{"as_of":"2026-08-11T02:11:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:dff4c3f5fc9f7cfdf1d3de2bef3028a3a995b4d6becbc9f9cee250d92fd88ea4","coverage":[{"denominator":50,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":50,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T11:00:18.258052Z","state":"measured"},{"denominator":50,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":50,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-10T06:31:04.303077+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/2506.04033/citation-record","integrity":"/paper/2506.04033/integrity","json":"/paper/2506.04033/citation-record.json","paper":"/paper/2506.04033"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.703022Z","title":"Group22: Proceedings of the xxii international colloquium on group theoretical methods in physics,","venue":null,"work_id":"9c9aaf6e-8dca-4011-b6e9-46294b983ef4","year":1999},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.117129Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:73eb71aeda9e81bbfc8f983f96d83e61b871bd11d7b5073e22b2e48ee64d68b3","observation_id":"d5bbe519-b695-408d-a01d-f546ef52e2f7","resolution":{"observed_at":"2026-08-07T11:00:18.706339Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.694201Z","title":"Universal quantum computation with ideal clifford gates and noisy ancillas,","venue":null,"work_id":"5ccca11a-0b5f-466d-ac64-56d01b0a0558","year":2005},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.120372Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:6c801e7457a8bfba682bc2d6687b5b9273b00596337720d8ad0564c2d34a1ecb","observation_id":"48788102-5004-47d0-a331-11a05834657c","resolution":{"observed_at":"2026-08-07T11:00:18.697117Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.685490Z","title":"Trading classical and quantum computational resources,","venue":null,"work_id":"02e37c94-93cd-4192-beb6-eb3d8d0f7f92","year":2016},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.123447Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:921b63afdbc291a17784bf3866cdcce40a19413dcfb0e48a9b3ac0a5d87172aa","observation_id":"f1e42ad6-ec85-4a16-99c6-e9bd301cb3a7","resolution":{"observed_at":"2026-08-07T11:00:18.688755Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.676673Z","title":"Improved classical simulation of quantum circuits dominated by clifford gates,","venue":null,"work_id":"0a60bca6-1736-4000-81c7-9076f46c9cb0","year":2016},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.126430Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:cfd0b15c9576b89fbbcf210ddf8565d44bedd61c525a29031ee96becf256b97b","observation_id":"8fead638-eef3-4267-864d-a41413da780f","resolution":{"observed_at":"2026-08-07T11:00:18.679843Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.667433Z","title":"Simulation of quantum circuits by low-rank stabilizer decompositions,","venue":null,"work_id":"f06248bb-c974-4b72-8309-0f38a92480dc","year":2019},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.129390Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:69a4fd91e634a7eaca66abf4d38ecb306609f12109a97da03541a05c690e70f9","observation_id":"3074f74d-9e20-428f-adf6-e27f6a2d06c2","resolution":{"observed_at":"2026-08-07T11:00:18.670540Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.658695Z","title":"Application of a resource theory for magic states to fault-tolerant quan- tum computing,","venue":null,"work_id":"82254878-a4e2-4929-bc6f-c2cd2413de31","year":2017},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.132370Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:478211b914fb8b1fae36bb25cf724356bd5f718656f8abffcddc806655ccb914","observation_id":"b224c26b-8256-4ed6-a250-97fe8f16d81f","resolution":{"observed_at":"2026-08-07T11:00:18.662037Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.135284Z","title":null,"venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.135284Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:b6bc69f57461fbf83bedc821d7f1c9588056a4fd581da54fdcb767bad75a1fe2","observation_id":"196148e5-0ab1-4a42-8627-97392b70c579","resolution":{"observed_at":"2026-08-07T11:00:18.135284Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.645398Z","title":"Improved simulation of stabilizer circuits,","venue":null,"work_id":"00d2c2c7-1f65-411c-aeb1-683ec573636e","year":2004},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.138048Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:15dac70008202b8c91e5cd4a3864a9bfb00b4d1ed79968b0f5ee728838d841b4","observation_id":"25534783-3118-4a2b-830b-89a734aff1d4","resolution":{"observed_at":"2026-08-07T11:00:18.648371Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.636758Z","title":"Quantifying