We identify a period-4 measurement schedule for the checks of the Bacon-Shor code that fully covers spacetime with constant-weight detectors, and is numerically observed to provide the code with a threshold. Unlike previous approaches, our method does not rely on code concatenation and instead arises as the solution to a coloring game on a square grid. Under a uniform circuit-level noise model, we observe a threshold of approximately $0.3\%$ when decoding with minimum weight perfect matching, and we conjecture that this could be improved using a more tailored decoder.

翻译：我们为 Bacon-Shor 码的校验设计了一种周期为 4 的测量调度方案，该方案能以恒定权重的探测器完全覆盖时空，且数值模拟结果表明该方案为该码提供了阈值。与先前方法不同，我们的方法不依赖于码的级联，而是源于一个在正方形网格上的着色游戏的解。在均匀电路级噪声模型下，使用最小权重完美匹配解码时，我们观察到的阈值约为 $0.3\%$，并推测使用更定制的解码器可能进一步提升该阈值。