Recorded 29 November 2023. Xie Chen of the California Institute of Technology presents "Topological defects in toric code and Sequential quantum circuit" at IPAM's Topology, Quantum Error Correction and Quantum Gravity Workshop. Abstract: 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. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-iv-topology-quantum-error-correction-and-quantum-gravity/