{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T08:18:44Z","timestamp":1770970724553,"version":"3.50.1"},"reference-count":69,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T00:00:00Z","timestamp":1768348800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T00:00:00Z","timestamp":1768348800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"DOI":"10.1007\/s11128-025-05039-3","type":"journal-article","created":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T05:34:41Z","timestamp":1768368881000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Novel unitary and entangling solutions to the parameter-dependent Yang\u2013Baxter equation in all dimensions"],"prefix":"10.1007","volume":"25","author":[{"given":"Arash","family":"Pourkia","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2026,1,14]]},"reference":[{"key":"5039_CR1","doi-asserted-by":"publisher","first-page":"1312","DOI":"10.1103\/PhysRevLett.19.1312","volume":"19","author":"CN Yang","year":"1967","unstructured":"Yang, C.N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Phys. Rev. Lett. 19, 1312 (1967)","journal-title":"Phys. Rev. Lett."},{"key":"5039_CR2","first-page":"2526","volume":"289","author":"RJ Baxter","year":"1978","unstructured":"Baxter, R.J.: Solvable eight-vertex model on an arbitrary planar lattice. Proc. Roy. Soc. A 289, 2526\u201347 (1978)","journal-title":"Proc. Roy. Soc. A"},{"issue":"15","key":"5039_CR3","doi-asserted-by":"publisher","first-page":"3759","DOI":"10.1142\/S0217751X89001503","volume":"4","author":"M Jimbo","year":"1989","unstructured":"Jimbo, M.: Introduction to the Yang-Baxter Equation. Int. J. Mod. Phys. A 4(15), 3759\u20133777 (1989)","journal-title":"Int. J. Mod. Phys. A"},{"key":"5039_CR4","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1103\/PhysRev.65.117","volume":"65","author":"A Onsager","year":"1944","unstructured":"Onsager, A.: Crystal statistics. I. A two-dimensional model with an order-disorder transition. Phys. Rev. 65, 117\u201349 (1944)","journal-title":"Phys. Rev."},{"key":"5039_CR5","doi-asserted-by":"crossref","unstructured":"Perk, J.H.H., Au-Yang, H.: Yang-baxter equation. In: Encyclopedia of Mathematical Physics, eds. J.-P. Fran\u00e7oise, G.L. Naber and Tsou S.T., Oxford: Elsevier, (ISBN 978-0-1251-2666-3), 5, 465\u2013473 (2006)","DOI":"10.1016\/B0-12-512666-2\/00191-7"},{"key":"5039_CR6","doi-asserted-by":"publisher","DOI":"10.1142\/1021","volume-title":"Yang-Baxter Equation in Integrable Systems","year":"1987","unstructured":"Jimbo, M. (ed.): Yang-Baxter Equation in Integrable Systems. World Scientific, Singapore (1987). https:\/\/doi.org\/10.1142\/1021"},{"key":"5039_CR7","doi-asserted-by":"crossref","unstructured":"Hietarinta, Jarmo: All solutions to the constant quantum Yang-Baxter equation in two dimensions. Physics Letters A 165, 245\u2013251 (1992) North Holland","DOI":"10.1016\/0375-9601(92)90044-M"},{"issue":"1","key":"5039_CR8","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1090\/S0273-0979-1985-15304-2","volume":"12","author":"VFR Jones","year":"1985","unstructured":"Jones, V.F.R.: A polynomial invariant for knots via Von Neumann algebras. Bullet. (New Series) Am. Math. Soc. 12(1), 103\u2013111 (1985)","journal-title":"Bullet. (New Series) Am. Math. Soc."},{"issue":"3","key":"5039_CR9","doi-asserted-by":"publisher","first-page":"527","DOI":"10.1007\/BF01393746","volume":"92","author":"VG Turaev","year":"1988","unstructured":"Turaev, V.G.: The Yang-Baxter equation and invariants of links. Invent. Math. 92(3), 527\u2013553 (1988)","journal-title":"Invent. Math."