{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:ZAFH4ZROILDLMAEF4MUBQFUH5F","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":"f30eff3da28714881afcd6c298c85d56d030c997765f92259e5d2a67599241b8","cross_cats_sorted":["cond-mat.str-el","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-11-03T20:57:11Z","title_canon_sha256":"62779c21e728caec468436bab9bd92f460319b595cddc45ee18eb004fc2e8ad5"},"schema_version":"1.0","source":{"id":"0911.0581","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.0581","created_at":"2026-05-18T02:11:00Z"},{"alias_kind":"arxiv_version","alias_value":"0911.0581v2","created_at":"2026-05-18T02:11:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.0581","created_at":"2026-05-18T02:11:00Z"},{"alias_kind":"pith_short_12","alias_value":"ZAFH4ZROILDL","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"ZAFH4ZROILDLMAEF","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"ZAFH4ZRO","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:a34f71254faad58de7d01ce36e33e9585d6e99784cb8c2c9b7a2c24c1fc46199","target":"graph","created_at":"2026-05-18T02:11:00Z","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"},"paper":{"abstract_excerpt":"We present a family of algorithms, combining real-space renormalization methods and belief propagation, to estimate the free energy of a topologically ordered system in the presence of defects. Such an algorithm is needed to preserve the quantum information stored in the ground space of a topologically ordered system and to decode topological error-correcting codes. For a system of linear size L, our algorithm runs in time log L compared to L^6 needed for the minimum-weight perfect matching algorithm previously used in this context and achieves a higher depolarizing error threshold.","authors_text":"David Poulin, Guillaume Duclos-Cianci","cross_cats":["cond-mat.str-el","hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-11-03T20:57:11Z","title":"Fast Decoders for Topological Quantum Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.0581","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":"sha256:21e6438a25e4f546523c5071f4ecc93f72070a5d32b34329eefbd7416fa44e29","target":"record","created_at":"2026-05-18T02:11:00Z","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":"f30eff3da28714881afcd6c298c85d56d030c997765f92259e5d2a67599241b8","cross_cats_sorted":["cond-mat.str-el","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-11-03T20:57:11Z","title_canon_sha256":"62779c21e728caec468436bab9bd92f460319b595cddc45ee18eb004fc2e8ad5"},"schema_version":"1.0","source":{"id":"0911.0581","kind":"arxiv","version":2}},"canonical_sha256":"c80a7e662e42c6b60085e328181687e96f3f22fe1755fd4b5914ee2495450b17","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c80a7e662e42c6b60085e328181687e96f3f22fe1755fd4b5914ee2495450b17","first_computed_at":"2026-05-18T02:11:00.184558Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:11:00.184558Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hziHKyX2t/JOv/CfJC36C1VQ+uhV56VStP2pYODGFGnjwts4XwaDG38cESDr1j0NzdKgYfvRi+QaG10NAROvBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:11:00.185230Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.0581","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21e6438a25e4f546523c5071f4ecc93f72070a5d32b34329eefbd7416fa44e29","sha256:a34f71254faad58de7d01ce36e33e9585d6e99784cb8c2c9b7a2c24c1fc46199"],"state_sha256":"9a7cd798f8cb4975851e77da251d411493f716792070be6b75eb3dc7bd5fbe3e"}