  We present a procedure to obtain the Hamiltonians of the toric code and
Kitaev quantum double models as the low-energy limits of entirely two-body
Hamiltonians. Our construction makes use of a new type of perturbation gadget
based on error-detecting subsystem codes. The procedure is motivated by a PEPS
description of the target models, and reproduces the target models' behavior
using only couplings which are natural in terms of the original Hamiltonians.
This allows our construction to exactly capture the symmetries of the target
models.
