{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:CD4SSPBLYRMOFCMYRUOG3654ZU","short_pith_number":"pith:CD4SSPBL","canonical_record":{"source":{"id":"2109.14599","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2021-09-29T17:52:16Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"817dd13870376e41a4ba108fc6bbd2598c3fd76dc91b2f9984af4f6366dc689d","abstract_canon_sha256":"740d02269a9a9753c114d5127d7f3bb66510df41ab8997a1681d597ccb70b70c"},"schema_version":"1.0"},"canonical_sha256":"10f9293c2bc458e289988d1c6dfbbccd0042289a1ae116618119afcaa839a91c","source":{"kind":"arxiv","id":"2109.14599","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.14599","created_at":"2026-07-05T03:18:36Z"},{"alias_kind":"arxiv_version","alias_value":"2109.14599v1","created_at":"2026-07-05T03:18:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.14599","created_at":"2026-07-05T03:18:36Z"},{"alias_kind":"pith_short_12","alias_value":"CD4SSPBLYRMO","created_at":"2026-07-05T03:18:36Z"},{"alias_kind":"pith_short_16","alias_value":"CD4SSPBLYRMOFCMY","created_at":"2026-07-05T03:18:36Z"},{"alias_kind":"pith_short_8","alias_value":"CD4SSPBL","created_at":"2026-07-05T03:18:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:CD4SSPBLYRMOFCMYRUOG3654ZU","target":"record","payload":{"canonical_record":{"source":{"id":"2109.14599","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2021-09-29T17:52:16Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"817dd13870376e41a4ba108fc6bbd2598c3fd76dc91b2f9984af4f6366dc689d","abstract_canon_sha256":"740d02269a9a9753c114d5127d7f3bb66510df41ab8997a1681d597ccb70b70c"},"schema_version":"1.0"},"canonical_sha256":"10f9293c2bc458e289988d1c6dfbbccd0042289a1ae116618119afcaa839a91c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:18:36.756481Z","signature_b64":"8aaNgShrXi1XAyPR4Ae2M3EBLGPNhENbEPt8kTua76YRH+4EACEwAcIdBqazuJnV/45YhaXIe3CLJCag1pStDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10f9293c2bc458e289988d1c6dfbbccd0042289a1ae116618119afcaa839a91c","last_reissued_at":"2026-07-05T03:18:36.756077Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:18:36.756077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2109.14599","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:18:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4DbE61IcWZhdmyrm3pYLaLGJeqa8QMtWAvThksERkXASqEu+u5vk5HLy0N348sWU6OhZHsLcw9jTR4i0vuS9Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-12T06:32:25.713452Z"},"content_sha256":"606ed5b61778ccde275bd46c018153427427a4fbd33036f2e9159b39ea8a440b","schema_version":"1.0","event_id":"sha256:606ed5b61778ccde275bd46c018153427427a4fbd33036f2e9159b39ea8a440b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:CD4SSPBLYRMOFCMYRUOG3654ZU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bounds on stabilizer measurement circuits and obstructions to local implementations of quantum LDPC codes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"quant-ph","authors_text":"Maxime A. Tremblay, Michael E. Beverland, Nicolas Delfosse","submitted_at":"2021-09-29T17:52:16Z","abstract_excerpt":"In this work we establish lower bounds on the size of Clifford circuits that measure a family of commuting Pauli operators. Our bounds depend on the interplay between a pair of graphs: the Tanner graph of the set of measured Pauli operators, and the connectivity graph which represents the qubit connections required to implement the circuit. For local-expander quantum codes, which are promising for low-overhead quantum error correction, we prove that any syndrome extraction circuit implemented with local Clifford gates in a 2D square patch of $N$ qubits has depth at least $\\Omega(n/\\sqrt{N})$ w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.14599","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2109.14599/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:18:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0yGwptbTeWtC/0YJK/nOx7ma52AkVUAOiu4WJNDmcGLvG3qfTqSG6+M3W3bNTwkBS0SVSSgJOouLM2z8RdLiDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-12T06:32:25.714084Z"},"content_sha256":"97c272d263990fdf6a221e6cf72395971174c0e69aac626d9fc94a26b23a382c","schema_version":"1.0","event_id":"sha256:97c272d263990fdf6a221e6cf72395971174c0e69aac626d9fc94a26b23a382c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CD4SSPBLYRMOFCMYRUOG3654ZU/bundle.json","state_url":"https://pith.science