{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:WF25RJATKECOXASYRITA6VQSYF","short_pith_number":"pith:WF25RJAT","schema_version":"1.0","canonical_sha256":"b175d8a4135104eb82588a260f5612c17604b552f4850ee0596dc33c8b049ab9","source":{"kind":"arxiv","id":"1706.03419","version":1},"attestation_state":"computed","paper":{"title":"Improved reversible and quantum circuits for Karatsuba-based integer multiplication","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.ET"],"primary_cat":"quant-ph","authors_text":"Alex Parent, Martin Roetteler, Michele Mosca","submitted_at":"2017-06-11T22:54:49Z","abstract_excerpt":"Integer arithmetic is the underpinning of many quantum algorithms, with applications ranging from Shor's algorithm over HHL for matrix inversion to Hamiltonian simulation algorithms. A basic objective is to keep the required resources to implement arithmetic as low as possible. This applies in particular to the number of qubits required in the implementation as for the foreseeable future this number is expected to be small. We present a reversible circuit for integer multiplication that is inspired by Karatsuba's recursive method. The main improvement over circuits that have been previously re"},"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":"1706.03419","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-06-11T22:54:49Z","cross_cats_sorted":["cs.ET"],"title_canon_sha256":"f58af10c94bdb60f1294ebe714276108a44934919dea1ca70e44df699bc20701","abstract_canon_sha256":"af73e4c129c1ceee19aaf815b5adc095a965907db509b6d30d6e5dbac8179523"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:35.724931Z","signature_b64":"DsO6iDRAp0WTv8dG5Jf41VZRfym6MbI6aIIuqky3+Qr+7a/X8JM3kFUYAzAoI3UplBwesHXke1dWk1qk+NDEAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b175d8a4135104eb82588a260f5612c17604b552f4850ee0596dc33c8b049ab9","last_reissued_at":"2026-05-18T00:42:35.724341Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:35.724341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Improved reversible and quantum circuits for Karatsuba-based integer multiplication","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.ET"],"primary_cat":"quant-ph","authors_text":"Alex Parent, Martin Roetteler, Michele Mosca","submitted_at":"2017-06-11T22:54:49Z","abstract_excerpt":"Integer arithmetic is the underpinning of many quantum algorithms, with applications ranging from Shor's algorithm over HHL for matrix inversion to Hamiltonian simulation algorithms. A basic objective is to keep the required resources to implement arithmetic as low as possible. This applies in particular to the number of qubits required in the implementation as for the foreseeable future this number is expected to be small. We present a reversible circuit for integer multiplication that is inspired by Karatsuba's recursive method. The main improvement over circuits that have been previously re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.03419","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":"1706.03419","created_at":"2026-05-18T00:42:35.724438+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.03419v1","created_at":"2026-05-18T00:42:35.724438+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.03419","created_at":"2026-05-18T00:42:35.724438+00:00"},{"alias_kind":"pith_short_12","alias_value":"WF25RJATKECO","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_16","alias_value":"WF25RJATKECOXASY","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_8","alias_value":"WF25RJAT","created_at":"2026-05-18T12:31:53.515858+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2409.17595","citing_title":"Magic state cultivation: growing T states as cheap as CNOT gates","ref_index":41,"is_internal_anchor":false},{"citing_arxiv_id":"2604.19481","citing_title":"Fault-Tolerant Quantum Computing with Trapped Ions: The Walking Cat Architecture","ref_index":221,"is_internal_anchor":false},{"citing_arxiv_id":"2604.09847","citing_title":"A Polylogarithmic-Depth Quantum Multiplier","ref_index":19,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WF25RJATKECOXASYRITA6VQSYF","json":"https://pith.science/pith/WF25RJATKECOXASYRITA6VQSYF.json","graph_json":"https://pith.science/api/pith-number/WF25RJATKECOXASYRITA6VQSYF/graph.json","events_json":"https://pith.science/api/pith-number/WF25RJATKECOXASYRITA6VQSYF/events.json","paper":"https://pith.science/paper/WF25RJAT"},"agent_actions":{"view_html":"https://pith.science/pith/WF25RJATKECOXASYRITA6VQSYF","download_json":"https://pith.science/pith/WF25RJATKECOXASYRITA6VQSYF.json","view_paper":"https://pith.science/paper/WF25RJAT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.03419&json=true","fetch_graph":"https://pith.science/api/pith-number/WF25RJATKECOXASYRITA6VQSYF/graph.json","fetch_events":"https://pith.science/api/pith-number/WF25RJATKECOXASYRITA6VQSYF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WF25RJATKECOXASYRITA6VQSYF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WF25RJATKECOXASYRITA6VQSYF/action/storage_attestation","attest_author":"https://pith.science/pith/WF25RJATKECOXASYRITA6VQSYF/action/author_attestation","sign_citation":"https://pith.science/pith/WF25RJATKECOXASYRITA6VQSYF/action/citation_signature","submit_replication":"https://pith.science/pith/WF25RJATKECOXASYRITA6VQSYF/action/replication_record"}},"created_at":"2026-05-18T00:42:35.724438+00:00","updated_at":"2026-05-18T00:42:35.724438+00:00"}