},{"key":"5039_CR10","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1007\/BF02096797","volume":"136","author":"Y Cheng","year":"1991","unstructured":"Cheng, Y., Ge, M.L., Xue, K.: Yang-baxterization of braid group representations. Commun. Math. Phys. 136, 195\u2013208 (1991)","journal-title":"Commun. Math. Phys."},{"issue":"1","key":"5039_CR11","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1090\/S0273-0979-02-00964-3","volume":"40","author":"M Freedman","year":"2003","unstructured":"Freedman, M., Kitaev, A., Larsen, M., Wang, Z.: Topological quantum computation. Bull. Am. Math. Soc. 40(1), 31\u201338 (2003)","journal-title":"Bull. Am. Math. Soc."},{"key":"5039_CR12","doi-asserted-by":"publisher","first-page":"1083","DOI":"10.1103\/RevModPhys.80.1083","volume":"80","author":"C Nayak","year":"2008","unstructured":"Nayak, C., Simon, S.H., Stern, A., Freedman, M., Das Sarma, S.: Non-abelian anyons and topological quantum computation. Rev. Mod. Phys. 80, 1083 (2008)","journal-title":"Rev. Mod. Phys."},{"key":"5039_CR13","doi-asserted-by":"publisher","first-page":"519","DOI":"10.1134\/S0021364020090027","volume":"111","author":"N Kolganov","year":"2020","unstructured":"Kolganov, N., Morozov, A.: Quantum $$ {R}$$-Matrices as Universal Qubit Gates. JETP Lett. 111, 519\u2013524 (2020). https:\/\/doi.org\/10.1134\/S0021364020090027","journal-title":"JETP Lett."},{"key":"5039_CR14","doi-asserted-by":"publisher","DOI":"10.1016\/j.nuclphysb.2023.116072","volume":"987","author":"N Kolganov","year":"2023","unstructured":"Kolganov, N., Mironov, S., Morozov, A.: Large k topological quantum computer. Nucl. Phys. B 987, 116072 (2023). https:\/\/doi.org\/10.1016\/j.nuclphysb.2023.116072","journal-title":"Nucl. Phys. B"},{"key":"5039_CR15","doi-asserted-by":"publisher","first-page":"134","DOI":"10.1088\/1367-2630\/6\/1\/134","volume":"6","author":"Louis H Kauffman","year":"2004","unstructured":"Kauffman, Louis H., Lomonaco, Samuel J.: Braiding operators are universal quantum gates. New Journal of Physics 6, 134 (2004)","journal-title":"New Journal of Physics"},{"key":"5039_CR16","doi-asserted-by":"crossref","unstructured":"Alagic, G., Jarret, M., Jordan, S.P.: Yang-Baxter operators need quantum entanglement to distinguish knots. J. Phys. A Math. Theor. 49(7), (2016)","DOI":"10.1088\/1751-8113\/49\/7\/075203"},{"key":"5039_CR17","doi-asserted-by":"publisher","first-page":"162","DOI":"10.1134\/S0001434611070170","volume":"90","author":"L Accardi","year":"2011","unstructured":"Accardi, L., Mukhamedov, F.M., Saburov, M.K.: Uniqueness of quantum Markov chains associated with an XY-model on a cayley tree of order 2. Math. Notes 90, 162 (2011)","journal-title":"Math. Notes"},{"issue":"3","key":"5039_CR18","doi-asserted-by":"publisher","first-page":"443","DOI":"10.1142\/S021902571100447X","volume":"14","author":"L Accardi","year":"2011","unstructured":"Accardi, L., Mukhamedov, F., Saburov, M.: On quantum Markov chains on Cayley Tree I: uniqueness of the associated chain with XY-model on the Cayley tree of order two. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 14(3), 443\u2013463 (2011)","journal-title":"Infin. Dimens. Anal. Quantum Probab. Relat. Top."},{"key":"5039_CR19","doi-asserted-by":"publisher","first-page":"1109","DOI":"10.1007\/s00023-011-0107-2","volume":"12","author":"L Accardi","year":"2011","unstructured":"Accardi, L., Mukhamedov, F., Saburov, M.: On quantum Markov chains on Cayley Tree II: phase transitions for the associated chain with XY-model on the Cayley tree of order three. Ann. Henri Poincar\u00e9 12, 1109\u20131144 (2011)","journal-title":"Ann. Henri Poincar\u00e9"},{"key":"5039_CR20","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1007\/s10955-014-1083-y","volume":"157","author":"L Accardi","year":"2014","unstructured":"Accardi, L., Mukhamedov, F., Saburov, M.: On quantum Markov chains on Cayley tree III: Ising model. J. Stat. Phys. 157, 303\u2013329 (2014)","journal-title":"J. Stat. Phys."