Lifting Topological Codes: Three-Dimensional Subsystem Codes from Two-Dimensional Anyon Models

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 pr...

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Bibliographic Details
Published in:PRX quantum 2024-04, Vol.5 (2), Article 020310
Main Authors: Bridgeman, Jacob C., Kubica, Aleksander, Vasmer, Michael
Format: Article
Language:English
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Summary: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. Commun. , 6272 (2022)] but also provides a new perspective on several aspects of the original model, including the origin of the Gauss law for gauge flux, and boundary conditions for the code family. We then numerically study the performance of the first few codes in this class against phenomenological noise to verify their single-shot property. Lastly, we discuss Hamiltonians naturally associated with these codes, and argue that they may be gapless.
ISSN:2691-3399
2691-3399
DOI:10.1103/PRXQuantum.5.020310