  We introduce a family of 2D topological subsystem quantum error-correcting
codes. The gauge group is generated by 2-local Pauli operators, so that 2-local
measurements are enough to recover the error syndrome. We study the
computational power of code deformation in these codes, and show that
boundaries cannot be introduced in the usual way. In addition, we give a
general mapping connecting suitable classical statistical mechanical models to
optimal error correction in subsystem stabilizer codes that suffer from
depolarizing noise.