quantum speedups: Improved classical simulation from tighter magic monotones,","venue":null,"work_id":"8d231664-3cc4-4d69-9928-8a573aa3650e","year":2021},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.140794Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:50342426cca360e9b0b99a5e74ab6cb4e193736131946881bd62de37dd8be3d6","observation_id":"5b707e8c-d721-4b2c-b8c1-715404c9eec3","resolution":{"observed_at":"2026-08-07T11:00:18.639810Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.628576Z","title":"Phase-space-simulation method for quantum computation with magic states on qubits,","venue":null,"work_id":"c4549585-9972-4650-a234-c7a1780db9ce","year":2020},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.143519Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:3760a5052703019d1e6e556921a3e8d16ee90d5fd777092f42bc40d0ca6e712c","observation_id":"529e6ef5-6c30-4299-a1ec-ecc35d1e2d4a","resolution":{"observed_at":"2026-08-07T11:00:18.631645Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.620233Z","title":"Negative quasi-probability as a resource for quantum computation,","venue":null,"work_id":"fdbbbdf6-7139-4599-b2c7-c9c11ea39843","year":2012},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.146161Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:d49c7b815d113f900cdb826def48fb4ffdfc1504bbc90c7472d32f04a2674ede","observation_id":"359ccb2e-e2e2-4212-aaaf-3c40ebb6c95d","resolution":{"observed_at":"2026-08-07T11:00:18.623369Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.611829Z","title":"Contextuality and wigner- function negativity in qubit quantum computation,","venue":null,"work_id":"616dc499-5ad6-4afe-817c-9c1741d0ca3f","year":2017},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.148989Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:fc921ed69fbac6db07ee4347328e6c576433af382b26b5132d3b6bbd468dcb12","observation_id":"5a5132ff-785b-45d8-a906-8756c23da8a7","resolution":{"observed_at":"2026-08-07T11:00:18.614886Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.603631Z","title":"Hidden variables and the two theorems of john bell,","venue":null,"work_id":"20e03c86-9230-4e34-a8ed-97305b72687a","year":1993},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.151820Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:ba58fe7cfc2d4a4c7e1a87d227718bf5726e8d271c26ecdb3828a90d302c4299","observation_id":"864bbac5-f8d1-4fb4-8fda-b99e1e20023b","resolution":{"observed_at":"2026-08-07T11:00:18.606804Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.595029Z","title":"Accessed: 2025-02-28","venue":null,"work_id":"785b4581-3d55-40c5-af39-2ebf963013f7","year":2025},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.154482Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:70d33448d87ea2af8a437361c35666171b10da29d44a4ba887ce4842947f5b2a","observation_id":"188540f1-5d80-46e6-88e0-bbd72a9f2661","resolution":{"observed_at":"2026-08-07T11:00:18.598229Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.585643Z","title":"Topological proofs of contextuality in qunatum mechanics,","venue":null,"work_id":"6ce4878d-0657-4ecb-8b63-057706ff197f","year":2017},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.157368Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:4102d80ac5864236c968ebbc9b770c64176c5a1accc0e2aeccf323a3d2342a0d","observation_id":"d770adfa-64a5-401b-9509-7da5e55f0d2c","resolution":{"observed_at":"2026-08-07T11:00:18.588625Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.577547Z","title":"Contextuality test of the nonclassicality of variational quantum eigen- solvers,","venue":null,"work_id":"edf01e4b-73a6-4d68-92b4-9b397c027564","year":2019},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.160129Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:744542d69efb12ba7be34bde14ad5cf4a56020d14989adfcf0a071da975446e8","observation_id":"a8566efd-0edc-487c-81c6-51a71ce035dc","resolution":{"observed_at":"2026-08-07T11:00:18.580607Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.568806Z","title":"Hidden variable model for universal quantum computation with magic states on qubits,","venue":null,"work_id":"9f155050-c5f5-40fe-92cc-8996ea2eb77d","year":2020},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.162784Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:66fef45bfc507b888f92a431b9fb331e6eb79945f6d130eb198b01b9fe19306f","observation_id":"477cd683-2211-4f42-b477-7692528ecf39","resolution":{"observed_at":"2026-08-07T11:00:18.571911Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.560265Z","title":"Estimating