind":"pith_short_12","alias_value":"CQVRYISCZUHI","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CQVRYISCZUHIEFH7","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CQVRYISC","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:c4ec3350ebc68bdf6e06321765687952f45201bc9c7a142ff31606d42f81026c","target":"graph","created_at":"2026-05-18T03:46:31Z","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":"Let $H$ be a fixed $k$-vertex graph with $m$ edges and minimum degree $d >0$. We use the learning graph framework of Belovs to show that the bounded-error quantum query complexity of determining if an $n$-vertex graph contains $H$ as a subgraph is $O(n^{2-2/k-t})$, where $ t = \\max{\\frac{k^2- 2(m+1)}{k(k+1)(m+1)}, \\frac{2k - d - 3}{k(d+1)(m-d+2)}}$. The previous best algorithm of Magniez et al. had complexity $\\widetilde O(n^{2-2/k})$.","authors_text":"Frederic Magniez, Miklos Santha, Troy Lee","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-09-23T17:27:24Z","title":"A learning graph based quantum query algorithm for finding constant-size subgraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5135","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:adde8d860c0954c3ce02f010e1ffd6e64a4e07fb141ce31cc483d1e607fc0a12","target":"record","created_at":"2026-05-18T03:46:31Z","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":"51da373f3c366e7f959809a496fdd89ecbf60159a041db40293ce1cbf2ff7753","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-09-23T17:27:24Z","title_canon_sha256":"54c87c71e4f98c80d72697a1fcf412cfaf3db16b25319d799262a36898d56465"},"schema_version":"1.0","source":{"id":"1109.5135","kind":"arxiv","version":3}},"canonical_sha256":"142b1c2242cd0e8214ffd236131f6cb5e0cefa6d1967a517f1d391524a21360c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"142b1c2242cd0e8214ffd236131f6cb5e0cefa6d1967a517f1d391524a21360c","first_computed_at":"2026-05-18T03:46:31.671624Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:31.671624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lrAWIi5KzDEQp+zh3gDicOkIXz0HF9oC7e+R0qry2McRZM6rNz0nUj4YQl77NvNVTxHI5LApY82Bjl6tvGc/Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:31.672876Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.5135","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:adde8d860c0954c3ce02f010e1ffd6e64a4e07fb141ce31cc483d1e607fc0a12","sha256:c4ec3350ebc68bdf6e06321765687952f45201bc9c7a142ff31606d42f81026c"],"state_sha256":"5b8a7039e3346ebac95d0a42fb2e781880767b4a32dc2b17a2ee31268291ee5b"}