Translation-invariant quantum low-density parity-check codes from compactified fracton models
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| author | Hopkin, Cassandra M. Albert, Victor V. Williamson, Dominic J. |
| author_facet | Hopkin, Cassandra M. Albert, Victor V. Williamson, Dominic J. |
| contents | Quantum error-correcting codes with translation symmetry and local checks have been studied extensively, leading to a wide variety of fracton codes in three or more dimensions which lack a complete unifying picture. Recently, the study of translation-invariant codes with long-range checks has revealed impressive performance for small fixed-size instances in two dimensions. Here, we provide a unifying picture for a large family of translation-invariant codes, both local and long-range, that captures many fracton codes and all Abelian Two-Block Group Algebra (A2BGA) codes, including the Bivariate Bicycle (BB) codes. The balanced product structure of A2BGA codes leads to a local parent code that is a hypergraph product fracton model in a higher dimension. Different compactifications of a parent code produce a wide variety of descendant codes which provides a unifying picture for their properties. In particular, all BB codes with the same check weight are derived from a single parent hypergraph product fracton model. This construction allows us to extend Wang and Pryadko's code-parameter bounds for Generalized Bicycle codes to A2BGA codes. We conjecture that the transversal gates and energy barriers of the translation-invariant descendant codes are limited by those of their parent fracton models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_19298 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Translation-invariant quantum low-density parity-check codes from compactified fracton models Hopkin, Cassandra M. Albert, Victor V. Williamson, Dominic J. Quantum Physics Strongly Correlated Electrons Quantum error-correcting codes with translation symmetry and local checks have been studied extensively, leading to a wide variety of fracton codes in three or more dimensions which lack a complete unifying picture. Recently, the study of translation-invariant codes with long-range checks has revealed impressive performance for small fixed-size instances in two dimensions. Here, we provide a unifying picture for a large family of translation-invariant codes, both local and long-range, that captures many fracton codes and all Abelian Two-Block Group Algebra (A2BGA) codes, including the Bivariate Bicycle (BB) codes. The balanced product structure of A2BGA codes leads to a local parent code that is a hypergraph product fracton model in a higher dimension. Different compactifications of a parent code produce a wide variety of descendant codes which provides a unifying picture for their properties. In particular, all BB codes with the same check weight are derived from a single parent hypergraph product fracton model. This construction allows us to extend Wang and Pryadko's code-parameter bounds for Generalized Bicycle codes to A2BGA codes. We conjecture that the transversal gates and energy barriers of the translation-invariant descendant codes are limited by those of their parent fracton models. |
| title | Translation-invariant quantum low-density parity-check codes from compactified fracton models |
| topic | Quantum Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2605.19298 |