outcome probabilities of quantum circuits using quasiprobabilities,","venue":null,"work_id":"d4caaa76-bd8d-413a-8f0f-8787c41e8a6f","year":2015},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.165683Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:f820abdb09f704a8f09c581e445cf623c145e245f571110104e5d228a8b24e2c","observation_id":"bd42b50f-93bb-4de3-bd0f-2626cdfc298b","resolution":{"observed_at":"2026-08-07T11:00:18.563418Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1909.08123","last_updated":"2019-11-11T18:10:19Z","snapshot_observed_at":"2026-08-03T21:35:37.570321Z","submitted_at":"2019-09-17T21:52:29Z","title":"On sets of commuting and anticommuting Paulis","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1909.08123","snapshot_observed_at":"2026-08-07T11:00:18.168426Z","title":"On sets of commuting and anticommuting paulis,","venue":null,"work_id":null,"year":1909},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.168426Z"},"links":{"cited_paper":"/paper/1909.08123","citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:20e07ac2e1e3da893320b90a3f0c45dea7267245138b18d3755921fabbc722ac","observation_id":"5a44edb7-04a5-44ea-bd72-831bd612e833","resolution":{"observed_at":"2026-08-07T11:00:18.168426Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.551887Z","title":"Lectures on symplectic geometry,","venue":null,"work_id":"e24ae58a-69d6-4823-8ce9-3bd003c67d25","year":2001},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.171638Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:7efa5aaab2a2c385aea7d49da97ca6226137dc6130ce34febb7b21a134358f20","observation_id":"cbb87bf2-6ce3-4eba-a5bb-782e732d1abb","resolution":{"observed_at":"2026-08-07T11:00:18.554859Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.543414Z","title":"How to efficiently select an arbitrary clifford group element,","venue":null,"work_id":"cbde35cc-124e-47d3-9ccc-0d3738296040","year":2014},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.174638Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:d82e64ff4fa93b770515fbb46fa90538c9b5b9808ddf58b3fb3e7692254bd189","observation_id":"441d2b39-c3aa-4665-810e-ba01f731a579","resolution":{"observed_at":"2026-08-07T11:00:18.546363Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.534231Z","title":"Hidden variable models and classical simulation algorithms for quantum computation with magic states on qubits,","venue":null,"work_id":"28b1d257-7a94-4745-b94c-9a3241846d66","year":2020},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.177277Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:6c330d5046c18eeaceaf7d26baf175fbd3864c8327e850aa0b9bdacbb5010b49","observation_id":"8614631a-fc82-42a3-941c-98f126c2b8b8","resolution":{"observed_at":"2026-08-07T11:00:18.537536Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.525288Z","title":"Python CHP Stabilizer Simulator","venue":null,"work_id":"a373de0a-8235-4170-8d1e-c4d9507c15a1","year":2025},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.179990Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:f452f61812ed15c8857c103255b25a0b32a77f476d6856d553ac613e89dea5f7","observation_id":"0d3ab677-bae1-4a00-8c9b-38338fecbc55","resolution":{"observed_at":"2026-08-07T11:00:18.528648Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.516501Z","title":"Watrous, The theory of quantum information","venue":null,"work_id":"5c4d92be-50d1-4995-8f2f-065fb1060f85","year":2018},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.182568Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:8103e400e6998f228cbaa33fe9c20198634ef41886a51526b1ad9ac03287a484","observation_id":"3a6648ba-3e24-4a53-a949-a8775ff4eb1b","resolution":{"observed_at":"2026-08-07T11:00:18.519641Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.508094Z","title":"Quantifying magic for multi-qubit operations,","venue":null,"work_id":"8a637627-720d-4899-ba33-edc551a8e166","year":2019},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.185576Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:8b77271ec2bca8ac20fc9d1d5ae57a1f9607772502de78d5208d2f2fe4af2353","observation_id":"ab7abd39-b6aa-4bbe-b923-af1dc3e780e9","resolution":{"observed_at":"2026-08-07T11:00:18.511128Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1305.6190","last_updated":"2013-05-27T12:22:52Z","snapshot_observed_at":"2026-08-05T10:54:55.895813Z","submitted_at":"2013-05-27T12:22:52Z","title":"Classical simulation complexity of extended Clifford circuits","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1305.6190","snapshot_observed_at":"2026-08-07T11:00:18.188345Z","title":"Classical simulation complexity