



01472nas a2200133   4500008004100000245008700041210006900128260001500197520101000212100002601222700003001248700002301278856003701301       2023                        eng d00aNon-invertible symmetry-protected topological order in a group-based cluster state0 aNoninvertible symmetryprotected topological order in a groupbase  c12/14/20233 a<p>Despite growing interest in beyond-group symmetries in quantum condensed matter systems, there are relatively few microscopic lattice models explicitly realizing these symmetries, and many phenomena have yet to be studied at the microscopic level. We introduce a one-dimensional stabilizer Hamiltonian composed of group-based Pauli operators whose ground state is a G&times;Rep(G)-symmetric state: the G cluster state introduced in Brell, New Journal of Physics 17, 023029 (2015) [at this http URL]. We show that this state lies in a symmetry-protected topological (SPT) phase protected by G&times;Rep(G) symmetry, distinct from the symmetric product state by a duality argument. We identify several signatures of SPT order, namely protected edge modes, string order parameters, and topological response. We discuss how G cluster states may be used as a universal resource for measurement-based quantum computation, explicitly working out the case where G is a semidirect product of abelian groups.</p>1 aFechisin, Christopher1 aTantivasadakarn, Nathanan1 aAlbert, Victor, V.  uhttps://arxiv.org/abs/2312.09272