  Conformal field theories have been extremely useful in our quest to
understand physical phenomena in many different branches of physics, starting
from condensed matter all the way up to high energy. Here we discuss
applications of two-dimensional conformal field theories to fault-tolerant
quantum computation based on the coset $ SU(2)_1^{\otimes k} / SU(2)_{k}$. We
calculate higher-dimensional braiding matrices by considering conformal blocks
involving $2N$ anyons, and search for gapped states that can be built from
these conformal blocks. We introduce a gapped wavefunction that generalizes the
Moore-Read state which is based on the critical Ising model, and show that our
generalization leads to universal quantum computing.
