{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:14:40Z","timestamp":1753884880318,"version":"3.41.2"},"reference-count":20,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Open Syst. Inf. Dyn."],"published-print":{"date-parts":[[2024,9]]},"abstract":"<jats:p>The subgroups XU(2), YU(2), and ZU(2) of the unitary group U(2) allow to find twenty-four different decompositions of an arbitrary [Formula: see text] unitary matrix. Because the group YU(2) has not been considered before, 20 out of the 24\u00a0decompositions are new. Introducing this YU(2) group allows to highlight, within quantum circuit design, a symmetry similar to the threefold symmetry of the Pauli matrices of spin systems. Similar subgroups of the unitary group U([Formula: see text]) lead to various new decompositions of an arbitrary [Formula: see text] unitary matrix. Whereas for [Formula: see text] equal 2, this leads to the synthesis of single-qubit quantum gates, for [Formula: see text] equal a power of\u00a02, this leads to new design methods for multiple-qubit circuits.<\/jats:p>","DOI":"10.1142\/s1230161224500148","type":"journal-article","created":{"date-parts":[[2024,8,31]],"date-time":"2024-08-31T03:30:20Z","timestamp":1725075020000},"source":"Crossref","is-referenced-by-count":1,"title":["X, Y, and Z Subgroups of the Unitary Group"],"prefix":"10.1142","volume":"31","author":[{"given":"Alexis","family":"De Vos","sequence":"first","affiliation":[{"name":"Universiteit Gent, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2024,8,26]]},"reference":[{"key":"S1230161224500148BIB001","doi-asserted-by":"publisher","DOI":"10.26421\/QIC13.7-8-4"},{"key":"S1230161224500148BIB002","doi-asserted-by":"publisher","DOI":"10.1063\/1.4927100"},{"key":"S1230161224500148BIB003","doi-asserted-by":"publisher","DOI":"10.26421\/QIC15.1-2-10"},{"key":"S1230161224500148BIB004","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.102.022406"},{"key":"S1230161224500148BIB005","doi-asserted-by":"publisher","DOI":"10.1088\/2058-9565\/ab8963"},{"key":"S1230161224500148BIB006","doi-asserted-by":"publisher","DOI":"10.1088\/2058-9565\/ac5d20"},{"volume-title":"26 th Conference on Quantum Information Processing, Gent","author":"Kliuchnikov V.","key":"S1230161224500148BIB007"},{"key":"S1230161224500148BIB008","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.88.042322"},{"key":"S1230161224500148BIB009","doi-asserted-by":"crossref","unstructured":"W. Castryck, J. Demeyer, A. De Vos, O. Keszocze, M. Soeken , 48 th International Symposium on Multiple-Valued Logic, Linz, 16\u201318 May 2018, pp. 254\u2013259.","DOI":"10.1109\/ISMVL.2018.00051"},{"key":"S1230161224500148BIB010","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.52.3457"},{"key":"S1230161224500148BIB011","doi-asserted-by":"publisher","DOI":"10.1109\/TCAD.2005.855930"},{"key":"S1230161224500148BIB012","volume":"11","author":"De Vos A.","year":"2014","journal-title":"A.C.M. Journal on Emerging Technologies in Computing Systems"},{"key":"S1230161224500148BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2015.06.019"},{"key":"S1230161224500148BIB015","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.94.052317"},{"key":"S1230161224500148BIB017","doi-asserted-by":"crossref","unstructured":"Z. Sasanian, D. Miller , 3 rd International Workshop on Reversible Computation, Gent, 4\u20135 July 2011, pp. 77\u201388.","DOI":"10.1007\/978-3-642-29517-1_7"},{"key":"S1230161224500148BIB018","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.88.012313"},{"key":"S1230161224500148BIB019","doi-asserted-by":"crossref","unstructured":"A. De Vos, S. De Baerdemacker , 10th International Conference on Reversible Computation, Leicester, 12\u201314 September 2018, pp. 133\u2013143.","DOI":"10.1007\/978-3-319-99498-7_9"},{"key":"S1230161224500148BIB020","first-page":"73","volume":"11","author":"Combescure M.","year":"2009","journal-title":"CUBO A\u00a0Mathematical Journal"},{"key":"S1230161224500148BIB021","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2014.12.031"},{"key":"S1230161224500148BIB022","doi-asserted-by":"publisher","DOI":"10.1142\/S1230161214500139"}],"container-title":["Open Systems &amp; Information Dynamics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1230161224500148","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,27]],"date-time":"2024-11-27T15:56:58Z","timestamp":1732723018000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S1230161224500148"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,26]]},"references-count":20,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2024,9]]}},"alternative-id":["10.1142\/S1230161224500148"],"URL":"https:\/\/doi.org\/10.1142\/s1230161224500148","relation":{},"ISSN":["1230-1612","1793-7191"],"issn-type":[{"type":"print","value":"1230-1612"},{"type":"electronic","value":"1793-7191"}],"subject":[],"published":{"date-parts":[[2024,8,26]]},"article-number":"2450014"}}