{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:U74OBOTQGJ435S2KS2HN2RMOIL","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":"c3281576566a4ec83058645f80a99b71970dee80d5a5a1e808bc9077ed90f62e","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2007-12-13T04:59:28Z","title_canon_sha256":"15e22ebb58f133b86fa996aa7a6c47cf07d1530310982356333985513ba4cc9b"},"schema_version":"1.0","source":{"id":"0712.2084","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.2084","created_at":"2026-07-04T17:22:57Z"},{"alias_kind":"arxiv_version","alias_value":"0712.2084v2","created_at":"2026-07-04T17:22:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.2084","created_at":"2026-07-04T17:22:57Z"},{"alias_kind":"pith_short_12","alias_value":"U74OBOTQGJ43","created_at":"2026-07-04T17:22:57Z"},{"alias_kind":"pith_short_16","alias_value":"U74OBOTQGJ435S2K","created_at":"2026-07-04T17:22:57Z"},{"alias_kind":"pith_short_8","alias_value":"U74OBOTQ","created_at":"2026-07-04T17:22:57Z"}],"graph_snapshots":[{"event_id":"sha256:7b5ae48f664aa2576ac578bb5bd42c0c1bc1883fa649a8dd9b938e2f2d20f119","target":"graph","created_at":"2026-07-04T17:22:57Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0712.2084/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Teleportation is a crucial element in fault-tolerant quantum computation and a complete understanding of its capacity is very important for the practical implementation of optimal fault-tolerant architectures. It is known that stabilizer codes support a natural set of gates that can be more easily implemented by teleportation than any other gates. These gates belong to the so called $\\mathcal{C}_k$ hierarchy introduced by Gottesman and Chuang (Nature \\textbf{402}, 390). Moreover, a subset of $\\mathcal{C}_k$ gates, called semi-Clifford operations, can be implemented by an even simpler architect","authors_text":"Bei Zeng, Isaac L. Chuang, Xie Chen","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2007-12-13T04:59:28Z","title":"Semi-Clifford operations, structure of $\\mathcal{C}_k$ hierarchy, and gate complexity for fault-tolerant quantum computation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.2084","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:bb18f0464ae6b65b9008df818cac7c3d9e6d71dfb73a6757949f06f2ba044346","target":"record","created_at":"2026-07-04T17:22:57Z","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":"c3281576566a4ec83058645f80a99b71970dee80d5a5a1e808bc9077ed90f62e","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2007-12-13T04:59:28Z","title_canon_sha256":"15e22ebb58f133b86fa996aa7a6c47cf07d1530310982356333985513ba4cc9b"},"schema_version":"1.0","source":{"id":"0712.2084","kind":"arxiv","version":2}},"canonical_sha256":"a7f8e0ba703279becb4a968edd458e42c71f8cc110a69bed7995ad8b174b25be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7f8e0ba703279becb4a968edd458e42c71f8cc110a69bed7995ad8b174b25be","first_computed_at":"2026-07-04T17:22:57.979422Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:22:57.979422Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"emw90d5svNp7CnWfsy3LE9OnJEDf6jKjnS0wL3cpoUAyLVwPda+ePARixNPSpwSmNK9PMbblCagL+7InRO0dBg==","signature_status":"signed_v1","signed_at":"2026-07-04T17:22:57.979829Z","signed_message":"canonical_sha256_bytes"},"source_id":"0712.2084","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb18f0464ae6b65b9008df818cac7c3d9e6d71dfb73a6757949f06f2ba044346","sha256:7b5ae48f664aa2576ac578bb5bd42c0c1bc1883fa649a8dd9b938e2f2d20f119"],"state_sha256":"783a26304b772add695c1d9d08db72f6c86b5d1657cfc974824f32ec13ff4373"}