{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:2YLB7VZ67S53JLEY3BGQNFR65I","short_pith_number":"pith:2YLB7VZ6","schema_version":"1.0","canonical_sha256":"d6161fd73efcbbb4ac98d84d06963eea043e1266c9f5d35b11ec9ba5ac3b67be","source":{"kind":"arxiv","id":"2407.07685","version":2},"attestation_state":"computed","paper":{"title":"Quantum and classical algorithms for nonlinear unitary dynamics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Nathan Wiebe, Noah Br\\\"ustle","submitted_at":"2024-07-10T14:08:58Z","abstract_excerpt":"Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending this to a nonlinear problem has proven challenging, with exponential lower bounds having been demonstrated for the time scaling. We provide a quantum algorithm matching these bounds. Specifically, we find that for a non-linear differential equation of the form $\\frac{d|u\\rangle}{dt} = A|u\\rangle + B|u\\rangle^{\\otimes2}$ for evolution of time $T$, error toleranc"},"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":"2407.07685","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2024-07-10T14:08:58Z","cross_cats_sorted":[],"title_canon_sha256":"c8ce97fccb341d21ab267be33b1a690c6a48fff95bacc8f57c705592e52085ae","abstract_canon_sha256":"b8f9258ca4c8eb2ed0865b67a2db9b15c3c2997bf4d2d467d265c13181165ca8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:02:11.720583Z","signature_b64":"7TDnepIQZJyf4kJIjAQlVRAhJ0MHd6zkTZ1jLjuaZfJmnzTyNl9/6LowSn+jj2MMnw7/88XyrMiRbpjCN+KwCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d6161fd73efcbbb4ac98d84d06963eea043e1266c9f5d35b11ec9ba5ac3b67be","last_reissued_at":"2026-07-05T11:02:11.720120Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:02:11.720120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantum and classical algorithms for nonlinear unitary dynamics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Nathan Wiebe, Noah Br\\\"ustle","submitted_at":"2024-07-10T14:08:58Z","abstract_excerpt":"Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending this to a nonlinear problem has proven challenging, with exponential lower bounds having been demonstrated for the time scaling. We provide a quantum algorithm matching these bounds. Specifically, we find that for a non-linear differential equation of the form $\\frac{d|u\\rangle}{dt} = A|u\\rangle + B|u\\rangle^{\\otimes2}$ for evolution of time $T$, error toleranc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.07685","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/2407.07685/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":"2407.07685","created_at":"2026-07-05T11:02:11.720175+00:00"},{"alias_kind":"arxiv_version","alias_value":"2407.07685v2","created_at":"2026-07-05T11:02:11.720175+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.07685","created_at":"2026-07-05T11:02:11.720175+00:00"},{"alias_kind":"pith_short_12","alias_value":"2YLB7VZ67S53","created_at":"2026-07-05T11:02:11.720175+00:00"},{"alias_kind":"pith_short_16","alias_value":"2YLB7VZ67S53JLEY","created_at":"2026-07-05T11:02:11.720175+00:00"},{"alias_kind":"pith_short_8","alias_value":"2YLB7VZ6","created_at":"2026-07-05T11:02:11.720175+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.17170","citing_title":"Simulating Time Dependent and Nonlinear Classical Oscillators through Nonlinear Schr\\\"odingerization","ref_index":8,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2YLB7VZ67S53JLEY3BGQNFR65I","json":"https://pith.science/pith/2YLB7VZ67S53JLEY3BGQNFR65I.json","graph_json":"https://pith.science/api/pith-number/2YLB7VZ67S53JLEY3BGQNFR65I/graph.json","events_json":"https://pith.science/api/pith-number/2YLB7VZ67S53JLEY3BGQNFR65I/events.json","paper":"https://pith.science/paper/2YLB7VZ6"},"agent_actions":{"view_html":"https://pith.science/pith/2YLB7VZ67S53JLEY3BGQNFR65I","download_json":"https://pith.science/pith/2YLB7VZ67S53JLEY3BGQNFR65I.json","view_paper":"https://pith.science/paper/2YLB7VZ6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2407.07685&json=true","fetch_graph":"https://pith.science/api/pith-number/2YLB7VZ67S53JLEY3BGQNFR65I/graph.json","fetch_events":"https://pith.science/api/pith-number/2YLB7VZ67S53JLEY3BGQNFR65I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2YLB7VZ67S53JLEY3BGQNFR65I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2YLB7VZ67S53JLEY3BGQNFR65I/action/storage_attestation","attest_author":"https://pith.science/pith/2YLB7VZ67S53JLEY3BGQNFR65I/action/author_attestation","sign_citation":"https://pith.science/pith/2YLB7VZ67S53JLEY3BGQNFR65I/action/citation_signature","submit_replication":"https://pith.science/pith/2YLB7VZ67S53JLEY3BGQNFR65I/action/replication_record"}},"created_at":"2026-07-05T11:02:11.720175+00:00","updated_at":"2026-07-05T11:02:11.720175+00:00"}