Bacon-Shor Board Games

Abstract: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.

10 pages (+ appendix), 12 figures. Comments/feedback welcome

Quantum Physics (quant-ph); Information Theory (cs.IT)

arXiv:2504.02749 [quant-ph]

(or arXiv:2504.02749v4 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2504.02749 Focus to learn more arXiv-issued DOI via DataCite

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