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

Understand

Topological subsystem codes in three spatial dimensions allow for quantum error correction with no time overhead, even in the presence of measurement noise.

• The physical origins of this single-shot property remain elusive, in part due to the scarcity of known models.
• To address this challenge, we provide a systematic construction of a class of topological subsystem codes in three dimensions built from abelian quantum double models in one fewer dimension.
• Our construction not only generalizes the recently introduced subsystem toric code [Kubica and Vasmer, Nat.