{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T14:13:13Z","timestamp":1771855993687,"version":"3.50.1"},"reference-count":44,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T00:00:00Z","timestamp":1771804800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"\n Unitary designs are essential tools in several quantum information protocols. Similarly to other design concepts, unitary designs are mainly used to facilitate averaging over a relevant space, in this case, the unitary group\n \n \n U<\/mml:mi>\n <\/mml:mrow>\n (<\/mml:mo>\n d<\/mml:mi>\n )<\/mml:mo>\n <\/mml:math>\n . While it is known that exact unitary\n \n t<\/mml:mi>\n <\/mml:math>\n -designs exist for any degree\n \n t<\/mml:mi>\n <\/mml:math>\n and dimension\n \n d<\/mml:mi>\n <\/mml:math>\n , the most appealing type of designs, group designs (in which the elements of the design form a group), can provide at most\n \n 3<\/mml:mn>\n <\/mml:math>\n -designs. Moreover, even group\n \n 2<\/mml:mn>\n <\/mml:math>\n -designs can exist only in limited dimensions. In this paper, we present novel construction methods for creating exact generalized group designs based on the representation theory of the unitary group and its finite subgroups that overcome the\n \n 4<\/mml:mn>\n <\/mml:math>\n -design-barrier of unitary group designs. Furthermore, a construction is presented for creating generalized group\n \n 2<\/mml:mn>\n <\/mml:math>\n -designs in arbitrary dimensions.\n <\/jats:p>","DOI":"10.22331\/q-2026-02-23-2008","type":"journal-article","created":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T13:22:46Z","timestamp":1771852966000},"page":"2008","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Generalized group designs: constructing novel unitary 2-, 3- and 4-designs"],"prefix":"10.22331","volume":"10","author":[{"given":"\u00c1goston","family":"Kaposi","sequence":"first","affiliation":[{"name":"Quantum Computing and Quantum Information Research Group, HUN-REN Wigner Research Centre for Physics, Konkoly\u2013Thege Mikl\u00f3s \u00fat 29-33, Budapest, H-1525, Hungary"},{"name":"Department of Programming Languages and Compilers, E\u00f6tv\u00f6s Lor\u00e1nd University, P\u00e1zm\u00e1ny P\u00e9ter s\u00e9t\u00e1ny 1\/C, Budapest, H-1117, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zolt\u00e1n","family":"Kolarovszki","sequence":"additional","affiliation":[{"name":"Quantum Computing and Quantum Information Research Group, HUN-REN Wigner Research Centre for Physics, Konkoly\u2013Thege Mikl\u00f3s \u00fat 29-33, Budapest, H-1525, Hungary"},{"name":"Department of Programming Languages and Compilers, E\u00f6tv\u00f6s Lor\u00e1nd University, P\u00e1zm\u00e1ny P\u00e9ter s\u00e9t\u00e1ny 1\/C, Budapest, H-1117, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Adrian","family":"Solymos","sequence":"additional","affiliation":[{"name":"Quantum Computing and Quantum Information Research Group, HUN-REN Wigner Research Centre for Physics, Konkoly\u2013Thege Mikl\u00f3s \u00fat 29-33, Budapest, H-1525, Hungary"},{"name":"Department of Physics of Complex Systems, E\u00f6tv\u00f6s Lor\u00e1nd University, P\u00e1zm\u00e1ny P\u00e9ter s\u00e9t\u00e1ny 1\/A, Budapest, H-1117, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zolt\u00e1n","family":"Zimbor\u00e1s","sequence":"additional","affiliation":[{"name":"Quantum Computing and Quantum Information Research Group, HUN-REN Wigner Research Centre for Physics, Konkoly\u2013Thege Mikl\u00f3s \u00fat 29-33, Budapest, H-1525, Hungary"},{"name":"Department of Programming Languages and Compilers, E\u00f6tv\u00f6s Lor\u00e1nd University, P\u00e1zm\u00e1ny P\u00e9ter s\u00e9t\u00e1ny 1\/C, Budapest, H-1117, Hungary"},{"name":"Algorithmiq Ltd, Kanavakatu 3C, Helsinki, 00160, Finland"},{"name":"University of Helsinki, Yliopistonkatu 4, Helsinki, 00100, Finland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2026,2,23]]},"reference":[{"key":"0","unstructured":"Christoph Dankert. ``Efficient Simulation of Random Quantum States and Operators'' (2005). arXiv:quant-ph\/0512217."},{"key":"1","doi-asserted-by":"publisher","unstructured":"Christoph Dankert, Richard Cleve, Joseph Emerson, and Etera Livine. ``Exact and approximate unitary 2-designs and their application to fidelity estimation''. 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