of extended clifford circuits,","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.188345Z"},"links":{"cited_paper":"/paper/1305.6190","citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:fc2d2b55e343021abd728ab597f7d59abe805885988de5e5019aec5bb6382ffc","observation_id":"e5fed21d-fc6f-4c93-bfc5-851055db7e14","resolution":{"observed_at":"2026-08-07T11:00:18.188345Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.499141Z","title":"From estimation of quantum probabilities to simulation of quantum circuits,","venue":null,"work_id":"31d5b9dd-cc29-453f-81f2-c4d50140bd92","year":2020},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.191365Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:91bd9b258ad7bc9193eaf86e29ba61b59034c9f349f931a9255284d3d5ae4ebd","observation_id":"0ae24e3d-4429-4a7b-ad18-f447f339c699","resolution":{"observed_at":"2026-08-07T11:00:18.502243Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.490689Z","title":"Probability inequalities for sums of bounded random variables,","venue":null,"work_id":"c76aaeff-3fa2-4466-ad62-2396ec5f859b","year":1994},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.194045Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:55c12c44744fad46b57f148520451bd064f4c47aa4b666016abc1719360f5556","observation_id":"a221b663-de1a-45ce-a8ad-f5ba363b7c2f","resolution":{"observed_at":"2026-08-07T11:00:18.493642Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.482075Z","title":"Quantum algorithms for highly non-linear boolean functions,","venue":null,"work_id":"080852c4-9293-470d-b2cb-9e40424021dc","year":2010},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.197153Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:c86c6fa206785f2844eb1909957764256039898585ba08731a84e38b6c7073dc","observation_id":"e081decb-adc8-40a1-848d-7d082cdba063","resolution":{"observed_at":"2026-08-07T11:00:18.485202Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.199823Z","title":"Rapid solution of problems by quantum computation,","venue":null,"work_id":null,"year":1907},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.199823Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:85cebe46f38ac44f9a5d39a9ac37b4c688915e95977fb1c67e832e69af9ab435","observation_id":"a6424874-b01d-4968-9f63-5a9386c185be","resolution":{"observed_at":"2026-08-07T11:00:18.199823Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2101.12223","last_updated":"2022-06-24T16:36:03Z","snapshot_observed_at":"2026-07-31T04:14:15.218756Z","submitted_at":"2021-01-28T19:00:04Z","title":"Fast estimation of outcome probabilities for quantum circuits","version":3},"cited_work":{"arxiv_id":"2101.12223","doi":null,"metadata_source":"pith","pith_arxiv_id":"2101.12223","snapshot_observed_at":"2026-08-07T11:00:18.298899Z","title":"Fast estimation of outcome probabilities for quantum circuits","venue":"quant-ph","work_id":"be3cd358-2619-4fd4-8d58-cfa8922121f5","year":2021},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.202667Z"},"links":{"cited_paper":"/paper/2101.12223","citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:335cb4b3700cb68a1a5326b43a13d1e241c937ae9cb62955ed3dadf34d526205","observation_id":"e6ee38e7-66cc-4821-87b9-07b7c0a12bfd","resolution":{"observed_at":"2026-08-07T11:00:18.302098Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.468028Z","title":"Simulating quantum circuits with zx-calculus reduced stabiliser decompositions,","venue":null,"work_id":"bfb2b382-2e78-44bd-afe5-9c6ae496456d","year":2022},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.205800Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:8bceef89759bb0854f1de6b6327cf299729e2bc3368910c8b33369233a2fb82b","observation_id":"62675dbf-3172-4adb-a6da-7964491155da","resolution":{"observed_at":"2026-08-07T11:00:18.471048Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.459444Z","title":"Robustness of magic and symmetries of the stabiliser polytope,","venue":null,"work_id":"bd79ddd0-a2e8-401d-bc3f-b2d149658072","year":2019},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.208590Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:0680496f8e3c90565669b900735e44ee87b249a6136ba3efeada1f5abfc3e0ac","observation_id":"a1dd07d1-bdf6-490c-b650-6df4b0a14cc2","resolution":{"observed_at":"2026-08-07T11:00:18.462517Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.450691Z","title":"A one-way quantum