Title | Pauli topological subsystem codes from Abelian anyon theories |

Publication Type | Journal Article |

Year of Publication | 2022 |

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

Date Published | 11/7/2022 |

Keywords | FOS: Physical sciences, Quantum Physics (quant-ph), Strongly Correlated Electrons (cond-mat.str-el) |

Abstract | We construct Pauli topological subsystem codes characterized by arbitrary two-dimensional Abelian anyon theories--this includes anyon theories with degenerate braiding relations and those without a gapped boundary to the vacuum. Our work both extends the classification of two-dimensional Pauli topological subsystem codes to systems of composite-dimensional qudits and establishes that the classification is at least as rich as that of Abelian anyon theories. We exemplify the construction with topological subsystem codes defined on four-dimensional qudits based on the Z(1)4 anyon theory with degenerate braiding relations and the chiral semion theory--both of which cannot be captured by topological stabilizer codes. The construction proceeds by "gauging out" certain anyon types of a topological stabilizer code. This amounts to defining a gauge group generated by the stabilizer group of the topological stabilizer code and a set of anyonic string operators for the anyon types that are gauged out. The resulting topological subsystem code is characterized by an anyon theory containing a proper subset of the anyons of the topological stabilizer code. We thereby show that every Abelian anyon theory is a subtheory of a stack of toric codes and a certain family of twisted quantum doubles that generalize the double semion anyon theory. We further prove a number of general statements about the logical operators of translation invariant topological subsystem codes and define their associated anyon theories in terms of higher-form symmetries. |

URL | https://arxiv.org/abs/2211.03798 |

DOI | 10.48550/ARXIV.2211.03798 |