{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:MUDMMIY5CQCFJVJ4NJOO53TSVJ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e770d4bb7c5b032251352bcf595d425e264629901c1afd9a55a9f054e17b6bb8","cross_cats_sorted":["cs.CC","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-09-10T19:38:29Z","title_canon_sha256":"2faad0733470f32998c4d475c0d5ca71a648151d3160843859703bba2050dda8"},"schema_version":"1.0","source":{"id":"1409.3208","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.3208","created_at":"2026-05-18T01:30:35Z"},{"alias_kind":"arxiv_version","alias_value":"1409.3208v2","created_at":"2026-05-18T01:30:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.3208","created_at":"2026-05-18T01:30:35Z"},{"alias_kind":"pith_short_12","alias_value":"MUDMMIY5CQCF","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MUDMMIY5CQCFJVJ4","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MUDMMIY5","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:1a00fa4a3c64fd13ce3cfe192a4c381d22069d92e450b3c3e802b06b4cd9e1fa","target":"graph","created_at":"2026-05-18T01:30:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"$\\textit{Normalizer circuits}$ [1,2] are generalized Clifford circuits that act on arbitrary finite-dimensional systems $\\mathcal{H}_{d_1}\\otimes ... \\otimes \\mathcal{H}_{d_n}$ with a standard basis labeled by the elements of a finite Abelian group $G=\\mathbb{Z}_{d_1}\\times... \\times \\mathbb{Z}_{d_n}$. Normalizer gates implement operations associated with the group $G$ and can be of three types: quantum Fourier transforms, group automorphism gates and quadratic phase gates. In this work, we extend the normalizer formalism [1,2] to infinite dimensions, by allowing normalizer gates to act on sys","authors_text":"Cedric Yen-Yu Lin, Juan Bermejo-Vega, Maarten Van den Nest","cross_cats":["cs.CC","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-09-10T19:38:29Z","title":"Normalizer circuits and a Gottesman-Knill theorem for infinite-dimensional systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3208","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d8f935d7f14d4f71fa65e9ce60d4a282bb165d454581f49a157dea9d329ee84a","target":"record","created_at":"2026-05-18T01:30:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e770d4bb7c5b032251352bcf595d425e264629901c1afd9a55a9f054e17b6bb8","cross_cats_sorted":["cs.CC","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-09-10T19:38:29Z","title_canon_sha256":"2faad0733470f32998c4d475c0d5ca71a648151d3160843859703bba2050dda8"},"schema_version":"1.0","source":{"id":"1409.3208","kind":"arxiv","version":2}},"canonical_sha256":"6506c6231d140454d53c6a5ceeee72aa4d2d4366ebe4290011ae09e173161dbf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6506c6231d140454d53c6a5ceeee72aa4d2d4366ebe4290011ae09e173161dbf","first_computed_at":"2026-05-18T01:30:35.262364Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:35.262364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5Ya6PQ3K/AhWG3KimB46QxkTP3kyijIy6eG5qXLbfoxPkxEfMkWilY8smgS2Z0LvDLPysw9Km9783M7R9/T3Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:35.263181Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.3208","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d8f935d7f14d4f71fa65e9ce60d4a282bb165d454581f49a157dea9d329ee84a","sha256:1a00fa4a3c64fd13ce3cfe192a4c381d22069d92e450b3c3e802b06b4cd9e1fa"],"state_sha256":"37f5f9112579b4414f189fbf636814aa89fc5112abbb8e5d9831cb8fb2fc5782"}