Non-Abelian Topological Codes and Error Correction

Topological phases of matter lie at a rich intersection of many-body quantum physics and quantum information science. Their emergent anyonic quasiparticles can serve as the basis of topologically protected quantum memories, and in certain cases provide native implementations of quantum gates. The simplest example---Z2 topological order underlying the toric or surface code---has dominated much of the quantum information literature. However, a far broader landscape of topological phases exists. In particular, non-Abelian topological order offers powerful capabilities but has remained comparatively underexplored in quantum information due to its perceived increased complexity.

In this talk, I will review recent developments that help make non-Abelian approaches more accessible. These include insights into the phase transitions and error correction of non-Abelian mixed phases, and a first experimental demonstration of a universal gate set enabled by anyon braiding and fusion in S3 topological order on Quantinuum's trapped-ion processor.