{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T21:18:26Z","timestamp":1791407906390,"version":"4.3.3"},"reference-count":0,"publisher":"Rinton Press","issue":"15&16","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["QIC"],"published-print":{"date-parts":[[2014,11]]},"abstract":"<jats:p>We present a decomposition technique that uses non-deterministic circuits to approximate an arbitrary single-qubit unitary to within distance $\\epsilon$ and requires significantly fewer non-Clifford gates than existing techniques. We develop ``Repeat-Until-Success\" (RUS) circuits and characterize unitaries that can be exactly represented as an RUS circuit. Our RUS circuits operate by conditioning on a given measurement outcome and using only a small number of non-Clifford gates and ancilla qubits. We construct an algorithm based on RUS circuits that approximates an arbitrary single-qubit $Z$-axis rotation to within distance $\\epsilon$, where the number of $T$ gates scales as $1.26\\log_2(1\/\\epsilon) - 3.53$, an improvement of roughly three-fold over state-of-the-art techniques. We then extend our algorithm and show that a scaling of $2.4\\log_2(1\/\\epsilon) - 3.28$ can be achieved for arbitrary unitaries and a small range of $\\epsilon$, which is roughly twice as good as optimal deterministic decomposition methods.<\/jats:p>","DOI":"10.26421\/qic14.15-16-2","type":"journal-article","created":{"date-parts":[[2021,2,28]],"date-time":"2021-02-28T23:40:57Z","timestamp":1614555657000},"page":"1277-1301","source":"Crossref","is-referenced-by-count":40,"title":["Repeat-Until-Success: Non-deterministic decomposition of single-qubit unitaries"],"prefix":"10.26421","volume":"14","author":[{"given":"Adam","family":"Paetznick","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Krysta M.","family":"Svore","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"10955","published-online":{"date-parts":[[2014,11]]},"container-title":["Quantum Information and Computation"],"original-title":[],"deposited":{"date-parts":[[2021,2,28]],"date-time":"2021-02-28T23:40:59Z","timestamp":1614555659000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.rintonpress.com\/journals\/doi\/QIC14.15-16-2.html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,11]]},"references-count":0,"journal-issue":{"issue":"15&16","published-online":{"date-parts":[[2014,11]]},"published-print":{"date-parts":[[2014,11]]}},"URL":"https:\/\/doi.org\/10.26421\/qic14.15-16-2","relation":{},"ISSN":["1533-7146","1533-7146"],"issn-type":[{"value":"1533-7146","type":"print"},{"value":"1533-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,11]]}}}