},{"issue":"5","key":"5039_CR21","doi-asserted-by":"publisher","first-page":"1344","DOI":"10.1016\/j.laa.2011.08.012","volume":"436","author":"R Ganikhodzhaev","year":"2012","unstructured":"Ganikhodzhaev, R., Mukhamedov, F., Saburov, M.: G-decompositions of matrices and related problems I. Linear Algebra Appl. 436(5), 1344\u20131366 (2012)","journal-title":"Linear Algebra Appl."},{"key":"5039_CR22","doi-asserted-by":"crossref","unstructured":"Kauffman, Louis H., Lomonaco, Samuel J.: Quantum entanglement and topological entanglement. New J. Phys. 4, 731-7318 (2002)","DOI":"10.1088\/1367-2630\/4\/1\/373"},{"key":"5039_CR23","doi-asserted-by":"publisher","first-page":"134","DOI":"10.1088\/1367-2630\/6\/1\/134","volume":"6","author":"LH Kauffman","year":"2004","unstructured":"Kauffman, L.H., Lomonaco, S.J.: Braiding operators are universal quantum gates. New J. Phys. 6, 134 (2004)","journal-title":"New J. Phys."},{"issue":"1","key":"5039_CR24","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1023\/A:1025843426102","volume":"2","author":"HA Dye","year":"2003","unstructured":"Dye, H.A.: Unitary solutions to the Yang-Baxter equation in dimension four. Quantum Inf. Process. 2(1), 117\u2013152 (2003)","journal-title":"Quantum Inf. Process."},{"issue":"04","key":"5039_CR25","doi-asserted-by":"publisher","first-page":"669","DOI":"10.1142\/S0219749905001547","volume":"03","author":"Y Zhang","year":"2005","unstructured":"Zhang, Y., Kauffman, L.H., Ge, M.-L.: Universal Quantum Gates, Yang-Baxterizations and Hamiltonians. Int. J. Quant. Inf. 03(04), 669\u2013678 (2005). https:\/\/doi.org\/10.1142\/S0219749905001547","journal-title":"Int. J. Quant. Inf."},{"key":"5039_CR26","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1007\/s11128-005-7655-7","volume":"4","author":"Y Zhang","year":"2005","unstructured":"Zhang, Y., Kauffman, L.H., Ge, M.L.: Yang-Baxterizations, Universal Quantum Gates and Hamiltonians. Quantum Inf Process 4, 159\u2013197 (2005). https:\/\/doi.org\/10.1007\/s11128-005-7655-7","journal-title":"Quantum Inf Process"},{"key":"5039_CR27","doi-asserted-by":"publisher","first-page":"413","DOI":"10.1142\/S0218216506004580","volume":"15","author":"J Franko","year":"2006","unstructured":"Franko, J., Rowell, E.C., Wang, Z.J.: Extraspecial 2-groups and images of braid group representations. Knot Theory Ramif. 15, 413 (2006)","journal-title":"Knot Theory Ramif."},{"key":"5039_CR28","doi-asserted-by":"publisher","first-page":"1145","DOI":"10.1007\/s11232-014-0205-7","volume":"181","author":"ML Ge","year":"2014","unstructured":"Ge, M.L., Yu, L.W., Xue, K., et al.: Solutions of the Yang-Baxter equation associated with a topological basis and applications in quantum information. Theor. Math. Phys. 181, 1145\u20131163 (2014). https:\/\/doi.org\/10.1007\/s11232-014-0205-7","journal-title":"Theor. Math. Phys."},{"key":"5039_CR29","doi-asserted-by":"publisher","first-page":"11599","DOI":"10.1088\/0305-4470\/39\/37\/017","volume":"39","author":"Y Zhang","year":"2006","unstructured":"Zhang, Y.: Teleportation, braid group and Temperley-Lieb algebra. J. Phys. A: Math. Gen. 39, 11599 (2006). https:\/\/doi.org\/10.1088\/0305-4470\/39\/37\/017","journal-title":"J. Phys. A: Math. Gen."