{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:ATN4VRGXY5XSK4MPE4DE2ZPCVG","short_pith_number":"pith:ATN4VRGX","schema_version":"1.0","canonical_sha256":"04dbcac4d7c76f25718f27064d65e2a99825d06e75de7e6292e163400270750c","source":{"kind":"arxiv","id":"2106.02621","version":1},"attestation_state":"computed","paper":{"title":"Single-shot quantum error correction with the three-dimensional subsystem toric code","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el"],"primary_cat":"quant-ph","authors_text":"Aleksander Kubica, Michael Vasmer","submitted_at":"2021-06-04T17:35:00Z","abstract_excerpt":"We introduce a new topological quantum code, the three-dimensional subsystem toric code (3D STC), which is a generalization of the stabilizer toric code. The 3D STC can be realized by measuring geometrically-local parity checks of weight at most three on the cubic lattice with open boundary conditions. We prove that single-shot quantum error correction (QEC) is possible with the 3D STC, i.e., one round of local parity-check measurements suffices to perform reliable QEC even in the presence of measurement errors. We also propose an efficient single-shot QEC strategy for the 3D STC and investiga"},"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":"2106.02621","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2021-06-04T17:35:00Z","cross_cats_sorted":["cond-mat.str-el"],"title_canon_sha256":"03aa884499fcecd4cd0f850336c463892e1b3b8e13062d48a4dd0fee5118cb18","abstract_canon_sha256":"b40c5f1e2304bd6609c46ce99425c99acb437ad8a53c1514b610310139e68171"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:09:03.911191Z","signature_b64":"31ztHF8iUU1ZCdoVlpUXt6qzxRF3lPCz2xVC81ECF4cWUbqMfTMH17uzGjJXb/hOeJzuWhbocTBZ87UR4YlzAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04dbcac4d7c76f25718f27064d65e2a99825d06e75de7e6292e163400270750c","last_reissued_at":"2026-07-05T05:09:03.910779Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:09:03.910779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Single-shot quantum error correction with the three-dimensional subsystem toric code","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el"],"primary_cat":"quant-ph","authors_text":"Aleksander Kubica, Michael Vasmer","submitted_at":"2021-06-04T17:35:00Z","abstract_excerpt":"We introduce a new topological quantum code, the three-dimensional subsystem toric code (3D STC), which is a generalization of the stabilizer toric code. The 3D STC can be realized by measuring geometrically-local parity checks of weight at most three on the cubic lattice with open boundary conditions. We prove that single-shot quantum error correction (QEC) is possible with the 3D STC, i.e., one round of local parity-check measurements suffices to perform reliable QEC even in the presence of measurement errors. We also propose an efficient single-shot QEC strategy for the 3D STC and investiga"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.02621","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/2106.02621/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":"2106.02621","created_at":"2026-07-05T05:09:03.910834+00:00"},{"alias_kind":"arxiv_version","alias_value":"2106.02621v1","created_at":"2026-07-05T05:09:03.910834+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.02621","created_at":"2026-07-05T05:09:03.910834+00:00"},{"alias_kind":"pith_short_12","alias_value":"ATN4VRGXY5XS","created_at":"2026-07-05T05:09:03.910834+00:00"},{"alias_kind":"pith_short_16","alias_value":"ATN4VRGXY5XSK4MP","created_at":"2026-07-05T05:09:03.910834+00:00"},{"alias_kind":"pith_short_8","alias_value":"ATN4VRGX","created_at":"2026-07-05T05:09:03.910834+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2409.17595","citing_title":"Magic state cultivation: growing T states as cheap as CNOT gates","ref_index":155,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ATN4VRGXY5XSK4MPE4DE2ZPCVG","json":"https://pith.science/pith/ATN4VRGXY5XSK4MPE4DE2ZPCVG.json","graph_json":"https://pith.science/api/pith-number/ATN4VRGXY5XSK4MPE4DE2ZPCVG/graph.json","events_json":"https://pith.science/api/pith-number/ATN4VRGXY5XSK4MPE4DE2ZPCVG/events.json","paper":"https://pith.science/paper/ATN4VRGX"},"agent_actions":{"view_html":"https://pith.science/pith/ATN4VRGXY5XSK4MPE4DE2ZPCVG","download_json":"https://pith.science/pith/ATN4VRGXY5XSK4MPE4DE2ZPCVG.json","view_paper":"https://pith.science/paper/ATN4VRGX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2106.02621&json=true","fetch_graph":"https://pith.science/api/pith-number/ATN4VRGXY5XSK4MPE4DE2ZPCVG/graph.json","fetch_events":"https://pith.science/api/pith-number/ATN4VRGXY5XSK4MPE4DE2ZPCVG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ATN4VRGXY5XSK4MPE4DE2ZPCVG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ATN4VRGXY5XSK4MPE4DE2ZPCVG/action/storage_attestation","attest_author":"https://pith.science/pith/ATN4VRGXY5XSK4MPE4DE2ZPCVG/action/author_attestation","sign_citation":"https://pith.science/pith/ATN4VRGXY5XSK4MPE4DE2ZPCVG/action/citation_signature","submit_replication":"https://pith.science/pith/ATN4VRGXY5XSK4MPE4DE2ZPCVG/action/replication_record"}},"created_at":"2026-07-05T05:09:03.910834+00:00","updated_at":"2026-07-05T05:09:03.910834+00:00"}