{"as_of":"2026-08-14T08:09:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:897b056c96c80f6743bfbec6231b58f1ce887343d2ba30c4f9052400ef4d87d3","coverage":[{"denominator":54,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":54,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-04T18:59:22.126154Z","state":"measured"},{"denominator":54,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":54,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-14T06:32:32.682623+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/2509.09642/citation-record","integrity":"/paper/2509.09642/integrity","json":"/paper/2509.09642/citation-record.json","paper":"/paper/2509.09642"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T18:59:14.428597Z","title":"Quantum Computing in the NISQ era and beyond","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:14.428597Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:e2f1b8f244e24d11f620e68066016c94b84bdf3ed4be6a0272980b6b5c915f9c","observation_id":"3ddf95f6-5cc7-44ca-bfea-26ed6aa2d5da","resolution":{"observed_at":"2026-08-04T18:59:14.428597Z","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":"2026-08-04T18:59:14.496670Z","title":"A fast quantum mechanical algorithm for database search","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:14.496670Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:637cf7b18c660f037ceef4b000cb31dd10ffdba8e61167e965edddb1c4cf6dec","observation_id":"ff798ab5-d7f3-478c-b8ed-37b266422aa1","resolution":{"observed_at":"2026-08-04T18:59:14.496670Z","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":"2026-08-04T18:59:14.599121Z","title":"Polynomial-time algorithms for prime factorization and discrete loga- rithms on a quantum computer","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:14.599121Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:9f9ec726a4da0691753f620ea02a9fea317a00ac34e5d5cd547ca9514cd9879e","observation_id":"c4ee69d4-ce5b-4a7e-91be-7ccc929a0f7c","resolution":{"observed_at":"2026-08-04T18:59:14.599121Z","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":"2026-08-04T18:59:14.690196Z","title":"Quantum algorithm for linear systems of equations","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:14.690196Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:d629fc0c4901bdcf2aa11745c8e5478925dd4acd08bf1612b2d976280edb624b","observation_id":"99822bde-0e2b-4067-93ef-74f99425672a","resolution":{"observed_at":"2026-08-04T18:59:14.690196Z","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":"2026-08-04T18:59:14.787904Z","title":"Noisy intermediate-scale quantum algorithms","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:14.787904Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:f7cdfeb87e2e98559066d6508f4665b06d8fc4c3a895d6839880dcb14f968575","observation_id":"e0536db2-2e03-4da3-8892-342d5703f939","resolution":{"observed_at":"2026-08-04T18:59:14.787904Z","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":"2026-08-04T18:59:14.882833Z","title":"Shallowquantumcircuits: Algorithms, complexity, andfaulttolerance","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:14.882833Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:a91059d947f65428f13ba4ae106bd4d0a23508a47e1e0da7291c5cb967a20613","observation_id":"b2f2ca85-9834-4bc3-8166-acf97d0a3121","resolution":{"observed_at":"2026-08-04T18:59:14.882833Z","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":"2026-08-04T18:59:14.985474Z","title":"Quantum advantage with shallow circuits","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:14.985474Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:63a19f4848328bec226249f5220238022419c5964b616bffe1d2c867f4f94b36","observation_id":"76b0fc00-3f55-4e68-983c-9669abe42715","resolution":{"observed_at":"2026-08-04T18:59:14.985474Z","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":"2026-08-04T18:59:15.088817Z","title":"Exponential separation between shallow quantum circuits and unbounded fan-in shallow classical circuits","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:15.088817Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:a6a9aab15c91af6b686e199bab4237e3b886aee611433ec2d1ee5c16a1eb38bc","observation_id":"1543aa53-a3db-41d7-bd16-ed554937d237","resolution":{"observed_at":"2026-08-04T18:59:15.088817Z","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":"2026-08-04T18:59:15.186923Z","title":"Delegating private quantum