  We show that quantum systems of extended objects naturally give rise to a
large class of exotic phases - namely topological phases. These phases occur
when the extended objects, called ``string-nets'', become highly fluctuating
and condense. We derive exactly soluble Hamiltonians for 2D local bosonic
models whose ground states are string-net condensed states. Those ground states
correspond to 2D parity invariant topological phases. These models reveal the
mathematical framework underlying topological phases: tensor category theory.
One of the Hamiltonians - a spin-1/2 system on the honeycomb lattice - is a
simple theoretical realization of a fault tolerant quantum computer. The higher
dimensional case also yields an interesting result: we find that 3D string-net
condensation naturally gives rise to both emergent gauge bosons and emergent
fermions. Thus, string-net condensation provides a mechanism for unifying gauge
bosons and fermions in 3 and higher dimensions.
