{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:4K6PWUUSSY5O4KK43L33DNHIEX","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8f95da9ec88adf32fe14a1f8758bcbb7e4b83c9e0ccb8b598e69461ae1ea9363","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2006-06-14T19:53:25Z","title_canon_sha256":"48b175524b9291e375aabd6a72588f28be0c61186e7c84c829fd6cfc42af66c1"},"schema_version":"1.0","source":{"id":"quant-ph/0606126","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0606126","created_at":"2026-07-04T17:03:29Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0606126v2","created_at":"2026-07-04T17:03:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0606126","created_at":"2026-07-04T17:03:29Z"},{"alias_kind":"pith_short_12","alias_value":"4K6PWUUSSY5O","created_at":"2026-07-04T17:03:29Z"},{"alias_kind":"pith_short_16","alias_value":"4K6PWUUSSY5O4KK4","created_at":"2026-07-04T17:03:29Z"},{"alias_kind":"pith_short_8","alias_value":"4K6PWUUS","created_at":"2026-07-04T17:03:29Z"}],"graph_snapshots":[{"event_id":"sha256:1f38ce1da371ccb1a9ed555744e091e2f9e69954792080a9ee58e884d026fa8e","target":"graph","created_at":"2026-07-04T17:03:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/quant-ph/0606126/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the problem of optimally decoding a quantum error correction code -- that is to find the optimal recovery procedure given the outcomes of partial \"check\" measurements on the system. In general, this problem is NP-hard. However, we demonstrate that for concatenated block codes, the optimal decoding can be efficiently computed using a message passing algorithm. We compare the performance of the message passing algorithm to that of the widespread blockwise hard decoding technique. Our Monte Carlo results using the 5 qubit and Steane's code on a depolarizing channel demonstrate signifi","authors_text":"David Poulin","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2006-06-14T19:53:25Z","title":"Optimal and Efficient Decoding of Concatenated Quantum Block Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0606126","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2d89cc4ff58065e00a514623902e35ca2d3ed661ed472f148aa0eeea5c9dddc3","target":"record","created_at":"2026-07-04T17:03:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8f95da9ec88adf32fe14a1f8758bcbb7e4b83c9e0ccb8b598e69461ae1ea9363","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2006-06-14T19:53:25Z","title_canon_sha256":"48b175524b9291e375aabd6a72588f28be0c61186e7c84c829fd6cfc42af66c1"},"schema_version":"1.0","source":{"id":"quant-ph/0606126","kind":"arxiv","version":2}},"canonical_sha256":"e2bcfb5292963aee295cdaf7b1b4e825dbe98b7cc091f5a7158129d2450d8527","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e2bcfb5292963aee295cdaf7b1b4e825dbe98b7cc091f5a7158129d2450d8527","first_computed_at":"2026-07-04T17:03:29.460801Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:03:29.460801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5J+llfRrIOMiRUumvc5filKUlmInbpZVU5wk01LT1fL4rH0VEqMq3Ssjf7wX789IeNEbH2VY4H5SkQT8YGQLAw==","signature_status":"signed_v1","signed_at":"2026-07-04T17:03:29.461277Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0606126","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d89cc4ff58065e00a514623902e35ca2d3ed661ed472f148aa0eeea5c9dddc3","sha256:1f38ce1da371ccb1a9ed555744e091e2f9e69954792080a9ee58e884d026fa8e"],"state_sha256":"6c0a0ca3748a95c8cc005e7484ec0244ffeb044ba144223e668528e3c4ae1426"}