computations","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:15.186923Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:9310cd570161fa2525440095d45a11bdb5659b36ad302995e265d723f848fdca","observation_id":"cebd26d0-ba26-47b3-9e0a-05d4e226d8a2","resolution":{"observed_at":"2026-08-04T18:59:15.186923Z","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":"2026-08-04T18:59:15.289457Z","title":"A one-query lower bound for unitary synthesis and breaking quantum cryptography","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:15.289457Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:bb068ba05f953ed52889135143057d7533e72eeedabcd26b3065edb1fc673a39","observation_id":"f14d15d8-49d0-4f05-8317-2e4579ccceae","resolution":{"observed_at":"2026-08-04T18:59:15.289457Z","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":"2026-08-04T18:59:15.395922Z","title":"Programmable quantum gate arrays","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:15.395922Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:4e782871745896c3dda54656c5462c001baf8be0ebdb13601c9af69bd4bec63b","observation_id":"63f97500-bc5a-4cd6-94bd-075280cb8266","resolution":{"observed_at":"2026-08-04T18:59:15.395922Z","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":"2026-08-04T18:59:15.493996Z","title":"Probabilistic implementation of universal quantum processors","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:15.493996Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:b0e720ed69243d931146bcc24360b064b6ab156f3710e2999b8d426477e1e3a8","observation_id":"f32c556b-e915-4032-8952-4a9b35c8cd69","resolution":{"observed_at":"2026-08-04T18:59:15.493996Z","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":"2026-08-04T18:59:15.596984Z","title":"Measurement-based quantum computation beyond the one-way model","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:15.596984Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:1fd3d9a815504de356d9d2401252be7be85104090ad28577aeee228983041c9e","observation_id":"55f809d2-1988-46f9-8bd7-683d7b4355ad","resolution":{"observed_at":"2026-08-04T18:59:15.596984Z","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":"2026-08-04T18:59:15.711962Z","title":"Asymptotic teleportation scheme as a uni- versal programmable quantum processor","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:15.711962Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:d3e4e6933cb21cc15b86d9055e0a24ef31f911d001d67d9d2a6e8721acb25d20","observation_id":"0693fdd8-2b4d-4fac-b292-cede79564ee7","resolution":{"observed_at":"2026-08-04T18:59:15.711962Z","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":"2026-08-04T18:59:15.806484Z","title":"Resource quan- tification for the no-programing theorem","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:15.806484Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:5c71df324f462c93731b204d3307d96571511b3a87bbc4285d15168b702f729c","observation_id":"2316c581-c1d3-43da-8f6f-6f4cb9d4964e","resolution":{"observed_at":"2026-08-04T18:59:15.806484Z","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":"2026-08-04T18:59:15.903929Z","title":"Optimal universal program- ming of unitary gates","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:15.903929Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:71c5bdb5534617e932dc373c14040c0066fd584c75435bf4239f78fd02cc7dbd","observation_id":"a7eeb86e-b05e-4a63-a8be-5b294bf78db4","resolution":{"observed_at":"2026-08-04T18:59:15.903929Z","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":"2026-08-04T18:59:15.976309Z","title":"Programmability of covariant quantum channels","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:15.976309Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:cae284ce68b2e6521b7e547072078b298fb07e5831ddd0a4b9dc1bbb63f3d4d2","observation_id":"efa334dd-e1c3-474c-9dd0-9b23aadb9a0f","resolution":{"observed_at":"2026-08-04T18:59:15.976309Z","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":"2026-08-04T18:59:16.095660Z","title":"Port-Based State Preparation and Appli- cations","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:16.095660Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:ace1aed07dd919a15df853364135c583e50a7df193b585565f7ffc9205b0df44","observation_id":"66b9f84d-82dd-46e3-9e48-e4b6f85b4c15","resolution":{"observed_at":"2026-08-04T18:59:16.095660Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2507.10784","last_updated":"2026-04-17T07:38:57Z","snapshot_observed_at":"2026-08-01T16:33:33.147819Z","submitted_at":"2025-07-14T20:18:12Z","title":"Quantum Advantage in Storage and Retrieval of Isometry Channels","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.10784","snapshot_observed_at":"2026-08-04T18:59:16.169426Z","title":"Quantum