  Non-Abelian anyons promise to reveal spectacular features of quantum
mechanics that could ultimately provide the foundation for a decoherence-free
quantum computer. A key breakthrough in the pursuit of these exotic particles
originated from Read and Green's observation that the Moore-Read quantum Hall
state and a (relatively simple) two-dimensional p+ip superconductor both
support so-called Ising non-Abelian anyons. Here we establish a similar
correspondence between the Z_3 Read-Rezayi quantum Hall state and a novel
two-dimensional superconductor in which charge-2e Cooper pairs are built from
fractionalized quasiparticles. In particular, both phases harbor Fibonacci
anyons that---unlike Ising anyons---allow for universal topological quantum
computation solely through braiding. Using a variant of Teo and Kane's
construction of non-Abelian phases from weakly coupled chains, we provide a
blueprint for such a superconductor using Abelian quantum Hall states
interlaced with an array of superconducting islands. Fibonacci anyons appear as
neutral deconfined particles that lead to a two-fold ground-state degeneracy on
a torus. In contrast to a p+ip superconductor, vortices do not yield additional
particle types yet depending on non-universal energetics can serve as a trap
for Fibonacci anyons. These results imply that one can, in principle, combine
well-understood and widely available phases of matter to realize non-Abelian
anyons with universal braid statistics. Numerous future directions are
discussed, including speculations on alternative realizations with fewer
experimental requirements.
