{"as_of":"2026-08-13T17:04:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:b15db063dfabf5e67822220e34d3b1f5c5a4d94a81a73bf599b172d29e715d59","coverage":[{"denominator":17,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":17,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-04T09:25:13.943262Z","state":"measured"},{"denominator":17,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":17,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2608.02325/citation-record","integrity":"/paper/2608.02325/integrity","json":"/paper/2608.02325/citation-record.json","paper":"/paper/2608.02325"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T09:25:12.181807Z","title":"Finally, the state|χ f ⟩F is transformed into the desired probability-amplitude-encoded state|ψ f ⟩F by applying a tensor product ofdtwo-qubit gates","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.02325","last_updated":"2026-08-03T14:48:03Z","snapshot_observed_at":"2026-08-12T23:51:45.479682Z","submitted_at":"2026-08-03T14:48:03Z","title":"Learnable yet not simulable: a quantum resource theory of learning models","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-04T09:25:12.181807Z"},"links":{"citing_paper":"/paper/2608.02325"},"observation_digest":"sha256:deb59a8d2fc543e5735aa0d214f5ff474fd22d61490bfb1562b9cbc0138d94ad","observation_id":"958e0e5d-00ec-4925-a617-6fc1dfac7c5a","resolution":{"observed_at":"2026-08-04T09:25:12.181807Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T09:25:12.280979Z","title":"Sparse-Pauli block encoding of the observable We first construct the observable block encoding required for coherent expectation-value evaluation","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.02325","last_updated":"2026-08-03T14:48:03Z","snapshot_observed_at":"2026-08-12T23:51:45.479682Z","submitted_at":"2026-08-03T14:48:03Z","title":"Learnable yet not simulable: a quantum resource theory of learning models","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-04T09:25:12.280979Z"},"links":{"citing_paper":"/paper/2608.02325"},"observation_digest":"sha256:f32d51423ac7a7252d10abdeffb5c1b21e2124f1d9ef9b37f4aeb480062a266d","observation_id":"b15835ab-8a66-4fe2-9872-8b44c35ba0a8","resolution":{"observed_at":"2026-08-04T09:25:12.280979Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T09:25:12.384335Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.02325","last_updated":"2026-08-03T14:48:03Z","snapshot_observed_at":"2026-08-12T23:51:45.479682Z","submitted_at":"2026-08-03T14:48:03Z","title":"Learnable yet not simulable: a quantum resource theory of learning models","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-04T09:25:12.384335Z"},"links":{"citing_paper":"/paper/2608.02325"},"observation_digest":"sha256:7f2bf09fd274ee24514945684471d2153edd4e65cc53b9186e5b82260efa0c28","observation_id":"029bbcf3-1c55-4bb5-a7d0-fee1e44e6f48","resolution":{"observed_at":"2026-08-04T09:25:12.384335Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T09:25:12.493185Z","title":"Coherently controlled grid circuit","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.02325","last_updated":"2026-08-03T14:48:03Z","snapshot_observed_at":"2026-08-12T23:51:45.479682Z","submitted_at":"2026-08-03T14:48:03Z","title":"Learnable yet not simulable: a quantum resource theory of learning models","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-04T09:25:12.493185Z"},"links":{"citing_paper":"/paper/2608.02325"},"observation_digest":"sha256:e59b4ef0702340997f46ed38b51c875f58500d5a72083c00f672a878bf401367","observation_id":"dbee471b-8899-4582-bbc2-3318755cb6ba","resolution":{"observed_at":"2026-08-04T09:25:12.493185Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T09:25:12.601846Z","title":"r 2 3 f(α 0)− f(α 1) +f(α −1)√ 6 # = 1p3νf","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.02325","last_updated":"2026-08-03T14:48:03Z","snapshot_observed_at":"2026-08-12T23:51:45.479682Z","submitted_at":"2026-08-03T14:48:03Z","title":"Learnable yet not simulable: a quantum resource theory of learning models","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-04T09:25:12.601846Z"},"links":{"citing_paper":"/paper/2608.02325"},"observation_digest":"sha256:9d924ed28ed22cd1b2a9baf42a30eda1a9f1ebb6af1d1f06b1a208856a974705","observation_id":"258fe1b1-7b6a-41b0-b392-78e3ddd46f4d","resolution":{"observed_at":"2026-08-04T09:25:12.601846Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T09:25:12.708757Z","title":"Lemma 10 shows thatW f prepares the sampled expectation- value state|χ f ⟩in its good subspace with probabilityν f /∥a∥2","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.02325","last_updated":"2026-08-03T14:48:03Z","snapshot_observed_at":"2026-08-12T23:51:45.479682Z","submitted_at":"2026-08-03T14:48:03Z","title":"Learnable yet not simulable: a quantum resource theory of learning