{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T18:43:26Z","timestamp":1774032206666,"version":"3.50.1"},"reference-count":0,"publisher":"Rinton Press","issue":"11&12","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["QIC"],"published-print":{"date-parts":[[2015,9]]},"abstract":"<jats:p>We describe a new efficient algorithm to approximate $z$-rotations by ancilla-free Clifford+$V$ circuits, up to a given precision $\\epsilon$. Our algorithm is optimal in the presence of an oracle for integer factoring: it outputs the shortest Clifford+$V$ circuit solving the given problem instance. In the absence of such an oracle, our algorithm is still near-optimal, producing circuits of $V$\\!-count $m + O(\\log(\\log(1\/\\epsilon)))$, where $m$ is the $V$\\!-count of the third-to-optimal solution. A restricted version of the algorithm approximates $z$-rotations in the Pauli+$V$ gate set. Our method is based on previous work by the author and Selinger on the optimal ancilla-free approximation of $z$-rotations using Clifford+$T$ gates and on previous work by Bocharov, Gurevich, and Svore on the asymptotically optimal ancilla-free approximation of $z$-rotations using Clifford+$V$ gates.<\/jats:p>","DOI":"10.26421\/qic15.11-12-4","type":"journal-article","created":{"date-parts":[[2021,2,28]],"date-time":"2021-02-28T02:51:47Z","timestamp":1614480707000},"page":"932-950","source":"Crossref","is-referenced-by-count":12,"title":["Optimal ancilla-free Clifford+V approximation of z-rotations"],"prefix":"10.26421","volume":"15","author":[{"given":"Neil J.","family":"Ross","sequence":"first","affiliation":[]}],"member":"10955","published-online":{"date-parts":[[2015,9]]},"container-title":["Quantum Information and Computation"],"original-title":[],"deposited":{"date-parts":[[2021,2,28]],"date-time":"2021-02-28T02:51:52Z","timestamp":1614480712000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.rintonpress.com\/journals\/doi\/QIC15.11-12-4.html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,9]]},"references-count":0,"journal-issue":{"issue":"11&12","published-online":{"date-parts":[[2015,9]]},"published-print":{"date-parts":[[2015,9]]}},"URL":"https:\/\/doi.org\/10.26421\/qic15.11-12-4","relation":{},"ISSN":["1533-7146","1533-7146"],"issn-type":[{"value":"1533-7146","type":"print"},{"value":"1533-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,9]]}}}