},{"issue":"7\u20138","key":"5039_CR30","first-page":"685","volume":"10","author":"EC Rowell","year":"2010","unstructured":"Rowell, E.C., Zhang, Y., Wu, Y.S., Ge, M.L.: Extraspecial two-groups, generalized Yang-Baxter equations and braiding quantum gates. Quant. Inf. Comput. 10(7\u20138), 685\u2013702 (2010)","journal-title":"Quant. Inf. Comput."},{"key":"5039_CR31","doi-asserted-by":"publisher","first-page":"139","DOI":"10.21468\/SciPostPhys.18.4.139","volume":"18","author":"Luke Corcoran","year":"2025","unstructured":"Corcoran, Luke, de Leeuw, Marius, Pozsgay, Bal\u00e1zs: Integrable models on Rydberg atom chains. SciPost Phys. 18, 139 (2025). https:\/\/doi.org\/10.21468\/SciPostPhys.18.4.139","journal-title":"SciPost Phys."},{"key":"5039_CR32","unstructured":"Pudda, F., Chizzini, M., Crippa, L.: Generalised quan-tum gates for qudits and their application in quantum fourier transform (2024). https:\/\/arxiv.org\/abs\/2410.05122"},{"key":"5039_CR33","unstructured":"Valentine, N., Shah, N.M., Halim, U.A., Husain, S.K.S., Jellal, A.: Transforming qubits via quasi-geometric approaches. https:\/\/arxiv.org\/abs\/2407.07562"},{"key":"5039_CR34","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1007\/s11128-016-1512-8","volume":"16","author":"K Zhang","year":"2017","unstructured":"Zhang, K., Zhang, Y.: Quantum teleportation and Birman\u2013Murakami\u2013Wenzl algebra. Quantum Inf. Process. 16, 52 (2017). https:\/\/doi.org\/10.1007\/s11128-016-1512-8","journal-title":"Quantum Inf. Process."},{"key":"5039_CR35","doi-asserted-by":"publisher","DOI":"10.1088\/1402-4896\/ad7e57","volume":"99","author":"F Chouraqui","year":"2024","unstructured":"Chouraqui, F.: The Yang-Baxter equation, quantum computing and quantum entanglement. Phys. Scr. 99, 115215 (2024). https:\/\/doi.org\/10.1088\/1402-4896\/ad7e57","journal-title":"Phys. Scr."},{"key":"5039_CR36","doi-asserted-by":"publisher","first-page":"10","DOI":"10.1016\/j.aop.2016.06.023","volume":"373","author":"J Arash Pourkia","year":"2016","unstructured":"Arash Pourkia, J.: Batle, Cyclic groups and quantum logic gates. Ann. Phys. 373, 10\u201327 (2016). https:\/\/doi.org\/10.1016\/j.aop.2016.06.023","journal-title":"Ann. Phys."},{"issue":"1","key":"5039_CR37","doi-asserted-by":"publisher","first-page":"544","DOI":"10.1134\/S0040577924040032","volume":"219","author":"A Pourkia","year":"2024","unstructured":"Pourkia, A.: Yang-Baxter equation in all dimensions and universal Qudit gates. Theor. Math. Phys. 219(1), 544\u2013556 (2024). https:\/\/doi.org\/10.1134\/S0040577924040032","journal-title":"Theor. Math. Phys."},{"key":"5039_CR38","doi-asserted-by":"publisher","first-page":"86","DOI":"10.1016\/j.laa.2018.02.001","volume":"546","author":"A Smoktunowicz","year":"2018","unstructured":"Smoktunowicz, A., Smoktunowicz, A.: Set-theoretic solutions of the Yang-Baxter equation and new classes of R-matrices. Linear Algebra Appl. 546, 86\u2013114 (2018). https:\/\/doi.org\/10.1016\/j.laa.2018.02.001. (ISSN 0024-3795)","journal-title":"Linear Algebra Appl."},{"key":"5039_CR39","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1016\/j.laa.2023.04.005","volume":"669","author":"SK Mishra","year":"2023","unstructured":"Mishra, S.K., Das, A., Hazra, S.: K Non-abelian extensions of Rota-Baxter Lie algebras and inducibility of automorphisms. Linear Algebra Appl. 669, 147\u2013174 (2023)","journal-title":"Linear Algebra Appl."},{"key":"5039_CR40","doi-asserted-by":"publisher","unstructured":"de Leeuw, M. et al.: Classifying integrable spin-1\/2 chains with nearest neighbour interactions. J. Phys. A Math. Theor. 