{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:YCFF2BTFAP3EM5RSXSEBAXRUAD","short_pith_number":"pith:YCFF2BTF","schema_version":"1.0","canonical_sha256":"c08a5d066503f6467632bc88105e3400d5594df9092aa8dd4abf2630fbde39d1","source":{"kind":"arxiv","id":"1710.07256","version":1},"attestation_state":"computed","paper":{"title":"The disjointness of stabilizer codes and limitations on fault-tolerant logical gates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Aleksander Kubica, Theodore J. Yoder, Tomas Jochym-O'Connor","submitted_at":"2017-10-19T17:25:32Z","abstract_excerpt":"Stabilizer codes are a simple and successful class of quantum error-correcting codes. Yet this success comes in spite of some harsh limitations on the ability of these codes to fault-tolerantly compute. Here we introduce a new metric for these codes, the disjointness, which, roughly speaking, is the number of mostly non-overlapping representatives of any given non-trivial logical Pauli operator. We use the disjointness to prove that transversal gates on error-detecting stabilizer codes are necessarily in a finite level of the Clifford hierarchy. We also apply our techniques to topological code"},"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":"1710.07256","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-10-19T17:25:32Z","cross_cats_sorted":[],"title_canon_sha256":"cf6832f3075b4699dbdc7d9798e726ddbf183ebdbfa3329f5bb2df23f9011453","abstract_canon_sha256":"1faa290c78dbb4b98bfe436e9be30d26a41af9e58bff85bedebe4cdff4c3c789"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:47.166618Z","signature_b64":"GfCxTBf8GFXxlibEOHs185vijB3i0O3THYZz3bB/dZ+/nxp3zANmN3FBcOW7bMrbpEYjRimldg478mTCuul6AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c08a5d066503f6467632bc88105e3400d5594df9092aa8dd4abf2630fbde39d1","last_reissued_at":"2026-05-18T00:14:47.165958Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:47.165958Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The disjointness of stabilizer codes and limitations on fault-tolerant logical gates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Aleksander Kubica, Theodore J. Yoder, Tomas Jochym-O'Connor","submitted_at":"2017-10-19T17:25:32Z","abstract_excerpt":"Stabilizer codes are a simple and successful class of quantum error-correcting codes. Yet this success comes in spite of some harsh limitations on the ability of these codes to fault-tolerantly compute. Here we introduce a new metric for these codes, the disjointness, which, roughly speaking, is the number of mostly non-overlapping representatives of any given non-trivial logical Pauli operator. We use the disjointness to prove that transversal gates on error-detecting stabilizer codes are necessarily in a finite level of the Clifford hierarchy. We also apply our techniques to topological code"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.07256","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":""},"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":"1710.07256","created_at":"2026-05-18T00:14:47.166074+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.07256v1","created_at":"2026-05-18T00:14:47.166074+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.07256","created_at":"2026-05-18T00:14:47.166074+00:00"},{"alias_kind":"pith_short_12","alias_value":"YCFF2BTFAP3E","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_16","alias_value":"YCFF2BTFAP3EM5RS","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_8","alias_value":"YCFF2BTF","created_at":"2026-05-18T12:31:56.362134+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2602.14499","citing_title":"Homological origin of transversal implementability of logical diagonal gates in quantum CSS codes","ref_index":14,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YCFF2BTFAP3EM5RSXSEBAXRUAD","json":"https://pith.science/pith/YCFF2BTFAP3EM5RSXSEBAXRUAD.json","graph_json":"https://pith.science/api/pith-number/YCFF2BTFAP3EM5RSXSEBAXRUAD/graph.json","events_json":"https://pith.science/api/pith-number/YCFF2BTFAP3EM5RSXSEBAXRUAD/events.json","paper":"https://pith.science/paper/YCFF2BTF"},"agent_actions":{"view_html":"https://pith.science/pith/YCFF2BTFAP3EM5RSXSEBAXRUAD","download_json":"https://pith.science/pith/YCFF2BTFAP3EM5RSXSEBAXRUAD.json","view_paper":"https://pith.science/paper/YCFF2BTF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.07256&json=true","fetch_graph":"https://pith.science/api/pith-number/YCFF2BTFAP3EM5RSXSEBAXRUAD/graph.json","fetch_events":"https://pith.science/api/pith-number/YCFF2BTFAP3EM5RSXSEBAXRUAD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YCFF2BTFAP3EM5RSXSEBAXRUAD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YCFF2BTFAP3EM5RSXSEBAXRUAD/action/storage_attestation","attest_author":"https://pith.science/pith/YCFF2BTFAP3EM5RSXSEBAXRUAD/action/author_attestation","sign_citation":"https://pith.science/pith/YCFF2BTFAP3EM5RSXSEBAXRUAD/action/citation_signature","submit_replication":"https://pith.science/pith/YCFF2BTFAP3EM5RSXSEBAXRUAD/action/replication_record"}},"created_at":"2026-05-18T00:14:47.166074+00:00","updated_at":"2026-05-18T00:14:47.166074+00:00"}