Positional Symmetry Breaking in Decoders on Defective Surface Codes

We investigate how physical defects in surface-code lattices affect the placement of logical operator measurements. Motivated by the fact that fault-tolerant quantum hardware necessarily operates on imperfect lattices, we introduce a simple but general defect model for unrotated surface code patches and use it to systematically benchmark logical error rates by varying defect size and position. Under circuit-level depolarizing noise, we observe that widely used decoders exhibit positional bias where certain defect locations consistently yield higher or lower logical error rates, revealing an unexpected symmetry breaking in their correction behavior. We argue that the relevant quantity is not geometric symmetry but the connectivity between the defective region and the bulk code as perceived by the decoder graph. This connectivity asymmetry governs the effective protection of different logical operators and suggests a new lens for evaluating decoder robustness beyond traditional distance-based metrics.