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Higher-group symmetry of topological order and stabilizer codes

日程 : 2023年4月18日(火) 4:00 pm - 5:00 pm 場所 : 物性研究所本館6階 第5セミナー室 (A615) 講師 : 小林 良平 所属 : University of Maryland 世話人 : 押川 正毅 (ex. 63275)講演言語 : 英語

Topologically ordered phases can host interesting classes of non-trivial topological defects of varying codimensions. Among the topological defects, the invertible defects form an algebraic structure called higher-group. In this talk we explain how the higher-group structure of invertible global symmetry emerges in discrete gauge theory of generic dimensions, and show various examples of the higher-group symmetry in topological order mainly focusing on (3+1)-dimensional stabilizer codes. The emergent global symmetry of a stabilizer model is understood as a logical gate acting on the logical qubits. We explain that the higher-group structure of global symmetry in general leads to non-Pauli logical gate realized by the action of emergent global symmetry, e.g., Control-Z logical gate of (3+1)-dimensional Z2 toric code.

Participation in our seminar online is also welcomed. Please find the attached Zoom link below.


(公開日: 2023年04月17日)