{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:QXLXSRMEYTU5IEGF6IXXFB3U76","short_pith_number":"pith:QXLXSRME","canonical_record":{"source":{"id":"2309.09342","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2023-09-17T18:14:10Z","cross_cats_sorted":[],"title_canon_sha256":"4b06868d6d8533f869f6b3da816e1b96670cbf602919b86e09dc66d4df73b7c3","abstract_canon_sha256":"5a7cb7316b9f3146e778224cb385d5aec948fe166ebf83ab809645ea0fc2a02d"},"schema_version":"1.0"},"canonical_sha256":"85d7794584c4e9d410c5f22f728774ffb6f12d0bc4a061ea8e63126bb7702df6","source":{"kind":"arxiv","id":"2309.09342","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.09342","created_at":"2026-07-05T09:02:13Z"},{"alias_kind":"arxiv_version","alias_value":"2309.09342v3","created_at":"2026-07-05T09:02:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.09342","created_at":"2026-07-05T09:02:13Z"},{"alias_kind":"pith_short_12","alias_value":"QXLXSRMEYTU5","created_at":"2026-07-05T09:02:13Z"},{"alias_kind":"pith_short_16","alias_value":"QXLXSRMEYTU5IEGF","created_at":"2026-07-05T09:02:13Z"},{"alias_kind":"pith_short_8","alias_value":"QXLXSRME","created_at":"2026-07-05T09:02:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:QXLXSRMEYTU5IEGF6IXXFB3U76","target":"record","payload":{"canonical_record":{"source":{"id":"2309.09342","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2023-09-17T18:14:10Z","cross_cats_sorted":[],"title_canon_sha256":"4b06868d6d8533f869f6b3da816e1b96670cbf602919b86e09dc66d4df73b7c3","abstract_canon_sha256":"5a7cb7316b9f3146e778224cb385d5aec948fe166ebf83ab809645ea0fc2a02d"},"schema_version":"1.0"},"canonical_sha256":"85d7794584c4e9d410c5f22f728774ffb6f12d0bc4a061ea8e63126bb7702df6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:02:13.017238Z","signature_b64":"1mSt+QBpSYPrNkfWG5D1Sdxw/Qs6xuM/zZRj2yqNaOcforUABTMr4yxf2ZeqA46AiGHJenLo+n8X7XdZvKapBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85d7794584c4e9d410c5f22f728774ffb6f12d0bc4a061ea8e63126bb7702df6","last_reissued_at":"2026-07-05T09:02:13.016732Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:02:13.016732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2309.09342","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:02:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ptbx9HBFXChIkBANWrGIygSviNoKWUek3MXQXZClcmVUNtqJSfDUfTaDogihBpRe7/GaVXovVmJVw8b8S8YfBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T05:11:32.020949Z"},"content_sha256":"5522b1af03fc0315f9b9d14c87156d4182f7e47eb87f7441ec8998f6e2f0505e","schema_version":"1.0","event_id":"sha256:5522b1af03fc0315f9b9d14c87156d4182f7e47eb87f7441ec8998f6e2f0505e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:QXLXSRMEYTU5IEGF6IXXFB3U76","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Lie Algebraic Theory of Barren Plateaus for Deep Parameterized Quantum Circuits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Alexander F. Kemper, Bojko N. Bakalov, Carlos Ortiz Marrero, Fr\\'ed\\'eric Sauvage, Martin Larocca, M. Cerezo, Michael Ragone","submitted_at":"2023-09-17T18:14:10Z","abstract_excerpt":"Variational quantum computing schemes train a loss function by sending an initial state through a parametrized quantum circuit, and measuring the expectation value of some operator. Despite their promise, the trainability of these algorithms is hindered by barren plateaus (BPs) induced by the expressiveness of the circuit, the entanglement of the input data, the locality of the observable, or the presence of noise. Up to this point, these sources of BPs have been regarded as independent. In this work, we present a general Lie algebraic theory that provides an exact expression for the variance "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.09342","kind":"arxiv","version":3},"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/2309.09342/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":"2026-07-05T09:02:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jbgLGXAblMh5LNpjP27YYIUMKN4sMe+P2ZiUi0BSPRWbwc3UTySBjySsfI4WwoG5YVyNESYrXAs8dyEeZ6svDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T05:11:32.021440Z"},"content_sha256":"13dfb8a8c17cd03c8cabaa4ee81d9c52f50bc1801e82c35d85e28168ffbe2f1e","schema_version":"1.0","event_id":"sha256:13dfb8a8c17cd03c8cabaa4ee81d9c52f50bc1801e82c35d85e28168ffbe2f1e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QXLXSRMEYTU5IEGF6IXXFB3U76/bundle.json","state_url":"https://pith.science/pith