52(50), (2019). https:\/\/doi.org\/10.1088\/1751-8121\/ab529f","DOI":"10.1088\/1751-8121\/ab529f"},{"key":"5039_CR41","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.104.054123","volume":"104","author":"T Gombor","year":"2021","unstructured":"Gombor, T., Pozsgay, B.: Integrable spin chains and cellular automata with medium-range interaction. Phys. Rev. E 104, 054123 (2021)","journal-title":"Phys. Rev. E"},{"key":"5039_CR42","doi-asserted-by":"publisher","first-page":"609","DOI":"10.1134\/S0040577923050021","volume":"215","author":"VG Bardakov","year":"2023","unstructured":"Bardakov, V.G., Talalaev, D.V.: Extensions of Yang-Baxtersets. Theor Math Phys 215, 609\u2013621 (2023). https:\/\/doi.org\/10.1134\/S0040577923050021","journal-title":"Theor Math Phys"},{"key":"5039_CR43","doi-asserted-by":"publisher","DOI":"10.1016\/j.nuclphysb.2024.116664","volume":"1007","author":"P Padmanabhan","year":"2024","unstructured":"Padmanabhan, P., Korepin, V.: Solving the Yang-Baxter, tetrahedron and higher simplex equations using Clifford algebras. Nucl. Phys. B 1007, 116664 (2024). https:\/\/doi.org\/10.1016\/j.nuclphysb.2024.116664","journal-title":"Nucl. Phys. B"},{"key":"5039_CR44","doi-asserted-by":"publisher","DOI":"10.1016\/j.geomphys.2022.104687","volume":"183","author":"V Abramov","year":"2023","unstructured":"Abramov, V., Zappala, E.: 3-Lie algebras, ternary Nambu-Lie algebras and the Yang-Baxter equation. J. Geom. Phys. 183, 104687 (2023). https:\/\/doi.org\/10.1016\/j.geomphys.2022.104687","journal-title":"J. Geom. Phys."},{"key":"5039_CR45","doi-asserted-by":"publisher","DOI":"10.1016\/j.geomphys.2022.104499","volume":"176","author":"I Burban","year":"2022","unstructured":"Burban, I., Peruzzi, A.: On elliptic solutions of the associative Yang-Baxter equation. J. Geom. Phys. 176, 104499 (2022). https:\/\/doi.org\/10.1016\/j.geomphys.2022.104499","journal-title":"J. Geom. Phys."},{"key":"5039_CR46","doi-asserted-by":"publisher","first-page":"045","DOI":"10.21468\/SciPostPhysCore.7.3.045","volume":"7","author":"Luke Corcoran","year":"2024","unstructured":"Corcoran, Luke, de Leeuw, Marius: All regular 4x4 solutions of the Yang-Baxter equation. SciPost Phys. Core 7, 045 (2024). https:\/\/doi.org\/10.21468\/SciPostPhysCore.7.3.045","journal-title":"SciPost Phys. Core"},{"key":"5039_CR47","doi-asserted-by":"publisher","first-page":"078","DOI":"10.21468\/SciPostPhys.16.3.078","volume":"16","author":"Yuan Miao","year":"2024","unstructured":"Miao, Yuan, Gritsev, Vladimir, Kurlov, Denis V.: The Floquet Baxterisation. SciPost Phys. 16, 078 (2024). https:\/\/doi.org\/10.21468\/SciPostPhys.16.3.078","journal-title":"SciPost Phys."},{"key":"5039_CR48","doi-asserted-by":"publisher","unstructured":"Wang, H., Wei, S., Zheng, C., Kong, X., Wen, J., Nie, X., Li, J., Lu, D., Xin, T.: Experimental simulation of the four-dimensional Yang-Baxter equation on a spin quantum simulator. Phys. Rev. A 102, 012610. https:\/\/doi.org\/10.1103\/PhysRevA.102.012610","DOI":"10.1103\/PhysRevA.102.012610"},{"key":"5039_CR49","doi-asserted-by":"publisher","first-page":"846","DOI":"10.3390\/axioms13120846","volume":"13","author":"I Senturk","year":"2024","unstructured":"Senturk, I., Oner, T., \u00c7al\u0131k, A.E., \u015eirin, H., Bilge, M., Rajesh, N.: Set-theoretical solutions for the Yang-Baxter equation in GE-algebras: applications to quantum spin systems. Axioms 13, 846 (2024). https:\/\/doi.org\/10.3390\/axioms13120846","journal-title":"Axioms"},{"key":"5039_CR50","unstructured":"Chen, Y., Zhu, S.: Geometry of Yang-Baxter matrix equations over finite fields (2025) https:\/\/arxiv.org\/abs\/2506.17893"},{"key":"5039_CR51","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1016\/j.jalgebra.2025.03.034","volume":"676","author":"Andrea