advantage in storage and retrieval of isometry channels","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:16.169426Z"},"links":{"cited_paper":"/paper/2507.10784","citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:f07d74824492acbc2a210b7a29204b807ab1d50c8813075d89e47a010e93f56c","observation_id":"ab25b236-d728-4fb4-9284-7ecf10e2c278","resolution":{"observed_at":"2026-08-04T18:59:16.169426Z","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":"2026-08-04T18:59:16.313786Z","title":"Computational complexity: A modern approach","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:16.313786Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:b45b9409ff1725f0ead10552759f05784a9ef3339219dfdb5c344bbd00521be2","observation_id":"c301107f-14bc-4da4-83d4-0387c33aeb6b","resolution":{"observed_at":"2026-08-04T18:59:16.313786Z","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":"2026-08-04T18:59:16.467181Z","title":"Linear growth of quantum circuit complexity","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:16.467181Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:c331a6d6c4f189ce702bd0498b6d9d0fd898abad9f67f87df15ecb025afdb263","observation_id":"9186b78e-d999-4e94-847f-b157c37f960d","resolution":{"observed_at":"2026-08-04T18:59:16.467181Z","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":"2026-08-04T18:59:16.681767Z","title":"Approximatet-designs in generic circuit architectures","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:16.681767Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:46616f10042e1ffe6b90903e1799ce47e8950535e51908114e1825bd0a8ea3e9","observation_id":"e3166fa6-6190-49ff-b980-837a994d6840","resolution":{"observed_at":"2026-08-04T18:59:16.681767Z","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":"2026-08-04T18:59:16.820050Z","title":"Learning quantum states and unitaries of bounded gate complex- ity","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:16.820050Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:10e81676a8ec2c04e8c65ad6c2090b240c9c2363cbdca79ccf79b54f60bda7d5","observation_id":"a522ef84-d1e7-4715-b1a5-040879f73f88","resolution":{"observed_at":"2026-08-04T18:59:16.820050Z","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":"2026-08-04T18:59:17.022362Z","title":"Learning shallow quantum circuits","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:17.022362Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:11cfb0871ae59b22a744593ed7999813b8e6bc8ab434a9480a596fddbcce891e","observation_id":"056b952a-b2e9-42b9-a758-64d9233ed0b8","resolution":{"observed_at":"2026-08-04T18:59:17.022362Z","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":"2026-08-04T18:59:17.089399Z","title":"Compression of quantum shallow-circuit states","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:17.089399Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:bcbcce73ca0e092980aa0979053640adfbeca929237ad98663a13c5f6b4455af","observation_id":"50821610-4a75-4ac6-969d-7707238e377d","resolution":{"observed_at":"2026-08-04T18:59:17.089399Z","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":"2026-08-04T18:59:17.187779Z","title":"Quantum computation and quantum infor- mation: 10th anniversary edition","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:17.187779Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:c3e95f7341f11f6ee3e9a21774b061e36f2d5c39caa55335e52f26dfd69632c2","observation_id":"6ae1b8bb-e77b-4c35-9a03-93862edd5333","resolution":{"observed_at":"2026-08-04T18:59:17.187779Z","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":"2026-08-04T18:59:17.320003Z","title":"On the pauli spectrum ofQAC0","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:17.320003Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:bda6492a5d39e86c8b622e68877220482b2dc3418d1d286a3a0d125ab57f4d26","observation_id":"84ae3a4a-0377-4fe3-af18-cb20c91d81d8","resolution":{"observed_at":"2026-08-04T18:59:17.320003Z","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":"2026-08-04T18:59:17.449122Z","title":"Symmetry, representations, and invariants","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:17.449122Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:ae851ad8169078a8ac4acde2e71316ba8dfffe98304ca7a6641f013d7b2ee438","observation_id":"ca570eef-bfac-4b9f-8ac4-85d34a4796a8","resolution":{"observed_at":"2026-08-04T18:59:17.449122Z","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":"2026-08-04T18:59:17.638376Z","title":"Applications of coherent classical communication and the schur transform to quantum information