/pith/CD4SSPBLYRMOFCMYRUOG3654ZU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CD4SSPBLYRMOFCMYRUOG3654ZU/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-12T06:32:25Z","links":{"resolver":"https://pith.science/pith/CD4SSPBLYRMOFCMYRUOG3654ZU","bundle":"https://pith.science/pith/CD4SSPBLYRMOFCMYRUOG3654ZU/bundle.json","state":"https://pith.science/pith/CD4SSPBLYRMOFCMYRUOG3654ZU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CD4SSPBLYRMOFCMYRUOG3654ZU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:CD4SSPBLYRMOFCMYRUOG3654ZU","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":"740d02269a9a9753c114d5127d7f3bb66510df41ab8997a1681d597ccb70b70c","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2021-09-29T17:52:16Z","title_canon_sha256":"817dd13870376e41a4ba108fc6bbd2598c3fd76dc91b2f9984af4f6366dc689d"},"schema_version":"1.0","source":{"id":"2109.14599","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.14599","created_at":"2026-07-05T03:18:36Z"},{"alias_kind":"arxiv_version","alias_value":"2109.14599v1","created_at":"2026-07-05T03:18:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.14599","created_at":"2026-07-05T03:18:36Z"},{"alias_kind":"pith_short_12","alias_value":"CD4SSPBLYRMO","created_at":"2026-07-05T03:18:36Z"},{"alias_kind":"pith_short_16","alias_value":"CD4SSPBLYRMOFCMY","created_at":"2026-07-05T03:18:36Z"},{"alias_kind":"pith_short_8","alias_value":"CD4SSPBL","created_at":"2026-07-05T03:18:36Z"}],"graph_snapshots":[{"event_id":"sha256:97c272d263990fdf6a221e6cf72395971174c0e69aac626d9fc94a26b23a382c","target":"graph","created_at":"2026-07-05T03:18:36Z","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/2109.14599/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work we establish lower bounds on the size of Clifford circuits that measure a family of commuting Pauli operators. Our bounds depend on the interplay between a pair of graphs: the Tanner graph of the set of measured Pauli operators, and the connectivity graph which represents the qubit connections required to implement the circuit. For local-expander quantum codes, which are promising for low-overhead quantum error correction, we prove that any syndrome extraction circuit implemented with local Clifford gates in a 2D square patch of $N$ qubits has depth at least $\\Omega(n/\\sqrt{N})$ w","authors_text":"Maxime A. Tremblay, Michael E. Beverland, Nicolas Delfosse","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2021-09-29T17:52:16Z","title":"Bounds on stabilizer measurement circuits and obstructions to local implementations of quantum LDPC codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.14599","kind":"arxiv","version":1},"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":"sha256:606ed5b61778ccde275bd46c018153427427a4fbd33036f2e9159b39ea8a440b","target":"record","created_at":"2026-07-05T03:18:36Z","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":"740d02269a9a9753c114d5127d7f3bb66510df41ab8997a1681d597ccb70b70c","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2021-09-29T17:52:16Z","title_canon_sha256":"817dd13870376e41a4ba108fc6bbd2598c3fd76dc91b2f9984af4f6366dc689d"},"schema_version":"1.0","source":{"id":"2109.14599","kind":"arxiv","version":1}},"canonical_sha256":"10f9293c2bc458e289988d1c6dfbbccd0042289a1ae116618119afcaa839a91c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10f9293c2bc458e289988d1c6dfbbccd0042289a1ae116618119afcaa839a91c","first_computed_at":"2026-07-05T03:18:36.756077Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:18:36.756077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8aaNgShrXi1XAyPR4Ae2M3EBLGPNhENbEPt8kTua76YRH+4EACEwAcIdBqazuJnV/45YhaXIe3CLJCag1pStDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:18:36.756481Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.14599","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:606ed5b61778ccde275bd46c018153427427a4fbd33036f2e9159b39ea8a440b","sha256:97c272d263990fdf6a221e6cf72395971174c0e69aac626d9fc94a26b23a382c"],"state_sha256":"779c1c16c9a8694a0cc7dc683cb647084370db6ca4d00482eee08e3b93286149"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BQIbpwoONE/7QxrA2Qey+XkA2YUNbSbqy5xz81O580zwKvOC8WnleLRGNZJZQL2i1IwGO0NXWntAlzeLQ6h5Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-12T06:32:25.716508Z","bundle_sha256":"bc04906b87d2df66e5da86d830f53e25a0fc35b1f2a168aa239bd9f732f881c0"}}