{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:A2ECTQI7LMJOJ5FNWUDEICYOU4","short_pith_number":"pith:A2ECTQI7","schema_version":"1.0","canonical_sha256":"068829c11f5b12e4f4adb506440b0ea705a132af8a3ea6b30c03dd5eda0e1786","source":{"kind":"arxiv","id":"2411.15848","version":3},"attestation_state":"computed","paper":{"title":"Classifying Logical Gates in Quantum Codes via Cohomology Operations and Symmetry","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cond-mat.str-el","hep-th","math.QA"],"primary_cat":"quant-ph","authors_text":"Guanyu Zhu, Po-Shen Hsin, Ryohei Kobayashi","submitted_at":"2024-11-24T14:01:37Z","abstract_excerpt":"We systematically construct and classify fault-tolerant logical gates implemented by constant-depth circuits for quantum codes using cohomology operations and symmetry. These logical gates are obtained from unitary operators given by symmetry-protected topological responses, which correspond to generators of group cohomology and can be expressed explicitly on the lattice using cohomology operations including cup product, Steenrod squares and new combinations of higher cup products called higher Pontryagin powers. Our study covers most types of the cohomology operations in the literature. This "},"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":"2411.15848","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"quant-ph","submitted_at":"2024-11-24T14:01:37Z","cross_cats_sorted":["cond-mat.str-el","hep-th","math.QA"],"title_canon_sha256":"09a12fc6340eec17c9f7d7cb400dd962514051dd7674153f8525475592c19570","abstract_canon_sha256":"db50c9bf0083a9a167c55b76faf12e3447c718a0e2dabad685a7ae381026995d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:28:12.549521Z","signature_b64":"ewvbMwdw3ORupPUyCiw4XBEDkJUlGDbwjqgjY2rfK+mpj9Qi/LyWQscubn7pwbnoB5WiWVdWzASXBz1xaZUvAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"068829c11f5b12e4f4adb506440b0ea705a132af8a3ea6b30c03dd5eda0e1786","last_reissued_at":"2026-07-05T11:28:12.548857Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:28:12.548857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Classifying Logical Gates in Quantum Codes via Cohomology Operations and Symmetry","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cond-mat.str-el","hep-th","math.QA"],"primary_cat":"quant-ph","authors_text":"Guanyu Zhu, Po-Shen Hsin, Ryohei Kobayashi","submitted_at":"2024-11-24T14:01:37Z","abstract_excerpt":"We systematically construct and classify fault-tolerant logical gates implemented by constant-depth circuits for quantum codes using cohomology operations and symmetry. These logical gates are obtained from unitary operators given by symmetry-protected topological responses, which correspond to generators of group cohomology and can be expressed explicitly on the lattice using cohomology operations including cup product, Steenrod squares and new combinations of higher cup products called higher Pontryagin powers. Our study covers most types of the cohomology operations in the literature. This "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.15848","kind":"arxiv","version":3},"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/2411.15848/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":"2411.15848","created_at":"2026-07-05T11:28:12.548919+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.15848v3","created_at":"2026-07-05T11:28:12.548919+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.15848","created_at":"2026-07-05T11:28:12.548919+00:00"},{"alias_kind":"pith_short_12","alias_value":"A2ECTQI7LMJO","created_at":"2026-07-05T11:28:12.548919+00:00"},{"alias_kind":"pith_short_16","alias_value":"A2ECTQI7LMJOJ5FN","created_at":"2026-07-05T11:28:12.548919+00:00"},{"alias_kind":"pith_short_8","alias_value":"A2ECTQI7","created_at":"2026-07-05T11:28:12.548919+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":4,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2503.05003","citing_title":"Parallel Logical Measurements via Quantum Code Surgery","ref_index":26,"is_internal_anchor":false},{"citing_arxiv_id":"2511.02900","citing_title":"Clifford Hierarchy Stabilizer Codes: Transversal Non-Clifford Gates and Magic","ref_index":22,"is_internal_anchor":false},{"citing_arxiv_id":"2511.15783","citing_title":"Automorphism in Gauge Theories: Higher Symmetries and Transversal Non-Clifford Logical Gates","ref_index":15,"is_internal_anchor":false},{"citing_arxiv_id":"2605.11318","citing_title":"Spatial overhead reduction for 2D hypergraph product codes","ref_index":103,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/A2ECTQI7LMJOJ5FNWUDEICYOU4","json":"https://pith.science/pith/A2ECTQI7LMJOJ5FNWUDEICYOU4.json","graph_json":"https://pith.science/api/pith-number/A2ECTQI7LMJOJ5FNWUDEICYOU4/graph.json","events_json":"https://pith.science/api/pith-number/A2ECTQI7LMJOJ5FNWUDEICYOU4/events.json","paper":"https://pith.science/paper/A2ECTQI7"},"agent_actions":{"view_html":"https://pith.science/pith/A2ECTQI7LMJOJ5FNWUDEICYOU4","download_json":"https://pith.science/pith/A2ECTQI7LMJOJ5FNWUDEICYOU4.json","view_paper":"https://pith.science/paper/A2ECTQI7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.15848&json=true","fetch_graph":"https://pith.science/api/pith-number/A2ECTQI7LMJOJ5FNWUDEICYOU4/graph.json","fetch_events":"https://pith.science/api/pith-number/A2ECTQI7LMJOJ5FNWUDEICYOU4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A2ECTQI7LMJOJ5FNWUDEICYOU4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A2ECTQI7LMJOJ5FNWUDEICYOU4/action/storage_attestation","attest_author":"https://pith.science/pith/A2ECTQI7LMJOJ5FNWUDEICYOU4/action/author_attestation","sign_citation":"https://pith.science/pith/A2ECTQI7LMJOJ5FNWUDEICYOU4/action/citation_signature","submit_replication":"https://pith.science/pith/A2ECTQI7LMJOJ5FNWUDEICYOU4/action/replication_record"}},"created_at":"2026-07-05T11:28:12.548919+00:00","updated_at":"2026-07-05T11:28:12.548919+00:00"}