{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2003:4EDSFWD3XU2JJ4HNUKL26JSMEF","short_pith_number":"pith:4EDSFWD3","schema_version":"1.0","canonical_sha256":"e10722d87bbd3494f0eda297af264c215d4f4def50e1439052f797baca9af466","source":{"kind":"arxiv","id":"quant-ph/0302002","version":1},"attestation_state":"computed","paper":{"title":"Efficient Synthesis of Linear Reversible Circuits","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"I. L. Markov, J. P. Hayes, K. N. Patel","submitted_at":"2003-02-03T00:20:03Z","abstract_excerpt":"In this paper we consider circuit synthesis for n-wire linear reversible circuits using the C-NOT gate library. These circuits are an important class of reversible circuits with applications to quantum computation. Previous algorithms, based on Gaussian elimination and LU-decomposition, yield circuits with O(n^2) gates in the worst-case. However, an information theoretic bound suggests that it may be possible to reduce this to as few as O(n^2/log n) gates.\n  We present an algorithm that is optimal up to a multiplicative constant, as well as Theta(log n) times faster than previous methods. Whil"},"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":"quant-ph/0302002","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2003-02-03T00:20:03Z","cross_cats_sorted":[],"title_canon_sha256":"caf989e79d74db17383cff14351fde972508419e4326497a17bfcb41403c7e22","abstract_canon_sha256":"8740c10d24c68f2fae3b2b80e7718460a93329479ecb6212910ea60cfdc1b9bc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:24.116882Z","signature_b64":"/EvUBWk65jqBnzfO04y20izDYx+kaZbrq24ez6O83UE2giH67i7pqpIByEcOxXzWfY34gI+4szEAKyi9PiFmCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e10722d87bbd3494f0eda297af264c215d4f4def50e1439052f797baca9af466","last_reissued_at":"2026-05-18T02:18:24.114649Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:24.114649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Efficient Synthesis of Linear Reversible Circuits","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"I. L. Markov, J. P. Hayes, K. N. Patel","submitted_at":"2003-02-03T00:20:03Z","abstract_excerpt":"In this paper we consider circuit synthesis for n-wire linear reversible circuits using the C-NOT gate library. These circuits are an important class of reversible circuits with applications to quantum computation. Previous algorithms, based on Gaussian elimination and LU-decomposition, yield circuits with O(n^2) gates in the worst-case. However, an information theoretic bound suggests that it may be possible to reduce this to as few as O(n^2/log n) gates.\n  We present an algorithm that is optimal up to a multiplicative constant, as well as Theta(log n) times faster than previous methods. Whil"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0302002","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":"quant-ph/0302002","created_at":"2026-05-18T02:18:24.114760+00:00"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0302002v1","created_at":"2026-05-18T02:18:24.114760+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0302002","created_at":"2026-05-18T02:18:24.114760+00:00"},{"alias_kind":"pith_short_12","alias_value":"4EDSFWD3XU2J","created_at":"2026-05-18T12:25:51.375804+00:00"},{"alias_kind":"pith_short_16","alias_value":"4EDSFWD3XU2JJ4HN","created_at":"2026-05-18T12:25:51.375804+00:00"},{"alias_kind":"pith_short_8","alias_value":"4EDSFWD3","created_at":"2026-05-18T12:25:51.375804+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.19717","citing_title":"Qubit Routing for (Almost) Free","ref_index":21,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4EDSFWD3XU2JJ4HNUKL26JSMEF","json":"https://pith.science/pith/4EDSFWD3XU2JJ4HNUKL26JSMEF.json","graph_json":"https://pith.science/api/pith-number/4EDSFWD3XU2JJ4HNUKL26JSMEF/graph.json","events_json":"https://pith.science/api/pith-number/4EDSFWD3XU2JJ4HNUKL26JSMEF/events.json","paper":"https://pith.science/paper/4EDSFWD3"},"agent_actions":{"view_html":"https://pith.science/pith/4EDSFWD3XU2JJ4HNUKL26JSMEF","download_json":"https://pith.science/pith/4EDSFWD3XU2JJ4HNUKL26JSMEF.json","view_paper":"https://pith.science/paper/4EDSFWD3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=quant-ph/0302002&json=true","fetch_graph":"https://pith.science/api/pith-number/4EDSFWD3XU2JJ4HNUKL26JSMEF/graph.json","fetch_events":"https://pith.science/api/pith-number/4EDSFWD3XU2JJ4HNUKL26JSMEF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4EDSFWD3XU2JJ4HNUKL26JSMEF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4EDSFWD3XU2JJ4HNUKL26JSMEF/action/storage_attestation","attest_author":"https://pith.science/pith/4EDSFWD3XU2JJ4HNUKL26JSMEF/action/author_attestation","sign_citation":"https://pith.science/pith/4EDSFWD3XU2JJ4HNUKL26JSMEF/action/citation_signature","submit_replication":"https://pith.science/pith/4EDSFWD3XU2JJ4HNUKL26JSMEF/action/replication_record"}},"created_at":"2026-05-18T02:18:24.114760+00:00","updated_at":"2026-05-18T02:18:24.114760+00:00"}