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We introduce a solution-generating technique to solve the <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>d<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>m<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>l<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>-generalized Yang-Baxter equation, for <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>m<\/mml:mi><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mo>\/<\/mml:mo><\/mml:mrow><mml:mn>2<\/mml:mn><mml:mo>\u2264<\/mml:mo><mml:mi>l<\/mml:mi><mml:mo>\u2264<\/mml:mo><mml:mi>m<\/mml:mi><\/mml:math>, which allows to systematically construct such braiding operators. This is achieved by using partition algebras, a generalization of the Temperley-Lieb algebra encountered in statistical mechanics. We obtain families of unitary and non-unitary braiding operators that generate the full braid group. Explicit examples are given for a 2-, 3-, and 4-qubit system, including the classification of the entangled states generated by these operators based on Stochastic Local Operations and Classical Communication.<\/jats:p>","DOI":"10.22331\/q-2020-08-27-311","type":"journal-article","created":{"date-parts":[[2020,8,27]],"date-time":"2020-08-27T11:48:02Z","timestamp":1598528882000},"page":"311","source":"Crossref","is-referenced-by-count":11,"title":["Braiding quantum gates from partition algebras"],"prefix":"10.22331","volume":"4","author":[{"given":"Pramod","family":"Padmanabhan","sequence":"first","affiliation":[{"name":"Center for Theoretical Physics of Complex Systems, Institute for Basic Science, Daejeon, South Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fumihiko","family":"Sugino","sequence":"additional","affiliation":[{"name":"Center for Theoretical Physics of the Universe, Institute for Basic Science, Daejeon, South Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Diego","family":"Trancanelli","sequence":"additional","affiliation":[{"name":"Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Universit\u00e0 di Modena e Reggio Emilia, via Campi 213\/A, 41125 Modena, Italy"},{"name":"INFN Sezione di Bologna, via Irnerio 46, 40126 Bologna, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"9598","published-online":{"date-parts":[[2020,8,27]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"P. 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