{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:WIUN2X23FKJM5I4EANPQYZW3QC","short_pith_number":"pith:WIUN2X23","schema_version":"1.0","canonical_sha256":"b228dd5f5b2a92cea384035f0c66db8087e98e5bbaebaffcaac7854fc119e9f8","source":{"kind":"arxiv","id":"quant-ph/0507171","version":1},"attestation_state":"computed","paper":{"title":"An Introduction to Cartan's KAK Decomposition for QC Programmers","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Robert R. Tucci","submitted_at":"2005-07-18T17:12:08Z","abstract_excerpt":"This paper presents no new results; its goals are purely pedagogical. A special case of the Cartan Decomposition has found much utility in the field of quantum computing, especially in its sub-field of quantum compiling. This special case allows one to factor a general 2-qubit operation (i.e., an element of U(4)) into local operations applied before and after a three parameter, non-local operation. In this paper, we give a complete and rigorous proof of this special case of Cartan's Decomposition. From the point of view of QC programmers who might not be familiar with the subtleties of Lie Gro"},"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":"quant-ph/0507171","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2005-07-18T17:12:08Z","cross_cats_sorted":[],"title_canon_sha256":"13a89845726f13d1122c7de824d3eaf628896428e27751e148f7d86e851eff01","abstract_canon_sha256":"8602c38edc67e8c63c7dc516fffcd717d18d361a705ddef8e7243f393f572f48"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:47:00.791289Z","signature_b64":"g0X78ZdDBzKvX9SHckFwvZlLF6ULA3yrW9dGrus0pvxxoGrS7aOrdXzICzYdLTbb+g59tGCjAE8NwBNf6qy6Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b228dd5f5b2a92cea384035f0c66db8087e98e5bbaebaffcaac7854fc119e9f8","last_reissued_at":"2026-07-04T14:47:00.790944Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:47:00.790944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Introduction to Cartan's KAK Decomposition for QC Programmers","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Robert R. Tucci","submitted_at":"2005-07-18T17:12:08Z","abstract_excerpt":"This paper presents no new results; its goals are purely pedagogical. A special case of the Cartan Decomposition has found much utility in the field of quantum computing, especially in its sub-field of quantum compiling. This special case allows one to factor a general 2-qubit operation (i.e., an element of U(4)) into local operations applied before and after a three parameter, non-local operation. In this paper, we give a complete and rigorous proof of this special case of Cartan's Decomposition. From the point of view of QC programmers who might not be familiar with the subtleties of Lie Gro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0507171","kind":"arxiv","version":1},"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/quant-ph/0507171/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":"quant-ph/0507171","created_at":"2026-07-04T14:47:00.791000+00:00"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0507171v1","created_at":"2026-07-04T14:47:00.791000+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0507171","created_at":"2026-07-04T14:47:00.791000+00:00"},{"alias_kind":"pith_short_12","alias_value":"WIUN2X23FKJM","created_at":"2026-07-04T14:47:00.791000+00:00"},{"alias_kind":"pith_short_16","alias_value":"WIUN2X23FKJM5I4E","created_at":"2026-07-04T14:47:00.791000+00:00"},{"alias_kind":"pith_short_8","alias_value":"WIUN2X23","created_at":"2026-07-04T14:47:00.791000+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":9,"internal_anchor_count":9,"sample":[{"citing_arxiv_id":"2606.25330","citing_title":"Routing Codes: High-Rate Quantum LDPC Codes with Short, Parallel Non-Local Connectivity","ref_index":51,"is_internal_anchor":true},{"citing_arxiv_id":"2606.21452","citing_title":"Spin qubit operations by conveyor-mode shuttling","ref_index":47,"is_internal_anchor":true},{"citing_arxiv_id":"2606.20805","citing_title":"Distribution Complexity of Electronic Structure Simulations on Quantum Supercomputers","ref_index":78,"is_internal_anchor":true},{"citing_arxiv_id":"2606.29636","citing_title":"Lie Group Diffusion Models for Hardware-Aware Quantum Circuit Synthesis","ref_index":32,"is_internal_anchor":true},{"citing_arxiv_id":"2606.28169","citing_title":"Time Evolution on Hybrid Tensor Networks -- A Novel and Parallelizable Algorithm","ref_index":162,"is_internal_anchor":true},{"citing_arxiv_id":"2407.21278","citing_title":"Universal Euler-Cartan Circuits for Quantum Field Theories","ref_index":27,"is_internal_anchor":true},{"citing_arxiv_id":"2505.00543","citing_title":"GULPS: Two-Qubit Gate Synthesis via Linear Programming for Heterogeneous Instruction Sets","ref_index":29,"is_internal_anchor":true},{"citing_arxiv_id":"2605.21662","citing_title":"Fidelity-Aware Frequency Allocation and Transpilation Co-Design for Tunable Coupler Quantum Systems","ref_index":47,"is_internal_anchor":true},{"citing_arxiv_id":"2511.04608","citing_title":"Unifying Qubit Routing Across Diverse Quantum ISAs via Canonical Representation","ref_index":59,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WIUN2X23FKJM5I4EANPQYZW3QC","json":"https://pith.science/pith/WIUN2X23FKJM5I4EANPQYZW3QC.json","graph_json":"https://pith.science/api/pith-number/WIUN2X23FKJM5I4EANPQYZW3QC/graph.json","events_json":"https://pith.science/api/pith-number/WIUN2X23FKJM5I4EANPQYZW3QC/events.json","paper":"https://pith.science/paper/WIUN2X23"},"agent_actions":{"view_html":"https://pith.science/pith/WIUN2X23FKJM5I4EANPQYZW3QC","download_json":"https://pith.science/pith/WIUN2X23FKJM5I4EANPQYZW3QC.json","view_paper":"https://pith.science/paper/WIUN2X23","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=quant-ph/0507171&json=true","fetch_graph":"https://pith.science/api/pith-number/WIUN2X23FKJM5I4EANPQYZW3QC/graph.json","fetch_events":"https://pith.science/api/pith-number/WIUN2X23FKJM5I4EANPQYZW3QC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WIUN2X23FKJM5I4EANPQYZW3QC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WIUN2X23FKJM5I4EANPQYZW3QC/action/storage_attestation","attest_author":"https://pith.science/pith/WIUN2X23FKJM5I4EANPQYZW3QC/action/author_attestation","sign_citation":"https://pith.science/pith/WIUN2X23FKJM5I4EANPQYZW3QC/action/citation_signature","submit_replication":"https://pith.science/pith/WIUN2X23FKJM5I4EANPQYZW3QC/action/replication_record"}},"created_at":"2026-07-04T14:47:00.791000+00:00","updated_at":"2026-07-04T14:47:00.791000+00:00"}