{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,15]],"date-time":"2023-09-15T15:17:32Z","timestamp":1694791052097},"reference-count":0,"publisher":"Rinton Press","issue":"11&12","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["QIC"],"abstract":"<jats:p>An algorithm of Ross and Selinger for the factorization of diagonal elements of PU(2) to within distance $\\varepsilon$ was adapted by Parzanchevski and Sarnak into an efficient probabilistic algorithm for any element of PU(2) using at most effective $3\\log_p\\frac{1}{\\varepsilon^{3}}$ factors from certain well-chosen sets associated to a number field and a prime $p$. The icosahedral super golden gates are one such set associated to $\\mathbb{Q}(\\sqrt{5})$. We leverage recent work of Carvalho Pinto, Petit, and Stier to reduce this bound to $\\frac{7}{3}\\log_{59}\\frac{1}{\\varepsilon^3}$, and we implement the algorithm in Python. This represents an improvement by a multiplicative factor of $\\log_259\\approx5.9$ over the analogous result for the Clifford+$T$ gates. This is of interest because the icosahedral gates have shortest factorization lengths among all super golden gates.<\/jats:p>","DOI":"10.26421\/qic23.11-12-1","type":"journal-article","created":{"date-parts":[[2023,9,14]],"date-time":"2023-09-14T19:42:40Z","timestamp":1694720560000},"page":"901-923","source":"Crossref","is-referenced-by-count":0,"title":["Fast naviation with icosahedral golden gates"],"prefix":"10.26421","volume":"23","author":[{"given":"Terrence R","family":"Blackman","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zachary","family":"Stier","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"10955","published-online":{"date-parts":[[2023,9]]},"container-title":["Quantum Information and Computation"],"original-title":[],"deposited":{"date-parts":[[2023,9,14]],"date-time":"2023-09-14T19:42:41Z","timestamp":1694720561000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.rintonpress.com\/journals\/doi\/QIC23.11-12-1.html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,9]]},"references-count":0,"journal-issue":{"issue":"11&12","published-online":{"date-parts":[[2023,9]]}},"URL":"https:\/\/doi.org\/10.26421\/qic23.11-12-1","relation":{},"ISSN":["1533-7146"],"issn-type":[{"value":"1533-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,9]]}}}