{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:3AU42BAJPIBKXHHA5S4NV6NBIB","short_pith_number":"pith:3AU42BAJ","schema_version":"1.0","canonical_sha256":"d829cd04097a02ab9ce0ecb8daf9a1407c843f24e508e081b704a33c599ea872","source":{"kind":"arxiv","id":"2210.03556","version":1},"attestation_state":"computed","paper":{"title":"TQFTs and quantum computing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.CT","math.DG"],"primary_cat":"quant-ph","authors_text":"Mahmud Azam, Steven Rayan","submitted_at":"2022-10-07T13:41:43Z","abstract_excerpt":"Quantum computing is captured in the formalism of the monoidal subcategory of $\\textbf{Vect}_{\\mathbb C}$ generated by $\\mathbb C^2$ -- in particular, quantum circuits are diagrams in $\\textbf{Vect}_{\\mathbb C}$ -- while topological quantum field theories, in the sense of Atiyah, are diagrams in $\\textbf{Vect}_{\\mathbb C}$ indexed by cobordisms. We initiate a program that formalizes this connection. In doing so, we equip cobordisms with machinery for producing linear maps by parallel transport along curves under a connection and then assemble these structures into a double category. Finite-dim"},"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":"2210.03556","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2022-10-07T13:41:43Z","cross_cats_sorted":["hep-th","math.CT","math.DG"],"title_canon_sha256":"1f8d8e576ddc69c34be55fde5f87e9a4d15507e6a958f30b8faa4a745e77d617","abstract_canon_sha256":"3e0491665aa326e4761ed78c02c709b2a766847de9e28d6776077acc24333a19"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:26:09.919091Z","signature_b64":"nBpqzhz7Gfgx8lxvc0rv7fQwySIPFWlv3B3x/vHt4doRBJJf8mT1JbwtPsTic4JCn1nNwlpW2MNEUpLSBPI9BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d829cd04097a02ab9ce0ecb8daf9a1407c843f24e508e081b704a33c599ea872","last_reissued_at":"2026-07-05T08:26:09.918500Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:26:09.918500Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"TQFTs and quantum computing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.CT","math.DG"],"primary_cat":"quant-ph","authors_text":"Mahmud Azam, Steven Rayan","submitted_at":"2022-10-07T13:41:43Z","abstract_excerpt":"Quantum computing is captured in the formalism of the monoidal subcategory of $\\textbf{Vect}_{\\mathbb C}$ generated by $\\mathbb C^2$ -- in particular, quantum circuits are diagrams in $\\textbf{Vect}_{\\mathbb C}$ -- while topological quantum field theories, in the sense of Atiyah, are diagrams in $\\textbf{Vect}_{\\mathbb C}$ indexed by cobordisms. We initiate a program that formalizes this connection. In doing so, we equip cobordisms with machinery for producing linear maps by parallel transport along curves under a connection and then assemble these structures into a double category. Finite-dim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.03556","kind":"arxiv","version":1},"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/2210.03556/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":"2210.03556","created_at":"2026-07-05T08:26:09.918568+00:00"},{"alias_kind":"arxiv_version","alias_value":"2210.03556v1","created_at":"2026-07-05T08:26:09.918568+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.03556","created_at":"2026-07-05T08:26:09.918568+00:00"},{"alias_kind":"pith_short_12","alias_value":"3AU42BAJPIBK","created_at":"2026-07-05T08:26:09.918568+00:00"},{"alias_kind":"pith_short_16","alias_value":"3AU42BAJPIBKXHHA","created_at":"2026-07-05T08:26:09.918568+00:00"},{"alias_kind":"pith_short_8","alias_value":"3AU42BAJ","created_at":"2026-07-05T08:26:09.918568+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.08911","citing_title":"A diagrammatic field theory of quantum error correction","ref_index":69,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3AU42BAJPIBKXHHA5S4NV6NBIB","json":"https://pith.science/pith/3AU42BAJPIBKXHHA5S4NV6NBIB.json","graph_json":"https://pith.science/api/pith-number/3AU42BAJPIBKXHHA5S4NV6NBIB/graph.json","events_json":"https://pith.science/api/pith-number/3AU42BAJPIBKXHHA5S4NV6NBIB/events.json","paper":"https://pith.science/paper/3AU42BAJ"},"agent_actions":{"view_html":"https://pith.science/pith/3AU42BAJPIBKXHHA5S4NV6NBIB","download_json":"https://pith.science/pith/3AU42BAJPIBKXHHA5S4NV6NBIB.json","view_paper":"https://pith.science/paper/3AU42BAJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2210.03556&json=true","fetch_graph":"https://pith.science/api/pith-number/3AU42BAJPIBKXHHA5S4NV6NBIB/graph.json","fetch_events":"https://pith.science/api/pith-number/3AU42BAJPIBKXHHA5S4NV6NBIB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3AU42BAJPIBKXHHA5S4NV6NBIB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3AU42BAJPIBKXHHA5S4NV6NBIB/action/storage_attestation","attest_author":"https://pith.science/pith/3AU42BAJPIBKXHHA5S4NV6NBIB/action/author_attestation","sign_citation":"https://pith.science/pith/3AU42BAJPIBKXHHA5S4NV6NBIB/action/citation_signature","submit_replication":"https://pith.science/pith/3AU42BAJPIBKXHHA5S4NV6NBIB/action/replication_record"}},"created_at":"2026-07-05T08:26:09.918568+00:00","updated_at":"2026-07-05T08:26:09.918568+00:00"}