Universal quantum computing with anyons is fault tolerant

In a seminal work, Alexei Kitaev proposed topological quantum computing, where the logic gates of a quantum computer are conducted by braiding anyonic particles on a two-dimensional plane. Furthermore, he showed the proposal is inherently robust to local noise when anyons are created as quasiparticle excitations of topologically ordered lattice model prepared at zero temperature. Over the decades following this proposal there have been considerable technological developments towards the construction of a quantum computer. Rather than maintaining some target ground state at zero temperature, a more modern approach for fault-tolerant quantum computing is to actively correct errors, where we use quantum circuits to identify and correct for deviations from the ideal target state. Here we present an error correction scheme that enables us to carry out universal topological quantum computing. We show that, given a suitably large device, universal quantum computation by anyon braiding can be carried out with an arbitrarily small failure rate assuming circuit elements are below some threshold error rate. Our results therefore show how topological quantum computation can be carried out using modern quantum hardware that is now under development.