{"paper":{"title":"How to efficiently select an arbitrary Clifford group element","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"John A. Smolin, Robert Koenig","submitted_at":"2014-06-09T13:17:15Z","abstract_excerpt":"We give an algorithm which produces a unique element of the Clifford group $\\mathcal{C}_n$ on $n$ qubits from an integer $0\\le i < |\\mathcal{C}_n|$ (the number of elements in the group). The algorithm involves $O(n^3)$ operations. It is a variant of the subgroup algorithm by Diaconis and Shahshahani which is commonly applied to compact Lie groups. We provide an adaption for the symplectic group $Sp(2n,\\mathbb{F}_2)$ which provides, in addition to a canonical mapping from the integers to group elements $g$, a factorization of $g$ into a sequence of at most $4n$ symplectic transvections. The alg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2170","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/1406.2170/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"}