Symmetry and non-Hermiticity controlled Majorana braiding

The braiding of Majorana zero modes (MZMs) paves the way for realizing fault-tolerant topological quantum computation (TQC). We propose a reinterpretation of MZM migration and braiding phenomena in 1D topological superconductors (TSCs), based on a MZM deconfinement-reconfinement transition in open quantum systems, which can be equivalently explained via symmetry perspectives from a Hermitian picture, or via non-Hermitian skin effect (NHSE) perspectives from a non-Hermitian picture. In the deconfinement-reconfinement transition, the MZM in the system first evolves into a deconfined mode in the environment, before reconfines into a localized mode at the edge of the environment. From the symmetry perspective, this is because coupling with the environment breaks the symmetry of the system that protects the MZM as a topological edge state within the system, so the MZM diffuses into the environment. From the NHSE perspective, this is because NHSE has pulled the MZM from the system into the environment. This symmetry/NHSE controlled deconfinement-reconfinement process can be exploited to physically migrate the MZM, which eventually results in their braidings. We also prove that adiabaticity is preserved in the braiding process, realizing a promising avenue for achieving TQC.