Topological defects in toric code and Sequential quantum circuit

Xie Chen
California Institute of Technology

Toric code, an exactly solvable topological model, has a simple spectrum. However, it was recently proposed that the excitations in 3+1D toric code form a nontrivial higher-category structure. In this talk, we attempt to understand equivalence classes of topological excitations from a unitary perspective. We start from a particular defect called the Cheshire string -- a condensate line of the point charge excitations. We show that to create a Cheshire string, one needs the Sequential Quantum Circuit -- a linear depth circuit that acts sequentially along the length of the string. Once a Cheshire string is created, its deformation, movement, and fusion can be realized by finite depths circuits. Quantum circuits hence provide a way to define equivalence classes of gapped topological defects, potentially giving rise to an operational meaning of the higher category description of topological orders in 3+1D or higher.

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