Bare-ancilla fault-tolerant syndrome extraction: General extensions of distance-three codes and structural criteria for graph codes
This work develops a systematic method to create fault-tolerant bare ancilla codes from graph states for quantum error correction. It constructs and analyzes a family of non-CSS [[n, 1, 3]] codes that are resilient against 'hook errors'—correlated errors during syndrome extraction. The results show these codes maintain distance-three properties and perform well against various noise models.