Title | Pauli Stabilizer Models of Twisted Quantum Doubles |

Publication Type | Journal Article |

Year of Publication | 2022 |

Authors | Ellison, TD, Chen, Y-A, Dua, A, Shirley, W, Tantivasadakarn, N, Williamson, DJ |

Journal | PRX Quantum |

Volume | 3 |

Date Published | 3/30/2022 |

Abstract | 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. |

URL | https://arxiv.org/abs/2112.11394 |

DOI | 10.1103%2Fprxquantum.3.010353 |