  Condensation of quantum loops naturally leads to topological phases with
Abelian excitations. Here, I propose that non-Abelian topological phases can
arise from merging two (or several) identical Abelian quantum loop condensates.
I define merging through a symmetrization operation, which makes the two loop
condensates indistinguishable, inducing the possibility of a topological
degeneracy in the space of quasiparticles. To illustrate the construction, the
case of two identical toric-code quantum loop gases is considered. A spin-1
model for the two dimensional square lattice is presented for which the
resulting merged state is the exact unique ground state. This Hamiltonian
involves four-body interactions between spins located at the same plaquette or
vertex, which are quadratic in the spin-1 operators. Vertex and plaquette
interaction terms are not mutually commuting. The model displays gapped
excitations which result from merging anyons in both toric-code copies. These
excitations exhibit non-Abelian braiding properties.
