Bacon-Shor Board Games

We show that the Bacon-Shor subsytem code obtains a threshold through a fairly straight-forward adjustment of its measurement prescription. Specifically, we identify a measurement schedule for its check operators with period 4 that produces constant weight detectors for arbitrary lattice sizes. These detectors are dynamical, and bear resemblance to the dynamically evolving logical operators in Floquet codes. Unlike previous constructions, our method does not rely on code concatenation. It instead exploits the subsystem structure of the code, and can be described intuitively as a board game. Under a uniform circuit-level noise model, we find a threshold of approximately 0.3% using minimum weight perfect matching as our decoder.