{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:KH4OW4LOZRT23DKHAJCN3AOQEK","short_pith_number":"pith:KH4OW4LO","schema_version":"1.0","canonical_sha256":"51f8eb716ecc67ad8d470244dd81d022b4679caa6f09478efe78f7545a544b5c","source":{"kind":"arxiv","id":"1806.06472","version":2},"attestation_state":"computed","paper":{"title":"Calderbank-Steane-Shor Holographic Quantum Error Correcting Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Gavin K. Brennen, Nathan A. McMahon, Robert J. Harris, Thomas M. Stace","submitted_at":"2018-06-18T01:04:25Z","abstract_excerpt":"We expand the class of holographic quantum error correcting codes by developing the notion of block perfect tensors, a wider class that includes previously defined perfect tensors. The relaxation of this constraint opens up a range of other holographic codes. We demonstrate this by introducing the self-dual CSS heptagon holographic code, based on the 7-qubit Steane code. Finally we show promising thresholds for the erasure channel by applying a straightforward, optimal erasure decoder to the heptagon code and benchmark it against existing holographic codes."},"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":"1806.06472","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-06-18T01:04:25Z","cross_cats_sorted":[],"title_canon_sha256":"93445993d4f300c790b0a31135171c3eac4ddeeb062387d61cd0d9c91117f10b","abstract_canon_sha256":"654c4fdbc356841d614ed9eafeca176a09d8fca50ca996c8ba30a4e04ba982d7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:29.281709Z","signature_b64":"OpZmDrf/zKdHXBCb+vG7oq22WzV5Es2s0nd9E0NYMF+FWuYAijlIDJ2c3OPEn06HgdtyzHnZy4dpCvk92UEACg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51f8eb716ecc67ad8d470244dd81d022b4679caa6f09478efe78f7545a544b5c","last_reissued_at":"2026-05-18T00:01:29.281285Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:29.281285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Calderbank-Steane-Shor Holographic Quantum Error Correcting Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Gavin K. Brennen, Nathan A. McMahon, Robert J. Harris, Thomas M. Stace","submitted_at":"2018-06-18T01:04:25Z","abstract_excerpt":"We expand the class of holographic quantum error correcting codes by developing the notion of block perfect tensors, a wider class that includes previously defined perfect tensors. The relaxation of this constraint opens up a range of other holographic codes. We demonstrate this by introducing the self-dual CSS heptagon holographic code, based on the 7-qubit Steane code. Finally we show promising thresholds for the erasure channel by applying a straightforward, optimal erasure decoder to the heptagon code and benchmark it against existing holographic codes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06472","kind":"arxiv","version":2},"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":"1806.06472","created_at":"2026-05-18T00:01:29.281354+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.06472v2","created_at":"2026-05-18T00:01:29.281354+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.06472","created_at":"2026-05-18T00:01:29.281354+00:00"},{"alias_kind":"pith_short_12","alias_value":"KH4OW4LOZRT2","created_at":"2026-05-18T12:32:33.847187+00:00"},{"alias_kind":"pith_short_16","alias_value":"KH4OW4LOZRT23DKH","created_at":"2026-05-18T12:32:33.847187+00:00"},{"alias_kind":"pith_short_8","alias_value":"KH4OW4LO","created_at":"2026-05-18T12:32:33.847187+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2512.23005","citing_title":"Graph restricted tensors: building blocks for holographic networks","ref_index":22,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KH4OW4LOZRT23DKHAJCN3AOQEK","json":"https://pith.science/pith/KH4OW4LOZRT23DKHAJCN3AOQEK.json","graph_json":"https://pith.science/api/pith-number/KH4OW4LOZRT23DKHAJCN3AOQEK/graph.json","events_json":"https://pith.science/api/pith-number/KH4OW4LOZRT23DKHAJCN3AOQEK/events.json","paper":"https://pith.science/paper/KH4OW4LO"},"agent_actions":{"view_html":"https://pith.science/pith/KH4OW4LOZRT23DKHAJCN3AOQEK","download_json":"https://pith.science/pith/KH4OW4LOZRT23DKHAJCN3AOQEK.json","view_paper":"https://pith.science/paper/KH4OW4LO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.06472&json=true","fetch_graph":"https://pith.science/api/pith-number/KH4OW4LOZRT23DKHAJCN3AOQEK/graph.json","fetch_events":"https://pith.science/api/pith-number/KH4OW4LOZRT23DKHAJCN3AOQEK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KH4OW4LOZRT23DKHAJCN3AOQEK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KH4OW4LOZRT23DKHAJCN3AOQEK/action/storage_attestation","attest_author":"https://pith.science/pith/KH4OW4LOZRT23DKHAJCN3AOQEK/action/author_attestation","sign_citation":"https://pith.science/pith/KH4OW4LOZRT23DKHAJCN3AOQEK/action/citation_signature","submit_replication":"https://pith.science/pith/KH4OW4LOZRT23DKHAJCN3AOQEK/action/replication_record"}},"created_at":"2026-05-18T00:01:29.281354+00:00","updated_at":"2026-05-18T00:01:29.281354+00:00"}