



02101nas a2200217   4500008004100000245007000041210006900111260001500180520136900195653002101564653002701585653004201612653003001654653003101684653005201715100002301767700001601790700001801806700002201824856003701846       2022                        eng d00aHigher-group symmetry in finite gauge theory and stabilizer codes0 aHighergroup symmetry in finite gauge theory and stabilizer codes  c11/21/20223 a<p>A large class of gapped phases of matter can be described by topological finite group gauge theories. In this paper, we derive the d-group global symmetry and its &#39;t Hooft anomaly for topological finite group gauge theories in (d+1) space-time dimensions, including non-Abelian gauge groups and Dijkgraaf-Witten twists. We focus on the 1-form symmetry generated by invertible (Abelian) magnetic defects and the higher-form symmetries generated by invertible topological defects decorated with lower dimensional gauged symmetry-protected topological (SPT) phases. We show that due to a generalization of the Witten effect and charge-flux attachment, the 1-form symmetry generated by the magnetic defects mixes with other symmetries into a higher group. We describe such higher-group symmetry in various lattice model examples. We discuss several applications, including the classification of fermionic SPT phases in (3+1)D for general fermionic symmetry groups, where we also derive a simpler formula for the [O5]&isin;H5(BG,U(1)) obstruction than has appeared in previous work. We also show how the d-group symmetry is related to fault-tolerant non-Pauli logical gates and a refined Clifford hierarchy in stabilizer codes. We construct new logical gates in stabilizer codes using the d-group symmetry, such as the control-Z gate in (3+1)D Z2 toric code.</p>10aFOS: Mathematics10aFOS: Physical sciences10aHigh Energy Physics - Theory (hep-th)10aQuantum Algebra (math.QA)10aQuantum Physics (quant-ph)10aStrongly Correlated Electrons (cond-mat.str-el)1 aBarkeshli, Maissam1 aChen, Yu-An1 aHsin, Po-Shen1 aKobayashi, Ryohei  uhttps://arxiv.org/abs/2211.11764