{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:WGQTQ7ELMWUUVQ3RBAUH5VPSGF","short_pith_number":"pith:WGQTQ7EL","schema_version":"1.0","canonical_sha256":"b1a1387c8b65a94ac37108287ed5f231758f86a3de1f56a8aa98e1d526f619cc","source":{"kind":"arxiv","id":"2311.07741","version":2},"attestation_state":"computed","paper":{"title":"Exact Synthesis of Multiqubit Clifford-Cyclotomic Circuits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Andrew N. Glaudell, Matthew Amy, Neil J. Ross, Samuel S. Mendelson, Shaun Kelso, William Maxwell","submitted_at":"2023-11-13T20:46:51Z","abstract_excerpt":"Let $n\\geq 8$ be divisible by 4. The Clifford-cyclotomic gate set $\\mathcal{G}_n$ is the universal gate set obtained by extending the Clifford gates with the $z$-rotation $T_n = \\mathrm{diag}(1,\\zeta_n)$, where $\\zeta_n$ is a primitive $n$-th root of unity. In this note, we show that, when $n$ is a power of 2, a multiqubit unitary matrix $U$ can be exactly represented by a circuit over $\\mathcal{G}_n$ if and only if the entries of $U$ belong to the ring $\\mathbb{Z}[1/2,\\zeta_n]$. We moreover show that $\\log(n)-2$ ancillas are always sufficient to construct a circuit for $U$. Our results genera"},"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":"2311.07741","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2023-11-13T20:46:51Z","cross_cats_sorted":[],"title_canon_sha256":"3a45fa01b4d60d0acc75bb108805146cb009c3769b5c08e0eabc4835fd3e1296","abstract_canon_sha256":"adcb22f1291805ee954c4e8fbd45007b06917b9c0fa183b5fc901c63b3a8e577"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:07:30.799820Z","signature_b64":"TFgdN5Hj3r62xgvnhKeo0butcfknmYMd3+GD4PO9eL8QAyPJkN8b3H8n2XDAefSIv8Ny9fYuvwDrsacKpzbzDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1a1387c8b65a94ac37108287ed5f231758f86a3de1f56a8aa98e1d526f619cc","last_reissued_at":"2026-07-05T08:07:30.799325Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:07:30.799325Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exact Synthesis of Multiqubit Clifford-Cyclotomic Circuits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Andrew N. Glaudell, Matthew Amy, Neil J. Ross, Samuel S. Mendelson, Shaun Kelso, William Maxwell","submitted_at":"2023-11-13T20:46:51Z","abstract_excerpt":"Let $n\\geq 8$ be divisible by 4. The Clifford-cyclotomic gate set $\\mathcal{G}_n$ is the universal gate set obtained by extending the Clifford gates with the $z$-rotation $T_n = \\mathrm{diag}(1,\\zeta_n)$, where $\\zeta_n$ is a primitive $n$-th root of unity. In this note, we show that, when $n$ is a power of 2, a multiqubit unitary matrix $U$ can be exactly represented by a circuit over $\\mathcal{G}_n$ if and only if the entries of $U$ belong to the ring $\\mathbb{Z}[1/2,\\zeta_n]$. We moreover show that $\\log(n)-2$ ancillas are always sufficient to construct a circuit for $U$. Our results genera"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.07741","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/2311.07741/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":"2311.07741","created_at":"2026-07-05T08:07:30.799401+00:00"},{"alias_kind":"arxiv_version","alias_value":"2311.07741v2","created_at":"2026-07-05T08:07:30.799401+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.07741","created_at":"2026-07-05T08:07:30.799401+00:00"},{"alias_kind":"pith_short_12","alias_value":"WGQTQ7ELMWUU","created_at":"2026-07-05T08:07:30.799401+00:00"},{"alias_kind":"pith_short_16","alias_value":"WGQTQ7ELMWUUVQ3R","created_at":"2026-07-05T08:07:30.799401+00:00"},{"alias_kind":"pith_short_8","alias_value":"WGQTQ7EL","created_at":"2026-07-05T08:07:30.799401+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.20033","citing_title":"Direct U(2) approximation via repeat-until-success circuits","ref_index":1,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WGQTQ7ELMWUUVQ3RBAUH5VPSGF","json":"https://pith.science/pith/WGQTQ7ELMWUUVQ3RBAUH5VPSGF.json","graph_json":"https://pith.science/api/pith-number/WGQTQ7ELMWUUVQ3RBAUH5VPSGF/graph.json","events_json":"https://pith.science/api/pith-number/WGQTQ7ELMWUUVQ3RBAUH5VPSGF/events.json","paper":"https://pith.science/paper/WGQTQ7EL"},"agent_actions":{"view_html":"https://pith.science/pith/WGQTQ7ELMWUUVQ3RBAUH5VPSGF","download_json":"https://pith.science/pith/WGQTQ7ELMWUUVQ3RBAUH5VPSGF.json","view_paper":"https://pith.science/paper/WGQTQ7EL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2311.07741&json=true","fetch_graph":"https://pith.science/api/pith-number/WGQTQ7ELMWUUVQ3RBAUH5VPSGF/graph.json","fetch_events":"https://pith.science/api/pith-number/WGQTQ7ELMWUUVQ3RBAUH5VPSGF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WGQTQ7ELMWUUVQ3RBAUH5VPSGF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WGQTQ7ELMWUUVQ3RBAUH5VPSGF/action/storage_attestation","attest_author":"https://pith.science/pith/WGQTQ7ELMWUUVQ3RBAUH5VPSGF/action/author_attestation","sign_citation":"https://pith.science/pith/WGQTQ7ELMWUUVQ3RBAUH5VPSGF/action/citation_signature","submit_replication":"https://pith.science/pith/WGQTQ7ELMWUUVQ3RBAUH5VPSGF/action/replication_record"}},"created_at":"2026-07-05T08:07:30.799401+00:00","updated_at":"2026-07-05T08:07:30.799401+00:00"}