models","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-04T09:25:12.708757Z"},"links":{"citing_paper":"/paper/2608.02325"},"observation_digest":"sha256:ef2b47b6d914fb65bfd31c2a7afca4f02d91bb8928e83c7fb213841edf088df7","observation_id":"d9ec7ca2-859e-4fb7-a523-69bfbf723aa6","resolution":{"observed_at":"2026-08-04T09:25:12.708757Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T09:25:12.789417Z","title":"Reinitializing all registers makes repeated outcomes independent, and retaining their distinct values gives|Λ q| ≤mf","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.02325","last_updated":"2026-08-03T14:48:03Z","snapshot_observed_at":"2026-08-12T23:51:45.479682Z","submitted_at":"2026-08-03T14:48:03Z","title":"Learnable yet not simulable: a quantum resource theory of learning models","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-04T09:25:12.789417Z"},"links":{"citing_paper":"/paper/2608.02325"},"observation_digest":"sha256:6018bd6e0c808774d20fede16710d70fc08d2ff0671d4ead6e716ecdbba211ff","observation_id":"5f8b45fb-fb34-4489-bda7-2b1850adeb41","resolution":{"observed_at":"2026-08-04T09:25:12.789417Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T09:25:12.871862Z","title":"(F9) and completes the proof","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.02325","last_updated":"2026-08-03T14:48:03Z","snapshot_observed_at":"2026-08-12T23:51:45.479682Z","submitted_at":"2026-08-03T14:48:03Z","title":"Learnable yet not simulable: a quantum resource theory of learning models","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-04T09:25:12.871862Z"},"links":{"citing_paper":"/paper/2608.02325"},"observation_digest":"sha256:8bff42a19fb8db61024f2fc960d4af263f798a29bd6d7d4f296f7337a8633a26","observation_id":"ef535ae3-7579-488e-b746-a9c7ce2d070c","resolution":{"observed_at":"2026-08-04T09:25:12.871862Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T09:25:12.958249Z","title":"Lemma 14.Letp(ω) = 2 −∥ω∥0 Tr(ρ0Qω)2/νf be a probability distribution induced by the circuit expectationf(x) = Tr(ρ0U(x) †OU(x))over the frequencyω∈ {0,1,−1} d","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.02325","last_updated":"2026-08-03T14:48:03Z","snapshot_observed_at":"2026-08-12T23:51:45.479682Z","submitted_at":"2026-08-03T14:48:03Z","title":"Learnable yet not simulable: a quantum resource theory of learning models","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-04T09:25:12.958249Z"},"links":{"citing_paper":"/paper/2608.02325"},"observation_digest":"sha256:b3a5461d24c31bd41d09be23e1d7b909a6a2514b7ecc4ba71b6f99d61a531afd","observation_id":"6ff214e7-ce74-4451-9237-fd88529a26b5","resolution":{"observed_at":"2026-08-04T09:25:12.958249Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T09:25:13.058717Z","title":"[60], the core of the proof is to show that theDSE-guided classical surrogateh q(x) in Eq","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.02325","last_updated":"2026-08-03T14:48:03Z","snapshot_observed_at":"2026-08-12T23:51:45.479682Z","submitted_at":"2026-08-03T14:48:03Z","title":"Learnable yet not simulable: a quantum resource theory of learning models","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-04T09:25:13.058717Z"},"links":{"citing_paper":"/paper/2608.02325"},"observation_digest":"sha256:925f0e9437fd9e0222d6e3a62a8b80be008921c5a280df6c7c1f94034eec4f27","observation_id":"fde9a66d-3244-4813-b646-113319fbe58d","resolution":{"observed_at":"2026-08-04T09:25:13.058717Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T09:25:13.194439Z","title":"First, letX:=−log(p(ω)), whereω∈ {0,1,−1} d follows the distribution p(ω)","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.02325","last_updated":"2026-08-03T14:48:03Z","snapshot_observed_at":"2026-08-12T23:51:45.479682Z","submitted_at":"2026-08-03T14:48:03Z","title":"Learnable yet not simulable: a quantum resource theory of learning models","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-04T09:25:13.194439Z"},"links":{"citing_paper":"/paper/2608.02325"},"observation_digest":"sha256:64b2f787407510a4df91eaf9ce2e542d773e7d9128c6775267c768dcabaefd19","observation_id":"2c42b37d-7ae1-4f70-870d-c7a592c2d1ca","resolution":{"observed_at":"2026-08-04T09:25:13.194439Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T09:25:13.318834Z","title":"In this regard, we first recall theBQPcomplexity class","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.02325","last_updated":"2026-08-03T14:48:03Z","snapshot_observed_at":"2026-08-12T23:51:45.479682Z","submitted_at":"2026-08-03T14:48:03Z","title":"Learnable yet not simulable: a quantum resource theory of learning models","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-04T09:25:13.318834Z"},"links":{"citing_paper":"/paper/2608.02325"},"observation_digest":"sha256:c97e58ef53657e2bba4e366e3bec164e8d473f9b7d424052448934eb9ea44ccb","observation_id":"0da2a8ff-4467-4598-a16a-b8b5a33ff45c","resolution":{"observed_at":"2026-08-04T09:25:13.318834Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T09:25:13.426752Z","title":"Proof