We introduce a family of two-dimensional (2D) topological subsystem quantum error-correcting codes. The gauge group is generated by two-local Pauli operators, so that two-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.
Physical Review A
- Pub Date:
- March 2010
- Quantum error correction and other methods for protection against decoherence;
- Quantum Physics
- 16 pages, 11 figures, explanations added, typos corrected