{"paper":{"title":"Cartan-Khaneja-Glaser decomposition of $SU(2^n)$ via involutive automorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Arthur C. R. Dutra, Henrique N. S\\'a Earp, John A. Mora Rodr\\'iguez, Marcelo Terra Cunha","submitted_at":"2025-09-05T19:46:50Z","abstract_excerpt":"We present a novel algorithm for performing the Cartan-Khaneja-Glaser decomposition of unitary matrices in $SU(2^n)$, a critical task for efficient quantum circuit design. Building upon the approach introduced by S\\'a Earp and Pachos (2005), we overcome key limitations of their method, such as reliance on ill-defined matrix logarithms and the convergence issues of truncated Baker-Campbell-Hausdorff(BCH) series. Our reformulation leverages the algebraic structure of involutive automorphisms and symmetric Lie algebra decompositions to yield a stable and recursive factorization process. We provid"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.05468","kind":"arxiv","version":2},"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/2509.05468/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"}