{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:P4UVKHMJ5SME7NZJ3X4HB6UD4I","short_pith_number":"pith:P4UVKHMJ","schema_version":"1.0","canonical_sha256":"7f29551d89ec984fb729ddf870fa83e23f0e1af761d018d4229bc902c47f8814","source":{"kind":"arxiv","id":"1706.07884","version":2},"attestation_state":"computed","paper":{"title":"Factoring with n+2 clean qubits and n-1 dirty qubits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Craig Gidney","submitted_at":"2017-06-23T23:36:09Z","abstract_excerpt":"We present reversible classical circuits for performing various arithmetic operations aided by dirty ancillae (i.e. extra qubits in an unknown state that must be restored before the circuit ends). We improve the number of clean qubits needed to factor an n-bit number with Shor's algorithm from 1.5n+O(1) to n+2, assisted by n-1 dirty qubits, without increasing the asymptotic size or depth of the circuit."},"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":"1706.07884","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-06-23T23:36:09Z","cross_cats_sorted":[],"title_canon_sha256":"5301518f5c3d8449b9bd74d4c6b6124e057988eb3ebc4053b409637b51a6b2f2","abstract_canon_sha256":"49b7c043bc447b6f0fe464472ff1f87292ddd010e9a3df7d135b4f218d590310"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:34.294528Z","signature_b64":"cVRQrEBhSpJ1iue8hdgQSyHSSZu9NhAlpAECccFDwnon7VZNhzdIkzr9jd1Y11/zG0dLqy9Kp2h7SHds4FBgDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f29551d89ec984fb729ddf870fa83e23f0e1af761d018d4229bc902c47f8814","last_reissued_at":"2026-05-18T00:25:34.293778Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:34.293778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Factoring with n+2 clean qubits and n-1 dirty qubits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Craig Gidney","submitted_at":"2017-06-23T23:36:09Z","abstract_excerpt":"We present reversible classical circuits for performing various arithmetic operations aided by dirty ancillae (i.e. extra qubits in an unknown state that must be restored before the circuit ends). We improve the number of clean qubits needed to factor an n-bit number with Shor's algorithm from 1.5n+O(1) to n+2, assisted by n-1 dirty qubits, without increasing the asymptotic size or depth of the circuit."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07884","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":""},"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":"1706.07884","created_at":"2026-05-18T00:25:34.293892+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.07884v2","created_at":"2026-05-18T00:25:34.293892+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.07884","created_at":"2026-05-18T00:25:34.293892+00:00"},{"alias_kind":"pith_short_12","alias_value":"P4UVKHMJ5SME","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_16","alias_value":"P4UVKHMJ5SME7NZJ","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_8","alias_value":"P4UVKHMJ","created_at":"2026-05-18T12:31:37.085036+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2312.10054","citing_title":"Efficient Quantum Oracle for Solving Bilinear Diophantine Equations on Digital Quantum Computers","ref_index":15,"is_internal_anchor":true},{"citing_arxiv_id":"2409.17595","citing_title":"Magic state cultivation: growing T states as cheap as CNOT gates","ref_index":22,"is_internal_anchor":false},{"citing_arxiv_id":"2604.12560","citing_title":"Design automation and space-time reduction for surface-code logical operations using a SAT-based EDA kernel compatible with general encodings","ref_index":10,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/P4UVKHMJ5SME7NZJ3X4HB6UD4I","json":"https://pith.science/pith/P4UVKHMJ5SME7NZJ3X4HB6UD4I.json","graph_json":"https://pith.science/api/pith-number/P4UVKHMJ5SME7NZJ3X4HB6UD4I/graph.json","events_json":"https://pith.science/api/pith-number/P4UVKHMJ5SME7NZJ3X4HB6UD4I/events.json","paper":"https://pith.science/paper/P4UVKHMJ"},"agent_actions":{"view_html":"https://pith.science/pith/P4UVKHMJ5SME7NZJ3X4HB6UD4I","download_json":"https://pith.science/pith/P4UVKHMJ5SME7NZJ3X4HB6UD4I.json","view_paper":"https://pith.science/paper/P4UVKHMJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.07884&json=true","fetch_graph":"https://pith.science/api/pith-number/P4UVKHMJ5SME7NZJ3X4HB6UD4I/graph.json","fetch_events":"https://pith.science/api/pith-number/P4UVKHMJ5SME7NZJ3X4HB6UD4I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P4UVKHMJ5SME7NZJ3X4HB6UD4I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P4UVKHMJ5SME7NZJ3X4HB6UD4I/action/storage_attestation","attest_author":"https://pith.science/pith/P4UVKHMJ5SME7NZJ3X4HB6UD4I/action/author_attestation","sign_citation":"https://pith.science/pith/P4UVKHMJ5SME7NZJ3X4HB6UD4I/action/citation_signature","submit_replication":"https://pith.science/pith/P4UVKHMJ5SME7NZJ3X4HB6UD4I/action/replication_record"}},"created_at":"2026-05-18T00:25:34.293892+00:00","updated_at":"2026-05-18T00:25:34.293892+00:00"}