/QXLXSRMEYTU5IEGF6IXXFB3U76/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QXLXSRMEYTU5IEGF6IXXFB3U76/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":"2026-08-20T05:11:32Z","links":{"resolver":"https://pith.science/pith/QXLXSRMEYTU5IEGF6IXXFB3U76","bundle":"https://pith.science/pith/QXLXSRMEYTU5IEGF6IXXFB3U76/bundle.json","state":"https://pith.science/pith/QXLXSRMEYTU5IEGF6IXXFB3U76/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QXLXSRMEYTU5IEGF6IXXFB3U76/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:QXLXSRMEYTU5IEGF6IXXFB3U76","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":"5a7cb7316b9f3146e778224cb385d5aec948fe166ebf83ab809645ea0fc2a02d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2023-09-17T18:14:10Z","title_canon_sha256":"4b06868d6d8533f869f6b3da816e1b96670cbf602919b86e09dc66d4df73b7c3"},"schema_version":"1.0","source":{"id":"2309.09342","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.09342","created_at":"2026-07-05T09:02:13Z"},{"alias_kind":"arxiv_version","alias_value":"2309.09342v3","created_at":"2026-07-05T09:02:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.09342","created_at":"2026-07-05T09:02:13Z"},{"alias_kind":"pith_short_12","alias_value":"QXLXSRMEYTU5","created_at":"2026-07-05T09:02:13Z"},{"alias_kind":"pith_short_16","alias_value":"QXLXSRMEYTU5IEGF","created_at":"2026-07-05T09:02:13Z"},{"alias_kind":"pith_short_8","alias_value":"QXLXSRME","created_at":"2026-07-05T09:02:13Z"}],"graph_snapshots":[{"event_id":"sha256:13dfb8a8c17cd03c8cabaa4ee81d9c52f50bc1801e82c35d85e28168ffbe2f1e","target":"graph","created_at":"2026-07-05T09:02:13Z","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/2309.09342/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Variational quantum computing schemes train a loss function by sending an initial state through a parametrized quantum circuit, and measuring the expectation value of some operator. Despite their promise, the trainability of these algorithms is hindered by barren plateaus (BPs) induced by the expressiveness of the circuit, the entanglement of the input data, the locality of the observable, or the presence of noise. Up to this point, these sources of BPs have been regarded as independent. In this work, we present a general Lie algebraic theory that provides an exact expression for the variance ","authors_text":"Alexander F. Kemper, Bojko N. Bakalov, Carlos Ortiz Marrero, Fr\\'ed\\'eric Sauvage, Martin Larocca, M. Cerezo, Michael Ragone","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2023-09-17T18:14:10Z","title":"A Lie Algebraic Theory of Barren Plateaus for Deep Parameterized Quantum Circuits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.09342","kind":"arxiv","version":3},"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":"sha256:5522b1af03fc0315f9b9d14c87156d4182f7e47eb87f7441ec8998f6e2f0505e","target":"record","created_at":"2026-07-05T09:02:13Z","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":"5a7cb7316b9f3146e778224cb385d5aec948fe166ebf83ab809645ea0fc2a02d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2023-09-17T18:14:10Z","title_canon_sha256":"4b06868d6d8533f869f6b3da816e1b96670cbf602919b86e09dc66d4df73b7c3"},"schema_version":"1.0","source":{"id":"2309.09342","kind":"arxiv","version":3}},"canonical_sha256":"85d7794584c4e9d410c5f22f728774ffb6f12d0bc4a061ea8e63126bb7702df6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85d7794584c4e9d410c5f22f728774ffb6f12d0bc4a061ea8e63126bb7702df6","first_computed_at":"2026-07-05T09:02:13.016732Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:02:13.016732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1mSt+QBpSYPrNkfWG5D1Sdxw/Qs6xuM/zZRj2yqNaOcforUABTMr4yxf2ZeqA46AiGHJenLo+n8X7XdZvKapBw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:02:13.017238Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.09342","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5522b1af03fc0315f9b9d14c87156d4182f7e47eb87f7441ec8998f6e2f0505e","sha256:13dfb8a8c17cd03c8cabaa4ee81d9c52f50bc1801e82c35d85e28168ffbe2f1e"],"state_sha256":"be8fb34aab36318b63a4a672b353fa09d23456b386a469df5f48b176657ed105"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6bcMvdXjPjo3PFiY1tMcHOVTmxxBvGQIK6NdS9bR4cGE3bDaQIT/tf+aIe1fwgTgUfh+x6YO3JXFQW9CbrSKBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T05:11:32.025175Z","bundle_sha256":"e667fde3e796fa1ca82447047e829b748217c33b4c615d9d9b1f5ec8b85748e5"}}