theory","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:17.638376Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:3cf5b14ad26db7e506b67d6299be3ce1a7718aefd800c05a9afd97825351750a","observation_id":"3be07542-525c-4931-8b70-067464bb01e9","resolution":{"observed_at":"2026-08-04T18:59:17.638376Z","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":"2026-08-04T18:59:17.817716Z","title":"Simple Con- structions of Linear-Depth t-Designs and Pseudorandom Unitaries","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:17.817716Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:a56c6ed65431ba3f79c6b1ff4218d9fe7b802740aac8978c53169dd6c791522c","observation_id":"c3ce7935-3145-4999-81ed-e49cf41360d4","resolution":{"observed_at":"2026-08-04T18:59:17.817716Z","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":"2026-08-04T18:59:18.167668Z","title":"Exact and approximate unitary 2-designs and their application to fidelity estimation","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:18.167668Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:aee927f5182f5806b954f3616e7acdec3d4ac0d650011a73187a88ba1e405489","observation_id":"50524999-5ca6-41a2-a5d8-cc03fd2d8de7","resolution":{"observed_at":"2026-08-04T18:59:18.167668Z","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":"2026-08-04T18:59:18.416198Z","title":"Optimal quantum learning of a unitary transformation","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:18.416198Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:3fcba0ecbb84cb9a9fd42a394deaf230dcea359aa3c341573a4ef488080dbad8","observation_id":"0430f2cb-08bb-4acf-88d0-8e8ff366f3cf","resolution":{"observed_at":"2026-08-04T18:59:18.416198Z","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":"2026-08-04T18:59:18.627573Z","title":"Scalable noise estimation with random unitary operators","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:18.627573Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:b8ecf804f14c58170f795a3227653b55018e8efdb620e0664d96ad6be08e1419","observation_id":"dc080732-36e3-491f-b464-92cf3f1c0c13","resolution":{"observed_at":"2026-08-04T18:59:18.627573Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"quant-ph/0208112","last_updated":"2002-08-15T23:00:04Z","snapshot_observed_at":"2026-08-11T09:53:13.384216Z","submitted_at":"2002-08-15T23:00:04Z","title":"Creating superpositions that correspond to efficiently integrable probability distributions","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"quant-ph/0208112","snapshot_observed_at":"2026-08-04T18:59:18.781520Z","title":"Creating superpositions that correspond to efficiently integrable probability distributions","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:18.781520Z"},"links":{"cited_paper":"/paper/quant-ph/0208112","citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:786e661d45179a910296a4813ac579509bc8c074d9c099ae2496dbfd81914d7e","observation_id":"a26557fa-c5a1-4ed5-8978-7561708bc024","resolution":{"observed_at":"2026-08-04T18:59:18.781520Z","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":"2026-08-04T18:59:18.912781Z","title":"An efficient high dimensional quantum Schur transform","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:18.912781Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:8d281998eb28d98dc6631c5f73bf947b5ca8a26faabe0954adfc212a7eb11746","observation_id":"6dbc155e-f147-4625-8ae6-f8295b5b2f0f","resolution":{"observed_at":"2026-08-04T18:59:18.912781Z","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":"2026-08-04T18:59:19.108909Z","title":"Quantum state preparation with optimal circuit depth: Implementations and applications","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:19.108909Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:4739798ad9ca2f28c14674d30f394536090d4f1266b9a2e7d0beebb2dcc2a866","observation_id":"a631a203-0c46-4f7c-a682-1247faad0be2","resolution":{"observed_at":"2026-08-04T18:59:19.108909Z","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":"2026-08-04T18:59:19.282665Z","title":"Approximate unitary t-designs by short ran- dom quantum circuits using nearest-neighbor and long-range gates","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:19.282665Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:6a690117835e7cd2558a5c9bdff9d99607fdbe6574f58455c456c90389130285","observation_id":"e7659a31-dec4-45b0-9efe-77ed09b41623","resolution":{"observed_at":"2026-08-04T18:59:19.282665Z","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":"2026-08-04T18:59:19.451070Z","title":"Efficient approximate unitary designs from random