Dynamic defects in the surface code with a transverse field

Topologically-ordered quantum states with abelian excitations can host defects that obey effective non-abelian statistics, in principle allowing for quantum information processing via defect braiding. However these defects (or "twists") are typically viewed as static features of the lattice, thereby preventing such "defect braiding" in real material systems. We instead consider a model of synthetic and dynamic defects, generated in a surface code under the application of a transverse field, as proposed by You, Jian, and Wen [Phys. Rev. B 87, 045106 (2013)]. We study the time dependence of these states under application of the field, the changes in topological degeneracy, and prospects for dynamically braiding and observing non-abelian phenomena. We anticipate these manipulations can be implemented on near-term quantum computers to realize real-time synthetic non-abelian dynamics.