{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:TQIHSVN3YURCEC4TEWBBWWTASY","short_pith_number":"pith:TQIHSVN3","schema_version":"1.0","canonical_sha256":"9c107955bbc522220b9325821b5a609628fa386a911bb567565d83f10261adce","source":{"kind":"arxiv","id":"1501.04944","version":2},"attestation_state":"computed","paper":{"title":"Exact synthesis of single-qubit unitaries over Clifford-cyclotomic gate sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"David Gosset, David McKinnon, Simon Forest, Vadym Kliuchnikov","submitted_at":"2015-01-20T20:12:49Z","abstract_excerpt":"We generalize an efficient exact synthesis algorithm for single-qubit unitaries over the Clifford+T gate set which was presented by Kliuchnikov, Maslov and Mosca. Their algorithm takes as input an exactly synthesizable single-qubit unitary--one which can be expressed without error as a product of Clifford and T gates--and outputs a sequence of gates which implements it. The algorithm is optimal in the sense that the length of the sequence, measured by the number of T gates, is smallest possible. In this paper, for each positive even integer $n$ we consider the \"Clifford-cyclotomic\" gate set co"},"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":"1501.04944","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-01-20T20:12:49Z","cross_cats_sorted":[],"title_canon_sha256":"85ccacdbcf6037ba2134190250517702c2fa30a40f0ab24fde8f801cf8afc418","abstract_canon_sha256":"8f522a444a76c87d39032cfa4b96cd4836f7545e0b0d2efa78a2f950ca18c68b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:03.404723Z","signature_b64":"cIK3O2MJ0KMxyTzJb5VpWo/Q3r4Of0Ozrg7Ng7QhDdC88NEmWc5v1319k+dPghogMXOex0oYgUIWF8q2L2F2AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c107955bbc522220b9325821b5a609628fa386a911bb567565d83f10261adce","last_reissued_at":"2026-05-18T01:31:03.404125Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:03.404125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exact synthesis of single-qubit unitaries over Clifford-cyclotomic gate sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"David Gosset, David McKinnon, Simon Forest, Vadym Kliuchnikov","submitted_at":"2015-01-20T20:12:49Z","abstract_excerpt":"We generalize an efficient exact synthesis algorithm for single-qubit unitaries over the Clifford+T gate set which was presented by Kliuchnikov, Maslov and Mosca. Their algorithm takes as input an exactly synthesizable single-qubit unitary--one which can be expressed without error as a product of Clifford and T gates--and outputs a sequence of gates which implements it. The algorithm is optimal in the sense that the length of the sequence, measured by the number of T gates, is smallest possible. In this paper, for each positive even integer $n$ we consider the \"Clifford-cyclotomic\" gate set co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04944","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":"1501.04944","created_at":"2026-05-18T01:31:03.404210+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.04944v2","created_at":"2026-05-18T01:31:03.404210+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04944","created_at":"2026-05-18T01:31:03.404210+00:00"},{"alias_kind":"pith_short_12","alias_value":"TQIHSVN3YURC","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_16","alias_value":"TQIHSVN3YURCEC4T","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_8","alias_value":"TQIHSVN3","created_at":"2026-05-18T12:29:42.218222+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/TQIHSVN3YURCEC4TEWBBWWTASY","json":"https://pith.science/pith/TQIHSVN3YURCEC4TEWBBWWTASY.json","graph_json":"https://pith.science/api/pith-number/TQIHSVN3YURCEC4TEWBBWWTASY/graph.json","events_json":"https://pith.science/api/pith-number/TQIHSVN3YURCEC4TEWBBWWTASY/events.json","paper":"https://pith.science/paper/TQIHSVN3"},"agent_actions":{"view_html":"https://pith.science/pith/TQIHSVN3YURCEC4TEWBBWWTASY","download_json":"https://pith.science/pith/TQIHSVN3YURCEC4TEWBBWWTASY.json","view_paper":"https://pith.science/paper/TQIHSVN3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.04944&json=true","fetch_graph":"https://pith.science/api/pith-number/TQIHSVN3YURCEC4TEWBBWWTASY/graph.json","fetch_events":"https://pith.science/api/pith-number/TQIHSVN3YURCEC4TEWBBWWTASY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TQIHSVN3YURCEC4TEWBBWWTASY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TQIHSVN3YURCEC4TEWBBWWTASY/action/storage_attestation","attest_author":"https://pith.science/pith/TQIHSVN3YURCEC4TEWBBWWTASY/action/author_attestation","sign_citation":"https://pith.science/pith/TQIHSVN3YURCEC4TEWBBWWTASY/action/citation_signature","submit_replication":"https://pith.science/pith/TQIHSVN3YURCEC4TEWBBWWTASY/action/replication_record"}},"created_at":"2026-05-18T01:31:03.404210+00:00","updated_at":"2026-05-18T01:31:03.404210+00:00"}