{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:UFBPG4VSCETEYO5LEHAN5DBEYR","short_pith_number":"pith:UFBPG4VS","schema_version":"1.0","canonical_sha256":"a142f372b211264c3bab21c0de8c24c4624fa190ddb098203b22f0a6413e7454","source":{"kind":"arxiv","id":"1907.03315","version":1},"attestation_state":"computed","paper":{"title":"A Quantum Algorithm for Finding $k$-Minima","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Kohei Miyamoto, Koichi Kise, Masakazu Iwamura","submitted_at":"2019-07-07T16:36:21Z","abstract_excerpt":"We propose a new finding $k$-minima algorithm and prove that its query complexity is $\\mathcal{O}(\\sqrt{kN})$, where $N$ is the number of data indices. Though the complexity is equivalent to that of an existing method, the proposed is simpler. The main idea of the proposed algorithm is to search a good threshold that is near the $k$-th smallest data. Then, by using the generalization of amplitude amplification, all $k$ data are found out of order and the query complexity is $\\mathcal{O}(\\sqrt{kN})$. This generalization of amplitude amplification is also not well discussed and we briefly prove "},"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":"1907.03315","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2019-07-07T16:36:21Z","cross_cats_sorted":[],"title_canon_sha256":"878b97f1c401fb09b1505b8b71bcb0a4b1620369ef4dc1471d430b4c8e6de835","abstract_canon_sha256":"d49ec45402d8c5aaa71cb527f4d00a82c0f5f8564572ad52bf561314713b0371"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:16.604752Z","signature_b64":"ICHmQmlVz19EAkA+Ve9Y3FeJRu2eTeyYho7nMCDJaUOgFp30QARhHD0jX96qoiHu3lEqXc8wtSwrjhSxB/AVAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a142f372b211264c3bab21c0de8c24c4624fa190ddb098203b22f0a6413e7454","last_reissued_at":"2026-05-17T23:41:16.604113Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:16.604113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Quantum Algorithm for Finding $k$-Minima","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Kohei Miyamoto, Koichi Kise, Masakazu Iwamura","submitted_at":"2019-07-07T16:36:21Z","abstract_excerpt":"We propose a new finding $k$-minima algorithm and prove that its query complexity is $\\mathcal{O}(\\sqrt{kN})$, where $N$ is the number of data indices. Though the complexity is equivalent to that of an existing method, the proposed is simpler. The main idea of the proposed algorithm is to search a good threshold that is near the $k$-th smallest data. Then, by using the generalization of amplitude amplification, all $k$ data are found out of order and the query complexity is $\\mathcal{O}(\\sqrt{kN})$. This generalization of amplitude amplification is also not well discussed and we briefly prove "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.03315","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1907.03315","created_at":"2026-05-17T23:41:16.604212+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.03315v1","created_at":"2026-05-17T23:41:16.604212+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.03315","created_at":"2026-05-17T23:41:16.604212+00:00"},{"alias_kind":"pith_short_12","alias_value":"UFBPG4VSCETE","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_16","alias_value":"UFBPG4VSCETEYO5L","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_8","alias_value":"UFBPG4VS","created_at":"2026-05-18T12:33:30.264802+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/UFBPG4VSCETEYO5LEHAN5DBEYR","json":"https://pith.science/pith/UFBPG4VSCETEYO5LEHAN5DBEYR.json","graph_json":"https://pith.science/api/pith-number/UFBPG4VSCETEYO5LEHAN5DBEYR/graph.json","events_json":"https://pith.science/api/pith-number/UFBPG4VSCETEYO5LEHAN5DBEYR/events.json","paper":"https://pith.science/paper/UFBPG4VS"},"agent_actions":{"view_html":"https://pith.science/pith/UFBPG4VSCETEYO5LEHAN5DBEYR","download_json":"https://pith.science/pith/UFBPG4VSCETEYO5LEHAN5DBEYR.json","view_paper":"https://pith.science/paper/UFBPG4VS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.03315&json=true","fetch_graph":"https://pith.science/api/pith-number/UFBPG4VSCETEYO5LEHAN5DBEYR/graph.json","fetch_events":"https://pith.science/api/pith-number/UFBPG4VSCETEYO5LEHAN5DBEYR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UFBPG4VSCETEYO5LEHAN5DBEYR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UFBPG4VSCETEYO5LEHAN5DBEYR/action/storage_attestation","attest_author":"https://pith.science/pith/UFBPG4VSCETEYO5LEHAN5DBEYR/action/author_attestation","sign_citation":"https://pith.science/pith/UFBPG4VSCETEYO5LEHAN5DBEYR/action/citation_signature","submit_replication":"https://pith.science/pith/UFBPG4VSCETEYO5LEHAN5DBEYR/action/replication_record"}},"created_at":"2026-05-17T23:41:16.604212+00:00","updated_at":"2026-05-17T23:41:16.604212+00:00"}