QM Research Seminar: Categorified quantum group representations from Fukaya-Seidel categories

Speaker: Ben Brown (​IBM).

Abstract:
In seminal work Alexei Kitaev proposed topological quantum computing, whereby logic gates of a quantum computer are conducted by creating, braiding and fusing anyonic particles on a two-dimensional plane. Furthermore, he showed the proposal is inherently robust to local perturbations when anyons are created as quasiparticle excitations of a 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 fault-tolerant quantum computer. Rather than maintaining some target ground state at zero temperature, a modern approach is to actively correct the errors a target state experiences, where we use noisy quantum circuit elements to identify and subsequently correct for deviations from the ideal state. We present an error-correction scheme that enables us to carry out robust universal quantum computation by braiding anyons. We show that our scheme can be carried out on a suitably large device with an arbitrarily small failure rate assuming circuit elements are below some threshold level of local noise. The error-corrected scheme we have developed therefore enables us to carry out fault-tolerant topological quantum computation using modern quantum hardware that is now under development.