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Topological subsystem codes in three spatial dimensions allow for quantumerror correction with no time overhead, even in the presence of measurementnoise. The physical origins of this single-shot property remain elusive, inpart due to the scarcity of known models. To address this challenge, we providea systematic construction of a class of topological subsystem codes in threedimensions built from abelian quantum double models in one fewer dimension. Ourconstruction not only generalizes the recently introduced subsystem toric code[Kubica and Vasmer, Nat. Commun. 13, 6272 (2022)] but also provides a newperspective on several aspects of the original model, including the origin ofthe Gauss law for gauge flux, and boundary conditions for the code family. Wethen numerically study the performance of the first few codes in this classagainst phenomenological noise to verify their single-shot property. Lastly, wediscuss Hamiltonians naturally associated with these codes, and argue that theymay be gapless.

Lifting topological codes: Three-dimensional subsystem codes from two-dimensional anyon models