{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:AD6X5VMHWQN6Q3LCC2KOYEVCNY","short_pith_number":"pith:AD6X5VMH","schema_version":"1.0","canonical_sha256":"00fd7ed587b41be86d621694ec12a26e0c7d5b694ffb185b227a9d3500f75c3f","source":{"kind":"arxiv","id":"1911.01973","version":2},"attestation_state":"computed","paper":{"title":"On the Quantum Complexity of Closest Pair and Related Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Chunhao Wang, Han-Hsuan Lin, Nai-Hui Chia, Ruizhe Zhang, Scott Aaronson","submitted_at":"2019-11-05T18:01:23Z","abstract_excerpt":"The closest pair problem is a fundamental problem of computational geometry: given a set of $n$ points in a $d$-dimensional space, find a pair with the smallest distance. A classical algorithm taught in introductory courses solves this problem in $O(n\\log n)$ time in constant dimensions (i.e., when $d=O(1)$). This paper asks and answers the question of the problem's quantum time complexity. Specifically, we give an $\\tilde{O}(n^{2/3})$ algorithm in constant dimensions, which is optimal up to a polylogarithmic factor by the lower bound on the quantum query complexity of element distinctness. Th"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1911.01973","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2019-11-05T18:01:23Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"eaee2ad63c16feca05a6a31dbc1685c7b5b6c8b8fcb4c8000dfa6c71950b42d4","abstract_canon_sha256":"99efbf8939c37d83da949c08129d04d30273e343f0f3cabb4b7a5b97e868f531"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:25:11.642512Z","signature_b64":"arUP3q7qEczVvcSDVU99BUQpa8fU76qFizqSRdKyZ/OU0T+cQTlfmBvOeSrNKdtRny43ggGsTZy1wForEULgBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00fd7ed587b41be86d621694ec12a26e0c7d5b694ffb185b227a9d3500f75c3f","last_reissued_at":"2026-07-05T01:25:11.641945Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:25:11.641945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Quantum Complexity of Closest Pair and Related Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Chunhao Wang, Han-Hsuan Lin, Nai-Hui Chia, Ruizhe Zhang, Scott Aaronson","submitted_at":"2019-11-05T18:01:23Z","abstract_excerpt":"The closest pair problem is a fundamental problem of computational geometry: given a set of $n$ points in a $d$-dimensional space, find a pair with the smallest distance. A classical algorithm taught in introductory courses solves this problem in $O(n\\log n)$ time in constant dimensions (i.e., when $d=O(1)$). This paper asks and answers the question of the problem's quantum time complexity. Specifically, we give an $\\tilde{O}(n^{2/3})$ algorithm in constant dimensions, which is optimal up to a polylogarithmic factor by the lower bound on the quantum query complexity of element distinctness. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.01973","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1911.01973/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1911.01973","created_at":"2026-07-05T01:25:11.642019+00:00"},{"alias_kind":"arxiv_version","alias_value":"1911.01973v2","created_at":"2026-07-05T01:25:11.642019+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.01973","created_at":"2026-07-05T01:25:11.642019+00:00"},{"alias_kind":"pith_short_12","alias_value":"AD6X5VMHWQN6","created_at":"2026-07-05T01:25:11.642019+00:00"},{"alias_kind":"pith_short_16","alias_value":"AD6X5VMHWQN6Q3LC","created_at":"2026-07-05T01:25:11.642019+00:00"},{"alias_kind":"pith_short_8","alias_value":"AD6X5VMH","created_at":"2026-07-05T01:25:11.642019+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AD6X5VMHWQN6Q3LCC2KOYEVCNY","json":"https://pith.science/pith/AD6X5VMHWQN6Q3LCC2KOYEVCNY.json","graph_json":"https://pith.science/api/pith-number/AD6X5VMHWQN6Q3LCC2KOYEVCNY/graph.json","events_json":"https://pith.science/api/pith-number/AD6X5VMHWQN6Q3LCC2KOYEVCNY/events.json","paper":"https://pith.science/paper/AD6X5VMH"},"agent_actions":{"view_html":"https://pith.science/pith/AD6X5VMHWQN6Q3LCC2KOYEVCNY","download_json":"https://pith.science/pith/AD6X5VMHWQN6Q3LCC2KOYEVCNY.json","view_paper":"https://pith.science/paper/AD6X5VMH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1911.01973&json=true","fetch_graph":"https://pith.science/api/pith-number/AD6X5VMHWQN6Q3LCC2KOYEVCNY/graph.json","fetch_events":"https://pith.science/api/pith-number/AD6X5VMHWQN6Q3LCC2KOYEVCNY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AD6X5VMHWQN6Q3LCC2KOYEVCNY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AD6X5VMHWQN6Q3LCC2KOYEVCNY/action/storage_attestation","attest_author":"https://pith.science/pith/AD6X5VMHWQN6Q3LCC2KOYEVCNY/action/author_attestation","sign_citation":"https://pith.science/pith/AD6X5VMHWQN6Q3LCC2KOYEVCNY/action/citation_signature","submit_replication":"https://pith.science/pith/AD6X5VMHWQN6Q3LCC2KOYEVCNY/action/replication_record"}},"created_at":"2026-07-05T01:25:11.642019+00:00","updated_at":"2026-07-05T01:25:11.642019+00:00"}