{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:JDTBSAEVB4V2V27U3S4LG2WDYK","short_pith_number":"pith:JDTBSAEV","schema_version":"1.0","canonical_sha256":"48e61900950f2baaebf4dcb8b36ac3c2969c3d1de04cf5eac35fff9632445eb0","source":{"kind":"arxiv","id":"2205.04485","version":3},"attestation_state":"computed","paper":{"title":"Polynomial Equivalence of Complexity Geometries","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th","math.DG"],"primary_cat":"quant-ph","authors_text":"Adam R. Brown","submitted_at":"2022-05-09T18:00:10Z","abstract_excerpt":"This paper proves the polynomial equivalence of a broad class of definitions of quantum computational complexity. We study right-invariant metrics on the unitary group -- often called `complexity geometries' following the definition of quantum complexity proposed by Nielsen -- and delineate the equivalence class of metrics that have the same computational power as quantum circuits. Within this universality class, any unitary that can be reached in one metric can be approximated in any other metric in the class with a slowdown that is at-worst polynomial in the length and number of qubits and i"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2205.04485","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2022-05-09T18:00:10Z","cross_cats_sorted":["hep-th","math.DG"],"title_canon_sha256":"324bc0349544110c5bb413eb8ad557e1ef47efd7b2d7765ef03aa99dd54293db","abstract_canon_sha256":"7704dea8077b70c2d9453da69cd30baf5ee7dc56f8db32540ba66c898cec3780"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:39:16.779957Z","signature_b64":"hC7nO1mYI4IHdPeyHaNOv7b9qQzqEw86Gu8BNpwSYX/HAeDDsJfqsBYpC6q2dZmtPL25S3ukOEIJYiH+25nVAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48e61900950f2baaebf4dcb8b36ac3c2969c3d1de04cf5eac35fff9632445eb0","last_reissued_at":"2026-07-05T08:39:16.779010Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:39:16.779010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Polynomial Equivalence of Complexity Geometries","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th","math.DG"],"primary_cat":"quant-ph","authors_text":"Adam R. Brown","submitted_at":"2022-05-09T18:00:10Z","abstract_excerpt":"This paper proves the polynomial equivalence of a broad class of definitions of quantum computational complexity. We study right-invariant metrics on the unitary group -- often called `complexity geometries' following the definition of quantum complexity proposed by Nielsen -- and delineate the equivalence class of metrics that have the same computational power as quantum circuits. Within this universality class, any unitary that can be reached in one metric can be approximated in any other metric in the class with a slowdown that is at-worst polynomial in the length and number of qubits and i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.04485","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2205.04485/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2205.04485","created_at":"2026-07-05T08:39:16.779574+00:00"},{"alias_kind":"arxiv_version","alias_value":"2205.04485v3","created_at":"2026-07-05T08:39:16.779574+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.04485","created_at":"2026-07-05T08:39:16.779574+00:00"},{"alias_kind":"pith_short_12","alias_value":"JDTBSAEVB4V2","created_at":"2026-07-05T08:39:16.779574+00:00"},{"alias_kind":"pith_short_16","alias_value":"JDTBSAEVB4V2V27U","created_at":"2026-07-05T08:39:16.779574+00:00"},{"alias_kind":"pith_short_8","alias_value":"JDTBSAEV","created_at":"2026-07-05T08:39:16.779574+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.14275","citing_title":"Generalized Complexity Distances and Non-Invertible Symmetries","ref_index":25,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JDTBSAEVB4V2V27U3S4LG2WDYK","json":"https://pith.science/pith/JDTBSAEVB4V2V27U3S4LG2WDYK.json","graph_json":"https://pith.science/api/pith-number/JDTBSAEVB4V2V27U3S4LG2WDYK/graph.json","events_json":"https://pith.science/api/pith-number/JDTBSAEVB4V2V27U3S4LG2WDYK/events.json","paper":"https://pith.science/paper/JDTBSAEV"},"agent_actions":{"view_html":"https://pith.science/pith/JDTBSAEVB4V2V27U3S4LG2WDYK","download_json":"https://pith.science/pith/JDTBSAEVB4V2V27U3S4LG2WDYK.json","view_paper":"https://pith.science/paper/JDTBSAEV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2205.04485&json=true","fetch_graph":"https://pith.science/api/pith-number/JDTBSAEVB4V2V27U3S4LG2WDYK/graph.json","fetch_events":"https://pith.science/api/pith-number/JDTBSAEVB4V2V27U3S4LG2WDYK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JDTBSAEVB4V2V27U3S4LG2WDYK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JDTBSAEVB4V2V27U3S4LG2WDYK/action/storage_attestation","attest_author":"https://pith.science/pith/JDTBSAEVB4V2V27U3S4LG2WDYK/action/author_attestation","sign_citation":"https://pith.science/pith/JDTBSAEVB4V2V27U3S4LG2WDYK/action/citation_signature","submit_replication":"https://pith.science/pith/JDTBSAEVB4V2V27U3S4LG2WDYK/action/replication_record"}},"created_at":"2026-07-05T08:39:16.779574+00:00","updated_at":"2026-07-05T08:39:16.779574+00:00"}