{"paper":{"title":"Single-qubit rotation algorithm with logarithmic Toffoli count and gate depth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Christoffer Hindlycke, Jan-{\\AA}ke Larsson","submitted_at":"2024-04-08T15:46:56Z","abstract_excerpt":"We propose a direct (non-recursive) algorithm for applying a rotation $R_{\\theta^\\ast}$, $\\epsilon$-close to a desired rotation $R_\\theta$, to a single qubit using the Clifford+Toffoli gate set. Our algorithm does not rely on repeatedly applying a fixed rotation, but immediately applies $R_{\\theta^\\ast}$. It succeeds with probability strictly greater than $1/2$, has an expected number of repetitions strictly less than 2, expected Toffoli count logarithmic in $\\tfrac{1}{\\epsilon}$, and expected gate depth also logarithmic in $\\tfrac{1}{\\epsilon}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.05618","kind":"arxiv","version":4},"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/2404.05618/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"}