Demonstrating non-Abelian braiding of surface code defects in a five quit experiment

Currently, themainstream approach to quantum computing is through surface codes. Oneway to store andmanipulate quantum informationwith these to create defects in the codeswhich can be moved and used as if theywere particles. Specifically, they simulate the behaviour of exotic particles known asMajoranas, which are a kind of non-Abelian anyon. By exchanging these particles, important gates for quantum computation can be implemented.Here we investigate the simplest possible exchange operation for two surface codeMajoranas. This is found to act non-trivially on only five qubits. The system is then truncated to these five qubits, so that the exchange process can be run on the IBM5Qprocessor. The results demonstrate the expected effect of the exchange. This paper has beenwritten in a style that should hopefully be accessible to both professional and amateur scientists. Surface codes are themostwell-knownstarting point for fault-tolerant quantumcomputation [1].Oneway to store andmanipulate information in these is to engineer certain kinds of defects [2, 3]. These canbemoved aroundand manipulated inmuch the sameway as particles.However, their restriction to the two-dimensional (2D) structure of the surface codes allows them to exhibit someof the exotic behaviourpossible forparticles in 2Duniverses. The important features of these particles are their their effects when fused and braided. These refer to the processes of combining particles and of exchanging the positions of particles, respectively. It has been predicted that the fusion rules for these defects identical to so-calledMajoranamodes or Ising anyons. Their braiding forms a projective representation of the braid group, but is otherwise also identical to that ofMajoranas.Wewill therefore refer to them simply asMajoranas fromhenceforth. In this paperwe present an experiment performed on a small patch of surface code. The patch is nevertheless large enough for these defects to be introduced and even for pair of them to exchange positions.We implement this and show that the effects of the process are consistent with the braiding ofMajoranas, as predicted.