Correcting for Y errors with the Bacon-Shor code

The use of quantum error correcting (QEC) codes is envisioned to enable quantum computers to overcome limitations imposed by error–prone hardware. The Bacon–Shor code is a QEC code that uses local, low-depth check circuits and thus presents an attractive candidate for near-term implementation. We study the Bacon-Shor code's performance under a noise model with only Pauli-Y errors. Such biased noise doubles the number of useful stabilizer checks, suggesting an improved effective error tolerance. We verify this understanding through combinatorial analysis to show that purely Y noise results in exponentially fewer harmful logical errors compared to X or Z noise. Furthermore, we design and analyze decoders that exploit this bias to raise the code's effective error tolerance under both static and dynamic check measurement schedules. We discuss the extension of these results to the finite bias regime, where X and Z errors are present but occur less frequently than Y errors.