of Lemma 15.This proof consists of two parts, which separately derive the product form off ℓ(x) given the evolved observableO(x, Uℓ) =U † ℓ (x)OUℓ(x) defined in Eq","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.02325","last_updated":"2026-08-03T14:48:03Z","snapshot_observed_at":"2026-08-12T23:51:45.479682Z","submitted_at":"2026-08-03T14:48:03Z","title":"Learnable yet not simulable: a quantum resource theory of learning models","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-04T09:25:13.426752Z"},"links":{"citing_paper":"/paper/2608.02325"},"observation_digest":"sha256:506cd29bf2e762a02f8cec386622669bd79543079244a5bb813bfe505c8eeef3","observation_id":"29428bb3-fc2c-4a86-9034-31f622b8950b","resolution":{"observed_at":"2026-08-04T09:25:13.426752Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T09:25:13.530500Z","title":"We first describe the learning-based surrogates and classical simulation methods considered in the benchmarks, and then specify the metric used to evaluate their performance","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.02325","last_updated":"2026-08-03T14:48:03Z","snapshot_observed_at":"2026-08-12T23:51:45.479682Z","submitted_at":"2026-08-03T14:48:03Z","title":"Learnable yet not simulable: a quantum resource theory of learning models","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-04T09:25:13.530500Z"},"links":{"citing_paper":"/paper/2608.02325"},"observation_digest":"sha256:41970c5d0cce295a8ecef9f973ddc0655b5e8c3c14e830db3ae7b9802dcd6acd","observation_id":"99645864-a06c-4d12-bbdb-25b9fab9ca3f","resolution":{"observed_at":"2026-08-04T09:25:13.530500Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T09:25:13.696717Z","title":"In this section, we complement the random-circuit experiments conducted in Fig","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.02325","last_updated":"2026-08-03T14:48:03Z","snapshot_observed_at":"2026-08-12T23:51:45.479682Z","submitted_at":"2026-08-03T14:48:03Z","title":"Learnable yet not simulable: a quantum resource theory of learning models","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-04T09:25:13.696717Z"},"links":{"citing_paper":"/paper/2608.02325"},"observation_digest":"sha256:490098331dacc9d240a4bfab99d17e6d5565d5656728328ce7e05142bb661927","observation_id":"657a2c14-30a1-4197-ab56-87171edae768","resolution":{"observed_at":"2026-08-04T09:25:13.696717Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T09:25:13.841352Z","title":"3 by further separating the effect of the system sizes and the number of rotation gates, the latter of which controls theDSEof the considered circuit","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.02325","last_updated":"2026-08-03T14:48:03Z","snapshot_observed_at":"2026-08-12T23:51:45.479682Z","submitted_at":"2026-08-03T14:48:03Z","title":"Learnable yet not simulable: a quantum resource theory of learning models","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-04T09:25:13.841352Z"},"links":{"citing_paper":"/paper/2608.02325"},"observation_digest":"sha256:47c50f0fab96ea7bb014452252b873a62725601dcbd533dae904c7d10d6eacfe","observation_id":"48aea026-27d0-453b-96aa-d08822c81d65","resolution":{"observed_at":"2026-08-04T09:25:13.841352Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T09:25:13.943262Z","title":"In the following, we first introduce how to use the classical surrogate to pre-train variational quantum eigensolvers, and then introduce the numerical settings and results","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.02325","last_updated":"2026-08-03T14:48:03Z","snapshot_observed_at":"2026-08-12T23:51:45.479682Z","submitted_at":"2026-08-03T14:48:03Z","title":"Learnable yet not simulable: a quantum resource theory of learning models","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-04T09:25:13.943262Z"},"links":{"citing_paper":"/paper/2608.02325"},"observation_digest":"sha256:1a6341f0749667c4060211a352062ca10f05944c61c184ad53af7203b5740b9c","observation_id":"559fb9db-7045-4c24-9818-009f00405a8e","resolution":{"observed_at":"2026-08-04T09:25:13.943262Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2608.02325","last_updated":"2026-08-03T14:48:03Z","latest_version":1,"primary_category":"quant-ph","snapshot_observed_at":"2026-08-12T23:51:45.479682Z","submitted_at":"2026-08-03T14:48:03Z","title":"Learnable yet not simulable: a quantum resource theory of learning models"},"reference_resolution":{"displayed":17,"state_counts":{"malformed_identifier":1,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":16,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":17},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 17 of 17 outbound references and 0 inbound Pith citation observations for arXiv:2608.02325."}