Non-Abelian braiding of graph vertices in a superconducting processor

The role of quantum mechanics in the fundamental nature of particles is especially rich in 2 spatial dimensions. The state space of several spatially separated particles can have a completely non-local, topological degeneracy. Even when these particles do not have a conventional interaction, probing their exchange statistics by braiding them around each other results in rotations in the state space. Such particles are called non-Abelian anyons, and have been discussed in various theoretical contexts since the 1980s. Recent interest has focused on their potential as central design elements of fault-tolerant quantum computers, and as a key aspect of the classification of gapped 2D phases. We first describe a particularly compact construction of models hosting non-Abelian excitations, based on emergent gauge fields in stabilizer codes. We then review experiments realizing fully 2D, scalable braiding of non-Abelian excitations by implementing this construction on a superconducting processor.