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

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×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×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.

1 aFechisin, Christopher1 aTantivasadakarn, Nathanan1 aAlbert, Victor, V. uhttps://arxiv.org/abs/2312.0927201519nas a2200133 4500008004100000245008200041210006900123260001500192520106200207100002601269700003001295700002301325856003701348 2023 eng d00aSubsystem CSS codes, a tighter stabilizer-to-CSS mapping, and Goursat's Lemma0 aSubsystem CSS codes a tighter stabilizertoCSS mapping and Goursa c11/29/20233 a

The CSS code construction is a powerful framework used to express features of a quantum code in terms of a pair of underlying classical codes. Its subsystem extension allows for similar expressions, but the general case has not been fully explored. Extending previous work of Aly et. al. [quant-ph/0610153], we determine subsystem CSS code parameters, express codewords, and develop a Steane-type decoder using only data from the two underlying classical codes. We show that any subsystem stabilizer code can be ``doubled'' to yield a subsystem CSS code with twice the number of physical, logical, and gauge qudits and up to twice the code distance. This mapping preserves locality and is tighter than the Majorana-based mapping of Bravyi, Leemhuis, and Terhal [New J. Phys. 12 083039 (2010)]. Using Goursat's Lemma, we show that every subsystem stabilizer code can be constructed from two nested subsystem CSS codes satisfying certain constraints, and we characterize subsystem stabilizer codes based on the nested codes' properties.

1 aLiu, Michael, Liaofan1 aTantivasadakarn, Nathanan1 aAlbert, Victor, V. uhttps://arxiv.org/abs/2311.1800301827nas a2200181 4500008004100000245005500041210005500096260001400151490000600165520130500171100002301476700001601499700001501515700002001530700003001550700002801580856003701608 2022 eng d00aPauli Stabilizer Models of Twisted Quantum Doubles0 aPauli Stabilizer Models of Twisted Quantum Doubles c3/30/20220 v33 a

We construct a Pauli stabilizer model for every two-dimensional Abelian topological order that admits a gapped boundary. Our primary example is a Pauli stabilizer model on four-dimensional qudits that belongs to the double semion (DS) phase of matter. The DS stabilizer Hamiltonian is constructed by condensing an emergent boson in a Z4 toric code, where the condensation is implemented by making certain two-body measurements. We rigorously verify the topological order of the DS stabilizer model by identifying an explicit finite-depth quantum circuit (with ancillary qubits) that maps its ground state subspace to that of a DS string-net model. We show that the construction of the DS stabilizer Hamiltonian generalizes to all twisted quantum doubles (TQDs) with Abelian anyons. This yields a Pauli stabilizer code on composite-dimensional qudits for each such TQD, implying that the classification of topological Pauli stabilizer codes extends well beyond stacks of toric codes - in fact, exhausting all Abelian anyon theories that admit a gapped boundary. We also demonstrate that symmetry-protected topological phases of matter characterized by type I and type II cocycles can be modeled by Pauli stabilizer Hamiltonians by gauging certain 1-form symmetries of the TQD stabilizer models.

1 aEllison, Tyler, D.1 aChen, Yu-An1 aDua, Arpit1 aShirley, Wilbur1 aTantivasadakarn, Nathanan1 aWilliamson, Dominic, J. uhttps://arxiv.org/abs/2112.11394