Bombin, H.Martín-Delgado Alcántara, Miguel Ángel2023-06-202023-06-202011-12-011367-263010.1088/1367-2630/13/12/125001https://hdl.handle.net/20.500.14352/42822© IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. We acknowledge financial support from research grant QUITEMAD S2009-ESP-1594, FIS2009-10061, UCM-BS/910758 and European STREP grant PICC.We introduce the concept of nested topological order in a class of exact quantum lattice Hamiltonian models with non-Abelian discrete gauge symmetry. The topological order present in the models can be partially destroyed by introducing a gauge symmetry reduction mechanism. When symmetry is reduced in several islands only, this imposes boundary conditions on the rest of the system, giving rise to topological ground-state degeneracy. This degeneracy is related to the existence of topological fluxes in between islands or, alternatively, hidden charges at islands. Additionally, island deformations give rise to extension of topological quantum computation beyond quasiparticles.engjournal articlehttp://dx.doi.org/10.1088/1367-2630/13/12/125001http://iopscience.iop.orgopen access53Quantum computationSymmetry.Física-Modelos matemáticos