Qutrit-based topological subsystem codes

We introduce a topological subsystem code based on a generalization of Kitaev's honeycomb model to qutrits. The code exhibits a number of beneficial properties, including a realization on a low-degree graph in a planar geometry, two-body checks, and high biased-noise error thresholds. We further demonstrate that topological twist defects can be constructed by two-body measurements, and the full Clifford group can be implemented fault tolerantly by braiding twist defects. Through a mapping to a statistical mechanical model, we compute the optimal error thresholds of the subsystem code. We also establish a mapping of the error thresholds to those of a Z₃ surface code with anisotropic pure Pauli X noise.