Albano","year":"2025","unstructured":"Albano, Andrea, Mazzotta, Marzia, Stefanelli, Paola: Reflections to set-theoretic solutions of the Yang-Baxter equation. J. Algebra 676, 106\u2013138 (2025). https:\/\/doi.org\/10.1016\/j.jalgebra.2025.03.034. (ISSN 0021-8693)","journal-title":"J. Algebra"},{"key":"5039_CR52","doi-asserted-by":"publisher","DOI":"10.1016\/j.physo.2025.100263","author":"A Pourkia","year":"2025","unstructured":"Pourkia, A.: Unitary and entangling solutions to the parametric Yang-Baxter equation in all dimensions. Physics Open (2025). https:\/\/doi.org\/10.1016\/j.physo.2025.100263","journal-title":"Physics Open"},{"key":"5039_CR53","doi-asserted-by":"publisher","DOI":"10.29020\/nybg.ejpam.v18i3.6344","author":"Arash Pourkia","year":"2025","unstructured":"Pourkia, Arash: Generalized SWAP and iSWAP and solutions to the Yang-Baxter equation in all dimensions. Eur. J. Pure Appl. Math. (2025). https:\/\/doi.org\/10.29020\/nybg.ejpam.v18i3.6344","journal-title":"Eur. J. Pure Appl. Math."},{"key":"5039_CR54","doi-asserted-by":"publisher","first-page":"5339","DOI":"10.1007\/s00023-024-01449-8","volume":"25","author":"M Nazarov","year":"2024","unstructured":"Nazarov, M.: An elliptic solution of the classical Yang-Baxter equation associated with the Queer Lie Superalgebra. Ann. Henri Poincar\u00e9 25, 5339\u20135347 (2024). https:\/\/doi.org\/10.1007\/s00023-024-01449-8","journal-title":"Ann. Henri Poincar\u00e9"},{"issue":"03","key":"5039_CR55","doi-asserted-by":"publisher","first-page":"547","DOI":"10.1142\/S0218196723500261","volume":"33","author":"F Chouraqui","year":"2023","unstructured":"Chouraqui, F.: The Yang-Baxter equation and Thompson\u2019s group F. Internat. J. Algebra Comput. 33(03), 547\u2013584 (2023). https:\/\/doi.org\/10.1142\/S0218196723500261","journal-title":"Internat. J. Algebra Comput."},{"issue":"8","key":"5039_CR56","doi-asserted-by":"publisher","first-page":"3221","DOI":"10.1080\/00927872.2023.2180181","volume":"51","author":"Fabienne Chouraqui","year":"2023","unstructured":"Chouraqui, Fabienne: On some Garsideness properties of structure groups of set-theoretic solutions of the Yang-Baxter equation. Commun. Algebra 51(8), 3221\u20133231 (2023). https:\/\/doi.org\/10.1080\/00927872.2023.2180181","journal-title":"Commun. Algebra"},{"key":"5039_CR57","unstructured":"Chouraqui, F.: Yang\u2013Baxter equation and cryptography. https:\/\/arxiv.org\/abs\/2212.13807 (2022)"},{"key":"5039_CR58","doi-asserted-by":"publisher","first-page":"328","DOI":"10.1016\/j.jalgebra.2021.12.036","volume":"596","author":"G Valeriy","year":"2022","unstructured":"Valeriy, G.: Bardakov, Vsevolod Gubarev, Rota-Baxter groups, skew left braces, and the Yang-Baxter equation. J. Algebra 596, 328\u2013351 (2022). https:\/\/doi.org\/10.1016\/j.jalgebra.2021.12.036","journal-title":"J. Algebra"},{"key":"5039_CR59","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1134\/S1055134424010012","volume":"34","author":"VG Bardakov","year":"2024","unstructured":"Bardakov, V.G., Chuzhinov, B.B., Emelyanenkov, I.A., et al.: Set-theoretical solutions of the n-simplex equation. Sib. Adv. Math. 34, 1\u201340 (2024). https:\/\/doi.org\/10.1134\/S1055134424010012","journal-title":"Sib. Adv. Math."