Decoherence and wavefunction deformation of $D_4$ non-Abelian topological order

Understand

The effect of decoherence on topological order (TO) has been most deeply understood for the toric code, the paragon of Abelian TOs.

• We show that certain non-Abelian TOs can be analyzed and understood to a similar degree, despite being significantly richer.
• We consider both wavefunction deformations and quantum channels acting on $D_4$ TO, which has recently been realized on a quantum processor.
• By identifying the corresponding local statistical mechanical spin or rotor model with $D_4$ symmetry, we find a remarkable stability against proliferating non-Abelian anyons.