{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:E2KZPE6EC4SF55BOFUYJXTZAZV","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"9867a8acc46712be2ff464ce8b1955cbc93ca53d0b61eb40b5363c24c0e3e5a0","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2006-11-14T18:31:23Z","title_canon_sha256":"7ec6535080115b7b812998546e100de281a2740105f4620c241daad09e832dad"},"schema_version":"1.0","source":{"id":"quant-ph/0611156","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0611156","created_at":"2026-07-04T15:00:29Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0611156v2","created_at":"2026-07-04T15:00:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0611156","created_at":"2026-07-04T15:00:29Z"},{"alias_kind":"pith_short_12","alias_value":"E2KZPE6EC4SF","created_at":"2026-07-04T15:00:29Z"},{"alias_kind":"pith_short_16","alias_value":"E2KZPE6EC4SF55BO","created_at":"2026-07-04T15:00:29Z"},{"alias_kind":"pith_short_8","alias_value":"E2KZPE6E","created_at":"2026-07-04T15:00:29Z"}],"graph_snapshots":[{"event_id":"sha256:d65a77edbc68b5e28dab608f4793a5235aad236fb2121273521c172764a98666","target":"graph","created_at":"2026-07-04T15:00:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/quant-ph/0611156/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this note we describe a simple and intriguing observation: the quantum Fourier transform (QFT) over $Z_q$, which is considered the most ``quantum'' part of Shor's algorithm, can in fact be simulated efficiently by classical computers.\n  More precisely, we observe that the QFT can be performed by a circuit of poly-logarithmic path-width, if the circuit is allowed to apply not only unitary gates but also general linear gates. Recalling the results of Markov and Shi [MaSh] and Jozsa [Jo] which provided classical simulations of such circuits in time exponential in the tree-width, this implies t","authors_text":"Dorit Aharonov, Johann Makowsky, Zeph Landau","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2006-11-14T18:31:23Z","title":"The quantum FFT can be classically simulated"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0611156","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:5cf8072b320b5e62a12ec0cc4ebd05c778b3dd790134bdc0a4c25d829fbd4a5c","target":"record","created_at":"2026-07-04T15:00:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"9867a8acc46712be2ff464ce8b1955cbc93ca53d0b61eb40b5363c24c0e3e5a0","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2006-11-14T18:31:23Z","title_canon_sha256":"7ec6535080115b7b812998546e100de281a2740105f4620c241daad09e832dad"},"schema_version":"1.0","source":{"id":"quant-ph/0611156","kind":"arxiv","version":2}},"canonical_sha256":"26959793c417245ef42e2d309bcf20cd74baa2f85c82e36dfb1b15909ee53c3a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26959793c417245ef42e2d309bcf20cd74baa2f85c82e36dfb1b15909ee53c3a","first_computed_at":"2026-07-04T15:00:29.377994Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:00:29.377994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8zpAPngpgD/y69j9gYfjh3SoQ99Y/l+Va2c9uxqlRt7vAU0hOmfW+zW4mBsjNnVs/LoCRcjw3IixW29NbVYXAg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:00:29.378468Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0611156","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5cf8072b320b5e62a12ec0cc4ebd05c778b3dd790134bdc0a4c25d829fbd4a5c","sha256:d65a77edbc68b5e28dab608f4793a5235aad236fb2121273521c172764a98666"],"state_sha256":"eee699342114a633a25dc03c6927ee56638bdefe33f5d288fd1106b464a34249"}