  We describe a method for engineering local $k+1$-body interactions
($k=1,2,3$) from two-body couplings in spin-${1}{2}$ systems. When implemented
in certain systems with a flat single-particle band with a unit Chern number,
the resulting many-body ground states are fractional Chern insulators which
exhibit abelian and non-abelian anyon excitations. The most complex of these,
with $k=3$, has Fibonacci anyon excitations; our system is thus capable of
universal topological quantum computation. We then demonstrate that an
appropriately tuned circuit of qubits could faithfully replicate this model up
to small corrections, and further, we describe the process by which one might
create and manipulate non-abelian vortices in these circuits, allowing for
direct control of the system's quantum information content.
