November 28, 2023

Speaker: Xie Chen (Caltech)

Title: Sequential circuit as string operator for topological defects

Abstract: Bosonic point charge excitations in 3+1D topological phases can condense along a line and form a descendant defect called the Cheshire string. Unlike the elementary flux loop excitations in the system, Cheshire strings do not have to appear as the boundary of a 2D disc and can exist on open-line segments. On the other hand, Cheshire strings are different from trivial excitations that can be created with either local unitaries in 0d or finite depth quantum circuits in 1d and higher. In this talk, 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,  giving rise to an operational meaning of the higher category description of topological orders in 3+1D or higher.