{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,13]],"date-time":"2026-08-13T00:17:01Z","timestamp":1786580221090,"version":"build-2736575974"},"reference-count":0,"publisher":"Rinton Press","issue":"11&12","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["QIC"],"published-print":{"date-parts":[[2016,9]]},"abstract":"<jats:p>We consider the problem of approximating arbitrary single-qubit z-rotations by ancillafree Clifford+T circuits, up to given epsilon. We present a fast new probabilistic algorithm for solving this problem optimally, i.e., for finding the shortest possible circuit whatsoever for the given problem instance. The algorithm requires a factoring oracle (such as a quantum computer). Even in the absence of a factoring oracle, the algorithm is still near-optimal under a mild number-theoretic hypothesis. In this case, the algorithm finds a solution of T-count m + O(log(log(1\/\u03b5))), where m is the T-count of the second-to-optimal solution. In the typical case, this yields circuit approximations of Tcount 3 log2 (1\/\u03b5) + O(log(log(1\/\u03b5))). Our algorithm is efficient in practice, and provably efficient under the above-mentioned number-theoretic hypothesis, in the sense that its expected runtime is O(polylog(1\/\u03b5)).<\/jats:p>","DOI":"10.26421\/qic16.11-12-1","type":"journal-article","created":{"date-parts":[[2021,2,25]],"date-time":"2021-02-25T02:50:21Z","timestamp":1614221421000},"page":"901-953","source":"Crossref","is-referenced-by-count":95,"title":["Optimal ancilla-free Clifford+T approximation of z-rotations"],"prefix":"10.26421","volume":"16","author":[{"given":"Neil J.","family":"Ross","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter","family":"Selinger","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"10955","published-online":{"date-parts":[[2016,9]]},"container-title":["Quantum Information and Computation"],"original-title":[],"deposited":{"date-parts":[[2021,2,25]],"date-time":"2021-02-25T02:50:22Z","timestamp":1614221422000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.rintonpress.com\/journals\/doi\/QIC16.11-12-1.html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,9]]},"references-count":0,"journal-issue":{"issue":"11&12","published-online":{"date-parts":[[2016,9]]},"published-print":{"date-parts":[[2016,9]]}},"URL":"https:\/\/doi.org\/10.26421\/qic16.11-12-1","relation":{},"ISSN":["1533-7146","1533-7146"],"issn-type":[{"value":"1533-7146","type":"print"},{"value":"1533-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,9]]}}}