{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:Y2AAFKTINEYQ2ETUGSNLYNAYZ7","short_pith_number":"pith:Y2AAFKTI","canonical_record":{"source":{"id":"2110.05517","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"quant-ph","submitted_at":"2021-10-11T18:00:20Z","cross_cats_sorted":["cs.CC","cs.LG","stat.ML"],"title_canon_sha256":"a586f4b62de9309c8e3c98d61c2efef018db34fb5e1d23b78f571bd70607c420","abstract_canon_sha256":"0dab3b362826a399741a9b8317f83720e9879c5b05f9c9e96b7d053474a233ee"},"schema_version":"1.0"},"canonical_sha256":"c68002aa6869310d1274349abc3418cfc398672732b741c3fb802a03db381b4f","source":{"kind":"arxiv","id":"2110.05517","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.05517","created_at":"2026-07-05T03:22:03Z"},{"alias_kind":"arxiv_version","alias_value":"2110.05517v1","created_at":"2026-07-05T03:22:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.05517","created_at":"2026-07-05T03:22:03Z"},{"alias_kind":"pith_short_12","alias_value":"Y2AAFKTINEYQ","created_at":"2026-07-05T03:22:03Z"},{"alias_kind":"pith_short_16","alias_value":"Y2AAFKTINEYQ2ETU","created_at":"2026-07-05T03:22:03Z"},{"alias_kind":"pith_short_8","alias_value":"Y2AAFKTI","created_at":"2026-07-05T03:22:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:Y2AAFKTINEYQ2ETUGSNLYNAYZ7","target":"record","payload":{"canonical_record":{"source":{"id":"2110.05517","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"quant-ph","submitted_at":"2021-10-11T18:00:20Z","cross_cats_sorted":["cs.CC","cs.LG","stat.ML"],"title_canon_sha256":"a586f4b62de9309c8e3c98d61c2efef018db34fb5e1d23b78f571bd70607c420","abstract_canon_sha256":"0dab3b362826a399741a9b8317f83720e9879c5b05f9c9e96b7d053474a233ee"},"schema_version":"1.0"},"canonical_sha256":"c68002aa6869310d1274349abc3418cfc398672732b741c3fb802a03db381b4f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:22:03.692890Z","signature_b64":"TRrUZ5xMbxLbkf4VmTvi/sSMT6Hesr99vNlNODh5ZOLuoNhg2hzptJcgYel4nAUx7uGZR078tU1ju87/WPZmAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c68002aa6869310d1274349abc3418cfc398672732b741c3fb802a03db381b4f","last_reissued_at":"2026-07-05T03:22:03.692390Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:22:03.692390Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2110.05517","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":"2026-07-05T03:22:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jJZyszfnWDVerLJwqrY8gz1t0zqrBC5XBp6SP33Y6rGM7d+7pEQuHsolL/xtSL18hmLasBryhdKLhsfZ6qi6Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T09:30:39.509848Z"},"content_sha256":"a7f350809f7a61ba28594d92d21687e48e82771b1bc1796db5f92b3e728a971a","schema_version":"1.0","event_id":"sha256:a7f350809f7a61ba28594d92d21687e48e82771b1bc1796db5f92b3e728a971a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:Y2AAFKTINEYQ2ETUGSNLYNAYZ7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Learnability of the output distributions of local quantum circuits","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.CC","cs.LG","stat.ML"],"primary_cat":"quant-ph","authors_text":"Alexander Nietner, Dominik Hangleiter, Jean-Pierre Seifert, Jens Eisert, Jonas Haferkamp, Marcel Hinsche, Marios Ioannou, Ryan Sweke, Yihui Quek","submitted_at":"2021-10-11T18:00:20Z","abstract_excerpt":"There is currently a large interest in understanding the potential advantages quantum devices can offer for probabilistic modelling. In this work we investigate, within two different oracle models, the probably approximately correct (PAC) learnability of quantum circuit Born machines, i.e., the output distributions of local quantum circuits. We first show a negative result, namely, that the output distributions of super-logarithmic depth Clifford circuits are not sample-efficiently learnable in the statistical query model, i.e., when given query access to empirical expectation values of bounde"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.05517","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/2110.05517/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":"2026-07-05T03:22:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LEsTDPB/qDQHmXwVFYJ7Nnkpo+Zs3INJt/twFbBZSo0G2dxThr9CztTTfDdh1lfNxj0D+PN4qCj09oiIJBHwCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T09:30:39.510744Z"},"content_sha256":"bb6b4fcb2ce3ad991fa8299e96a17e96b246971d29e11a82be72d07653a1fdc9","schema_version":"1.0","event_id":"sha256:bb6b4fcb2ce3ad991fa8299e96a17e96b246971d29e11a82be72d07653a1fdc9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y2AAFKTINEYQ2ETUGSNLYNAYZ7/bundle.json","state_url":"https://pith.science/pith/Y2AAFKTINEYQ2ETUGSNLYNAYZ7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y2AAFKTINEYQ2ETUGSNLYNAYZ7/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":"2026-08-13T09:30:39Z","links":{"resolver":"https://pith.science/pith/Y2AAFKTINEYQ2ETUGSNLYNAYZ7","bundle":"https://pith.science/pith/Y2AAFKTINEYQ2ETUGSNLYNAYZ7/bundle.json","state":"https://pith.science/pith/Y2AAFKTINEYQ2ETUGSNLYNAYZ7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y2AAFKTINEYQ2ETUGSNLYNAYZ7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:Y2AAFKTINEYQ2ETUGSNLYNAYZ7","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":"0dab3b362826a399741a9b8317f83720e9879c5b05f9c9e96b7d053474a233ee","cross_cats_sorted":["cs.CC","cs.LG","stat.ML"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"quant-ph","submitted_at":"2021-10-11T18:00:20Z","title_canon_sha256":"a586f4b62de9309c8e3c98d61c2efef018db34fb5e1d23b78f571bd70607c420"},"schema_version":"1.0","source":{"id":"2110.05517","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.05517","created_at":"2026-07-05T03:22:03Z"},{"alias_kind":"arxiv_version","alias_value":"2110.05517v1","created_at":"2026-07-05T03:22:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.05517","created_at":"2026-07-05T03:22:03Z"},{"alias_kind":"pith_short_12","alias_value":"Y2AAFKTINEYQ","created_at":"2026-07-05T03:22:03Z"},{"alias_kind":"pith_short_16","alias_value":"Y2AAFKTINEYQ2ETU","created_at":"2026-07-05T03:22:03Z"},{"alias_kind":"pith_short_8","alias_value":"Y2AAFKTI","created_at":"2026-07-05T03:22:03Z"}],"graph_snapshots":[{"event_id":"sha256:bb6b4fcb2ce3ad991fa8299e96a17e96b246971d29e11a82be72d07653a1fdc9","target":"graph","created_at":"2026-07-05T03:22:03Z","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/2110.05517/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"There is currently a large interest in understanding the potential advantages quantum devices can offer for probabilistic modelling. In this work we investigate, within two different oracle models, the probably approximately correct (PAC) learnability of quantum circuit Born machines, i.e., the output distributions of local quantum circuits. We first show a negative result, namely, that the output distributions of super-logarithmic depth Clifford circuits are not sample-efficiently learnable in the statistical query model, i.e., when given query access to empirical expectation values of bounde","authors_text":"Alexander Nietner, Dominik Hangleiter, Jean-Pierre Seifert, Jens Eisert, Jonas Haferkamp, Marcel Hinsche, Marios Ioannou, Ryan Sweke, Yihui Quek","cross_cats":["cs.CC","cs.LG","stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"quant-ph","submitted_at":"2021-10-11T18:00:20Z","title":"Learnability of the output distributions of local quantum circuits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.05517","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:a7f350809f7a61ba28594d92d21687e48e82771b1bc1796db5f92b3e728a971a","target":"record","created_at":"2026-07-05T03:22:03Z","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":"0dab3b362826a399741a9b8317f83720e9879c5b05f9c9e96b7d053474a233ee","cross_cats_sorted":["cs.CC","cs.LG","stat.ML"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"quant-ph","submitted_at":"2021-10-11T18:00:20Z","title_canon_sha256":"a586f4b62de9309c8e3c98d61c2efef018db34fb5e1d23b78f571bd70607c420"},"schema_version":"1.0","source":{"id":"2110.05517","kind":"arxiv","version":1}},"canonical_sha256":"c68002aa6869310d1274349abc3418cfc398672732b741c3fb802a03db381b4f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c68002aa6869310d1274349abc3418cfc398672732b741c3fb802a03db381b4f","first_computed_at":"2026-07-05T03:22:03.692390Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:22:03.692390Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TRrUZ5xMbxLbkf4VmTvi/sSMT6Hesr99vNlNODh5ZOLuoNhg2hzptJcgYel4nAUx7uGZR078tU1ju87/WPZmAA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:22:03.692890Z","signed_message":"canonical_sha256_bytes"},"source_id":"2110.05517","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a7f350809f7a61ba28594d92d21687e48e82771b1bc1796db5f92b3e728a971a","sha256:bb6b4fcb2ce3ad991fa8299e96a17e96b246971d29e11a82be72d07653a1fdc9"],"state_sha256":"447d9d6703017a982840377b59c822242c6320b382375dff76190eb766d5433f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LTN3gVdee8FmGovFdjjvMCGT1wH1cMCMoq5KoaNwIxeTnbtwMJvfjzB7/OmYIYDmVz4QX4lK4tReP1o33c/yBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T09:30:39.521755Z","bundle_sha256":"d135218e11f780d3a4a7f3d048b8aa6fc2e2b28edd7a386250eda6ae0181335d"}}