Single-shot error correction on the Bacon-Shor code

Single-shot quantum error correction removes the need for repeated syndrome extraction, yet implementing it with low-weight, local checks remains challenging for many stabilizer codes. Following Campbell's diagonalization procedure [1], any code can be adjusted for single-shot error correction with a suitable set of checks. We adapt this to the Bacon-Shor code by decomposing the highly non-local checks into products of local weight-2 gauge operators, and implement detectors that exploit redundancies in the non-local checks. Under a noise model with no memory errors, for single-round error correction, there is a slight improvement on logical error rate for non-local checks. Yet, non-local stabilizers with one round always perform worse than local checks with d rounds. However, we observe a relative improvement of the non-local checks as memory errors are introduced. This opens up new possibilities for single-shot error correction under locality constraints in 2D.

[1] E. T. Campbell, Quantum Sci. Technol. 4, 025006 (2019).