{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:N7JLFF2QLBKWTIELHXWL77JKSB","short_pith_number":"pith:N7JLFF2Q","schema_version":"1.0","canonical_sha256":"6fd2b29750585569a08b3decbffd2a90690000fbd85edb8e3f4e6b8cbe96b6b0","source":{"kind":"arxiv","id":"2507.10501","version":2},"attestation_state":"computed","paper":{"title":"A Rigorous Introduction to Hamiltonian Simulation via High-Order Product Formulas","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Javier Lopez-Cerezo","submitted_at":"2025-07-14T17:24:10Z","abstract_excerpt":"This work provides a rigorous and self-contained introduction to numerical methods for Hamiltonian simulation in quantum computing, with a focus on high-order product formulas for efficiently approximating the time evolution of quantum systems. Aimed at students and researchers seeking a clear mathematical treatment, the study begins with the foundational principles of quantum mechanics and quantum computation before presenting the Lie-Trotter product formula and its higher-order generalizations. In particular, Suzuki's recursive method is explored to achieve improved error scaling. Through 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":"2507.10501","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2025-07-14T17:24:10Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"a896bac35b31fc45d9b03ec8ca6e76a1099dcfdfc15a4df3c2269fb15316b3d5","abstract_canon_sha256":"07b0bbf9ebd7deacb98378f1771a559004b11d64870a17fbf151294a8ae21a03"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:37:26.834362Z","signature_b64":"wCZcVH2LhfObQbNuZ7ExfoT+yybSY9L11ZBFmaeEyxBQtV4wwLtHkkQtysZclGb7A8cllr8LlO1RnDYs5NyeAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6fd2b29750585569a08b3decbffd2a90690000fbd85edb8e3f4e6b8cbe96b6b0","last_reissued_at":"2026-07-05T11:37:26.833853Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:37:26.833853Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Rigorous Introduction to Hamiltonian Simulation via High-Order Product Formulas","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Javier Lopez-Cerezo","submitted_at":"2025-07-14T17:24:10Z","abstract_excerpt":"This work provides a rigorous and self-contained introduction to numerical methods for Hamiltonian simulation in quantum computing, with a focus on high-order product formulas for efficiently approximating the time evolution of quantum systems. Aimed at students and researchers seeking a clear mathematical treatment, the study begins with the foundational principles of quantum mechanics and quantum computation before presenting the Lie-Trotter product formula and its higher-order generalizations. In particular, Suzuki's recursive method is explored to achieve improved error scaling. Through th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.10501","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/2507.10501/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":"2507.10501","created_at":"2026-07-05T11:37:26.833902+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.10501v2","created_at":"2026-07-05T11:37:26.833902+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.10501","created_at":"2026-07-05T11:37:26.833902+00:00"},{"alias_kind":"pith_short_12","alias_value":"N7JLFF2QLBKW","created_at":"2026-07-05T11:37:26.833902+00:00"},{"alias_kind":"pith_short_16","alias_value":"N7JLFF2QLBKWTIEL","created_at":"2026-07-05T11:37:26.833902+00:00"},{"alias_kind":"pith_short_8","alias_value":"N7JLFF2Q","created_at":"2026-07-05T11:37:26.833902+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/N7JLFF2QLBKWTIELHXWL77JKSB","json":"https://pith.science/pith/N7JLFF2QLBKWTIELHXWL77JKSB.json","graph_json":"https://pith.science/api/pith-number/N7JLFF2QLBKWTIELHXWL77JKSB/graph.json","events_json":"https://pith.science/api/pith-number/N7JLFF2QLBKWTIELHXWL77JKSB/events.json","paper":"https://pith.science/paper/N7JLFF2Q"},"agent_actions":{"view_html":"https://pith.science/pith/N7JLFF2QLBKWTIELHXWL77JKSB","download_json":"https://pith.science/pith/N7JLFF2QLBKWTIELHXWL77JKSB.json","view_paper":"https://pith.science/paper/N7JLFF2Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.10501&json=true","fetch_graph":"https://pith.science/api/pith-number/N7JLFF2QLBKWTIELHXWL77JKSB/graph.json","fetch_events":"https://pith.science/api/pith-number/N7JLFF2QLBKWTIELHXWL77JKSB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/N7JLFF2QLBKWTIELHXWL77JKSB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/N7JLFF2QLBKWTIELHXWL77JKSB/action/storage_attestation","attest_author":"https://pith.science/pith/N7JLFF2QLBKWTIELHXWL77JKSB/action/author_attestation","sign_citation":"https://pith.science/pith/N7JLFF2QLBKWTIELHXWL77JKSB/action/citation_signature","submit_replication":"https://pith.science/pith/N7JLFF2QLBKWTIELHXWL77JKSB/action/replication_record"}},"created_at":"2026-07-05T11:37:26.833902+00:00","updated_at":"2026-07-05T11:37:26.833902+00:00"}