computer,","venue":null,"work_id":"0b791bc1-be17-4d53-827b-d0f55b98acf4","year":2001},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.211256Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:875db1e8de3673244c36972a036bf7903577322d769cbc23273ef13f01e8ca41","observation_id":"576448f1-3d2d-4506-b8cc-63813e433ce2","resolution":{"observed_at":"2026-08-07T11:00:18.453597Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2410.23734","last_updated":"2024-10-31T08:40:51Z","snapshot_observed_at":"2026-08-10T11:08:54.486064Z","submitted_at":"2024-10-31T08:40:51Z","title":"Classical simulation of universal measurement-based quantum computation using multipartite Bell scenarios","version":1},"cited_work":{"arxiv_id":"2410.23734","doi":null,"metadata_source":"pith","pith_arxiv_id":"2410.23734","snapshot_observed_at":"2026-08-07T11:00:18.284403Z","title":"Classical simulation of universal measurement-based quantum computation using multipartite Bell scenarios","venue":"quant-ph","work_id":"20afbce3-d8fc-4c3b-a62d-99430955cd31","year":2024},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.214082Z"},"links":{"cited_paper":"/paper/2410.23734","citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:69d4dd4e0037b1196964428864ffaa9f375d65e9cfce160a32bff608c0cbac31","observation_id":"f6a089f3-d880-432a-9bee-15225fb2c617","resolution":{"observed_at":"2026-08-07T11:00:18.289858Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.442561Z","title":"• Compute t ← 1 2 |Ab| • Swap rows in the tableau to place anti-commuting elements in the first 2 t rows:","venue":null,"work_id":"41b70aee-594c-4f6f-80ae-2177dbf25218","year":null},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.217628Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:315914fb12d96f3de67c740b1ed4ad9b335bd9da3d32d4527b534751eafb1439","observation_id":"2cde526c-c231-4e93-9bdb-f073bb603bc6","resolution":{"observed_at":"2026-08-07T11:00:18.445569Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.434339Z","title":"• First Stabilizer and Destabilizer: – F or i = K + 2t + 1, · · ·, 2n + 1: - RK+1 ← RK+1 + Ri – ˜RK+1 ← (RK+1, rb) and ˜RK+2 ← (RK+2, 0)","venue":null,"work_id":"85071491-8b68-4f9d-a92a-d4f1faec0fe1","year":null},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.220711Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:21218d2a4a86c05a29bb4c302930dd306d124a50315f74497288dcedf44c5f5d","observation_id":"85fe24ff-9d18-4273-888b-32262984cec1","resolution":{"observed_at":"2026-08-07T11:00:18.437283Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.426158Z","title":null,"venue":null,"work_id":"962601e3-0e1a-4baf-b568-17cba95d5260","year":null},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.223724Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:8985f729dad773e54f41b89b72e2f10a327798ce7a3e44d34a976a5f0f9ac195","observation_id":"67263567-554d-476f-92de-eda36f05d79e","resolution":{"observed_at":"2026-08-07T11:00:18.429116Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.417544Z","title":"- Rows n − m + 1, · · ·, n− m + t are the new destabilizer rows K + 2i (i = 1, · · ·, t)","venue":null,"work_id":"3c832465-de83-44a2-9fee-27a1440cee3b","year":null},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.226741Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:935ba828d3c512d7858bc1b5147ebe5c46eafdf3e2b361f441831ac7864f5dc5","observation_id":"2905be33-e97b-4b35-b7f2-55fb3714abb6","resolution":{"observed_at":"2026-08-07T11:00:18.420995Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.408744Z","title":null,"venue":null,"work_id":"088cbb96-01ea-4b7f-ab7b-6df6ec406c64","year":null},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.229635Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:baa324348f84fb80aca56ca10c4e06e41c0fac972b074da759c6b215a394d7b3","observation_id":"ef114d39-af6f-45bb-a5f0-6185e9954cc4","resolution":{"observed_at":"2026-08-07T11:00:18.412233Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.400669Z","title":"32 Algorithm 2: Algorithm for simulating measurement outcome and tableau update when b /∈ I ⊥","venue":null,"work_id":"e7091412-a693-430f-8819-5a9d73456524","year":null},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.232426Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:4cfe39b1cf34669316d0c3485adf256ee1da4562fea084863fe135d24ba59cfc","observation_id":"91eb4e1a-3ee1-4786-89f9-f5f1dc33d3f1","resolution":{"observed_at":"2026-08-07T11:00:18.403657Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.392491Z","title":null,"venue":null,"work_id":"ddecd26b-ea34-46d0-acc0-8d922c0701df","year":null},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.235583Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:6182151217ab4849348ba1b60b78d4b09320c65fc33535c74ab0573af2453b0d","observation_id":"b1c01495-6f8e-4c23-8363-9b57c62086b6","resolution":{"observed_at":"2026-08-07T11:00:18.395525Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.384703Z","title":null,"venue":null,"work_id":"a5322151-de09-47cc-9765-463477f203b3","year":null},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.238391Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:359d0f7293bcc05aa624a83be8cda3ddb71c58dd8b5dd90c3be7c79938042c43","observation_id":"50706539-f7a6-4363-a01f-f322a51753f6","resolution":{"observed_at":"2026-08-07T11:00:18.387445Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.376515Z","title":"- ˜Rλ ← (R(b), rb)","venue":null,"work_id":"ba3b4d94-58cf-4803-bed3-33bca661fbc5","year":null},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.241118Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:23d325192aacf70e723e9d0df7de5c1670fa54fb9571313acab32bc47bd14f99","observation_id":"62f670a4-cfbe-42c1-862c-dada27d3f8d9","resolution":{"observed_at":"2026-08-07T11:00:18.379447Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.367644Z","title":"33 Algorithm 3: Algorithm for creating a tableau from given maximal CNC operator Aγ Ω","venue":null,"work_id":"ab606065-c618-46c6-9607-586dfbbb2a32","year":null},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.244156Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:362973e4b94c0bb0a74c41a1989d44088767612a62c3d58e98113d5a934ec2f0","observation_id":"07133b5a-96e7-4d21-bd98-55377d19aebf","resolution":{"observed_at":"2026-08-07T11:00:18.370934Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.359140Z","title":"• Find a basis {e1,","venue":null,"work_id":"503be2df-2d48-4b5c-ba09-41eb91c7056d","year":null},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.246961Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:9e4f300e80a62fd2b03e105896d352c2c65408625e110cf19c37b34089b5d4f4","observation_id":"64a447f6-c46c-49ce-b03c-dba383d740d2","resolution":{"observed_at":"2026-08-07T11:00:18.361840Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.350657Z","title":", en−m} to a symplectic basis {e1, f1,","venue":null,"work_id":"4c5a3ebc-0d9b-49ec-9314-9497023bf790","year":null},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.249834Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:997b463bc2288f661f117ac17559fc5f03fbd3a806d918342c8e5f17ffaf8770","observation_id":"fa45c8d3-fe28-44f9-b3c3-462211b4cd84","resolution":{"observed_at":"2026-08-07T11:00:18.353683Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.342316Z","title":"• Let PW be the orthogonal projection onto W and set Ω ′ = Ω \\ I","venue":null,"work_id":"11e10152-e11b-4a4f-84a5-06be7617accb","year":null},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.252554Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:db906a661db52c3b2a0e9c0c084b5ca7f1352991e402e7ce6b90058ac57455ad","observation_id":"091066d9-f2eb-4038-9229-5b1b3bbdb3fd","resolution":{"observed_at":"2026-08-07T11:00:18.345180Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.334212Z","title":null,"venue":null,"work_id":"4a293260-b933-42e6-b356-de075a7076a6","year":null},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.255253Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:c159bd2781c5d80d7d496c8431a66316dc8872606140069db7d266e4b39f97b1","observation_id":"0e87413d-c363-4a87-bcec-868f22274c30","resolution":{"observed_at":"2026-08-07T11:00:18.336939Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:00:18.325281Z","title":"34 Algorithm 4: Algorithm for weak simulation using the phase space tableau","venue":null,"work_id":"df04487b-4811-4b7a-a8a2-cc6e240384d7","year":null},"citing_paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-07T11:00:18.258052Z"},"links":{"citing_paper":"/paper/2506.04033"},"observation_digest":"sha256:33e6f1a8c1f0fcc2bf9723c614ab159ca4cd7c10cc3d8fab18e4f9aa6572d88d","observation_id":"9c3840ad-d9c8-4775-aa7e-dd77300c95c8","resolution":{"observed_at":"2026-08-07T11:00:18.328404Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.04033","last_updated":"2025-06-04T14:56:42Z","latest_version":1,"primary_category":"quant-ph","snapshot_observed_at":"2026-08-09T08:12:18.537477Z","submitted_at":"2025-06-04T14:56:42Z","title":"Phase space tableau simulation for quantum computation"},"reference_resolution":{"displayed":50,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":9,"verified_exact":2,"verified_fuzzy":39},"total_outbound_references":50},"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":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"thesis":"As of 11 August 2026, this Paper Citation Record lists 50 of 50 outbound references and 0 inbound Pith citation observations for arXiv:2506.04033."}