},{"key":"5039_CR60","doi-asserted-by":"publisher","unstructured":"Bardakov, V.G., Kozlovskaya, T.A., Sololov, P.P., Zimireva, K.V., Zonov, M.N.: Some properties of relative Rota-Baxter operators on groups. Comm. Algebra 1\u201317,(2024). https:\/\/doi.org\/10.1080\/00927872.2024.2413691","DOI":"10.1080\/00927872.2024.2413691"},{"key":"5039_CR61","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2023.133937","volume":"456","author":"TE Kouloukas","year":"2023","unstructured":"Kouloukas, T.E.: Discrete integrable systems associated with relativistic collisions. Physica D: Nonlinear Phenomena 456, 133937 (2023). https:\/\/doi.org\/10.1016\/j.physd.2023.133937. (ISSN 0167\u20132789)","journal-title":"Physica D: Nonlinear Phenomena"},{"key":"5039_CR62","doi-asserted-by":"publisher","unstructured":"Bazhanov, V.V., Sergeev, S.M.: A distant descendant of the six-vertex model. Nuclear Phys. B 1004, 116558 (2024). https:\/\/doi.org\/10.1016\/j.nuclphysb.2024.116558. (ISSN 0550\u20133213)","DOI":"10.1016\/j.nuclphysb.2024.116558"},{"key":"5039_CR63","doi-asserted-by":"publisher","DOI":"10.1016\/j.nuclphysb.2025.116824","volume":"1012","author":"P Kassotakis","year":"2025","unstructured":"Kassotakis, P., Kouloukas, T., Nieszporski, M.: Non-Abelian elastic collisions, associated difference systems of equations and discrete analytic functions. Nuclear Phys. B 1012, 116824 (2025). https:\/\/doi.org\/10.1016\/j.nuclphysb.2025.116824. (ISSN 0550\u20133213)","journal-title":"Nuclear Phys. B"},{"key":"5039_CR64","doi-asserted-by":"publisher","DOI":"10.1016\/j.nuclphysb.2024.116777","volume":"1010","author":"G-L Li","year":"2025","unstructured":"Li, G.-L., Cao, J., Sun, P., Yang, W.-L., Shi, K., Wang, Y.: Exact solution of a quantum integrable system associated with the G2 exceptional Lie algebra. Nuclear Phys. B 1010, 116777 (2025). https:\/\/doi.org\/10.1016\/j.nuclphysb.2024.116777. (ISSN 0550\u20133213)","journal-title":"Nuclear Phys. B"},{"key":"5039_CR65","doi-asserted-by":"crossref","unstructured":"Sopena, A., Alonso, G., Solano, P.: Algebraic Bethe circuits: implementing the Yang-Baxter equation on quantum hardware. Quantum 6, (2022)","DOI":"10.22331\/q-2022-09-08-796"},{"key":"5039_CR66","volume":"108","author":"K Zhang","year":"2023","unstructured":"Zhang, K., Li, L., Wang, X.: Optimal realization of Yang-Baxter gates on quantum computers. Phys. Rev. A 108, 032408 (2023)","journal-title":"Phys. Rev. A"},{"key":"5039_CR67","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-60896-4","volume-title":"Quantum Groups and Their Representations","author":"A Klimyk","year":"1997","unstructured":"Klimyk, A., Schmudgen, K.: Quantum Groups and Their Representations. Springer (1997)"},{"key":"5039_CR68","volume-title":"R Brylinski","author":"JL Brylinski","year":"2002","unstructured":"Brylinski, J.L.: R Brylinski. Universal quantum gates, Mathematics of Quantum Computation (2002)"},{"key":"5039_CR69","unstructured":"Kapcak, S.: SageMath ile Matematik, Nesin Yay\u0131nevi, (2023)\/6"}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-025-05039-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-025-05039-3","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-025-05039-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T07:25:55Z","timestamp":1770967555000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-025-05039-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,14]]},"references-count":69,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,1]]}},"alternative-id":["5039"],"URL":"https:\/\/doi.org\/10.1007\/s11128-025-05039-3","relation":{},"ISSN":["1573-1332"],"issn-type":[{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,14]]},"assertion":[{"value":"28 August 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 December 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 January 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"25"}}