pauli rotations","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:19.451070Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:936d156fe05669d2a7f096b99a9709b2dc720da63b5a7808a3b28df7df07b801","observation_id":"8a6dd2c3-4786-47d6-9769-7fcf41696556","resolution":{"observed_at":"2026-08-04T18:59:19.451070Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2406.07478","last_updated":"2024-12-02T16:47:22Z","snapshot_observed_at":"2026-08-12T23:45:20.226697Z","submitted_at":"2024-06-11T17:23:16Z","title":"Incompressibility and spectral gaps of random circuits","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2406.07478","snapshot_observed_at":"2026-08-04T18:59:19.661409Z","title":"Incompressibility and spectral gaps of random circuits","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:19.661409Z"},"links":{"cited_paper":"/paper/2406.07478","citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:ab306bd179c0ab2598e905c8f3f1c8d07b5b4a6908d4b6da5dad8de3da1ef0d1","observation_id":"4aa6bc20-4e26-439d-b820-8f1d897003d5","resolution":{"observed_at":"2026-08-04T18:59:19.661409Z","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":"2026-08-04T18:59:19.829234Z","title":"Random unitaries in extremely low depth","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:19.829234Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:35f4e2e576fe8e3f4993026304f256c475e00dad7d15f36096bda22fabf1253b","observation_id":"389dccd9-2502-4376-8f8e-113397fa846d","resolution":{"observed_at":"2026-08-04T18:59:19.829234Z","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":"2026-08-04T18:59:19.994606Z","title":"Optimal estimation of group transformations using entanglement","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:19.994606Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:a3da96933335b7d0c007d990d8716ce9201e332494efa0c040eeb137d9e14e44","observation_id":"377a17be-f160-458a-a948-ffb5ef27ee3e","resolution":{"observed_at":"2026-08-04T18:59:19.994606Z","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":"2026-08-04T18:59:20.131146Z","title":"Query-optimal estimation of unitary channels in diamond distance","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:20.131146Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:08064b632b401572a38f081248776b52a26a9cc0fbef24f6850deeb0f09eadb7","observation_id":"ce062aba-ae4d-486e-b236-afb47e2dd2a3","resolution":{"observed_at":"2026-08-04T18:59:20.131146Z","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":"2026-08-04T18:59:20.325573Z","title":"Synthesis of quantum logic circuits","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:20.325573Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:3125368be2247a09c694f7e83cb81865a7d3c81f682de45b1d225117b4e3ca6c","observation_id":"b97cc8f0-56fd-4a3a-8f37-ae6dba7ef9e4","resolution":{"observed_at":"2026-08-04T18:59:20.325573Z","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":"2026-08-04T18:59:20.541021Z","title":"Classical and quantum computation","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:20.541021Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:2c443a9d0cfdce694f148ce73c7a281fc8d82508b36d6378bbc970847d51419d","observation_id":"4574e658-59d8-4aae-acc8-9a6f0fab508b","resolution":{"observed_at":"2026-08-04T18:59:20.541021Z","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":"2026-08-04T18:59:20.725544Z","title":"Bounds for the quantity of information transmitted by a quantum communication channel","venue":null,"work_id":null,"year":1973},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:20.725544Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:bfba53a118e7387972067b2f0cbebb8e348b96f4312ed041c3000e54c933e040","observation_id":"2dcbe4de-7f00-4f2d-976f-ca6e5059b0e9","resolution":{"observed_at":"2026-08-04T18:59:20.725544Z","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":"2026-08-04T18:59:20.860834Z","title":"Tight uniform continuity bounds for quantum entropies: Condi- tional entropy, relative entropy distance and energy constraints","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:20.860834Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:e8deca6719609c85e1402c37f17547d74e4e2abcc3d67b1ab86fcb2834febf50","observation_id":"1676e25f-7254-4758-89d0-669a9008e857","resolution":{"observed_at":"2026-08-04T18:59:20.860834Z","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":"2026-08-04T18:59:21.052153Z","title":"Asymptotic values for degrees associated with strips of young