{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:66MJUZF6GANVWS5EHFWRMDKPL6","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":"a4c72afa20b43d94e4ce55167236f517b115bd12ec0c126248f56cbd9b18874d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2019-09-15T04:31:50Z","title_canon_sha256":"100d3e3650d9a73a6ae44b2ebb63b5045801b06a0bf716d4c7aed9d777533f3c"},"schema_version":"1.0","source":{"id":"1909.06732","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.06732","created_at":"2026-07-05T01:26:05Z"},{"alias_kind":"arxiv_version","alias_value":"1909.06732v4","created_at":"2026-07-05T01:26:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.06732","created_at":"2026-07-05T01:26:05Z"},{"alias_kind":"pith_short_12","alias_value":"66MJUZF6GANV","created_at":"2026-07-05T01:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"66MJUZF6GANVWS5E","created_at":"2026-07-05T01:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"66MJUZF6","created_at":"2026-07-05T01:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:1451d1a3be1f55ae6f78c7b4a747be821d600abbf60671bdd29f6f0e498cc13c","target":"graph","created_at":"2026-07-05T01:26:05Z","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/1909.06732/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Error probability distribution associated with a given Clifford measurement circuit is described exactly in terms of the circuit error-equivalence group, or the circuit subsystem code previously introduced by Bacon, Flammia, Harrow, and Shi. This gives a prescription for maximum-likelihood decoding with a given measurement circuit. Marginal distributions for subsets of circuit errors are also analyzed; these generate a family of related asymmetric LDPC codes of varying degeneracy. More generally, such a family is associated with any quantum code. Implications for decoding highly-degenerate qua","authors_text":"Leonid P. Pryadko","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2019-09-15T04:31:50Z","title":"On maximum-likelihood decoding with circuit-level errors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.06732","kind":"arxiv","version":4},"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:ddd78d6cef79264acba5cd969ead143b563576771c368374e0abd200d35d4285","target":"record","created_at":"2026-07-05T01:26:05Z","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":"a4c72afa20b43d94e4ce55167236f517b115bd12ec0c126248f56cbd9b18874d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2019-09-15T04:31:50Z","title_canon_sha256":"100d3e3650d9a73a6ae44b2ebb63b5045801b06a0bf716d4c7aed9d777533f3c"},"schema_version":"1.0","source":{"id":"1909.06732","kind":"arxiv","version":4}},"canonical_sha256":"f7989a64be301b5b4ba4396d160d4f5fbb4f4d0b8dcceca6cf1fe2ad0d32d832","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f7989a64be301b5b4ba4396d160d4f5fbb4f4d0b8dcceca6cf1fe2ad0d32d832","first_computed_at":"2026-07-05T01:26:05.506482Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:26:05.506482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1Zf/PgpB11qHCWcy+13GjbrOJ0JHKDwTHKlNLxoznN70+Psvs1y3Y15gvTNACDj1xdN8VSfrJqxQwfQvT6iPAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:26:05.506947Z","signed_message":"canonical_sha256_bytes"},"source_id":"1909.06732","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ddd78d6cef79264acba5cd969ead143b563576771c368374e0abd200d35d4285","sha256:1451d1a3be1f55ae6f78c7b4a747be821d600abbf60671bdd29f6f0e498cc13c"],"state_sha256":"7068b3c8d2aa521051a8036661a51f8f8b174cb5124c747c4acc271294234937"}