Topological Subsystem Codes

Abstract

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.Comment: 16 pages, 11 figures, explanations added, typos correcte