dia- grams","venue":null,"work_id":null,"year":1981},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:21.052153Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:3e64daa0261458528fa361a15dcf9a6904570a957c9d155e64faa2945963d47a","observation_id":"222375b2-2b3c-4cb7-903c-2efe07c640de","resolution":{"observed_at":"2026-08-04T18:59:21.052153Z","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":"2026-08-04T18:59:21.197499Z","title":"Optimal compression for identically prepared qubit states","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:21.197499Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:2285a6e44bfed820f2a958456f01a709f15fecc14cec5b8eb92d35205af6ea37","observation_id":"90c3223a-af6f-4bee-906a-e8d76a008f7c","resolution":{"observed_at":"2026-08-04T18:59:21.197499Z","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":"2026-08-04T18:59:21.369173Z","title":"On the computa- tional power ofQAC 0 with barely superlinear ancillae","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:21.369173Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:5218675b1c2d4137e0aad6cd50751c8df776d149f5612641c6ac508030d11c26","observation_id":"04f38cd8-7d93-4561-bf16-74321f02eeff","resolution":{"observed_at":"2026-08-04T18:59:21.369173Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1611.01593","last_updated":"2016-11-05T03:14:50Z","snapshot_observed_at":"2026-07-06T05:17:29.499249Z","submitted_at":"2016-11-05T03:14:50Z","title":"Operator Lipschitz functions (English translation)","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1611.01593","snapshot_observed_at":"2026-08-04T18:59:21.528752Z","title":"Operator lipschitz functions (english trans- lation)","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:21.528752Z"},"links":{"cited_paper":"/paper/1611.01593","citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:50816a87d885e43a5bb27d74e417c94c3a4dbf13402e0897a2a6640cd4339480","observation_id":"236dcad7-1101-41b7-869a-a6881ad50d4e","resolution":{"observed_at":"2026-08-04T18:59:21.528752Z","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":"2026-08-04T18:59:21.763409Z","title":"Quantum state and unitary learn- ing implies circuit lower bounds","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:21.763409Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:216c38d34dec1fb6c96e892c363bdbd36da258e31f31111e468f0bae78e31dbf","observation_id":"cc122e69-3729-4764-946f-1b7e50261408","resolution":{"observed_at":"2026-08-04T18:59:21.763409Z","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":"2026-08-04T18:59:21.963762Z","title":"On the geometry of stabi- lizer states","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:21.963762Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:2ba13b654933627681f0e437222fd05c4584e43cef03896e34dba7f43a026b87","observation_id":"16187431-5ae5-4125-9a7f-aa5fd92badd8","resolution":{"observed_at":"2026-08-04T18:59:21.963762Z","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":"2026-08-04T18:59:22.126154Z","title":"Restrictions on realizable unitary operations imposed by symmetry and locality","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:22.126154Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:8d17c0d1a42c6099888050641a6e32e3e1047a849ba1bf1ef68559efc30e1efb","observation_id":"d7034119-22b2-436d-bc13-ff6035e29e50","resolution":{"observed_at":"2026-08-04T18:59:22.126154Z","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":"2026-08-04T18:59:17.992275Z","title":"IEEE Computer Society","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits","version":2},"reference_index":492,"source":"pdf_text","source_observed_at":"2026-08-04T18:59:17.992275Z"},"links":{"citing_paper":"/paper/2509.09642"},"observation_digest":"sha256:8ccfb8a22e498deceafaaf04ee4909fd1a518abbd34c29a5dcc1d3f767f6e519","observation_id":"8fb3f222-c0c6-4547-97ac-28d4411567dc","resolution":{"observed_at":"2026-08-04T18:59:17.992275Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2509.09642","last_updated":"2026-07-14T16:03:59Z","latest_version":2,"primary_category":"quant-ph","snapshot_observed_at":"2026-08-14T02:02:20.681780Z","submitted_at":"2025-09-11T17:30:32Z","title":"Resource quantification for programming low-depth quantum circuits"},"reference_resolution":{"displayed":54,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":54,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":54},"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":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"thesis":"As of 14 August 2026, this Paper Citation Record lists 54 of 54 outbound references and 0 inbound Pith citation observations for arXiv:2509.09642."}