Lifting a CSS code via its handlebody realization
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912384165085184 |
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| author | Guemard, Virgile |
| author_facet | Guemard, Virgile |
| contents | We present a topological approach to lifting a quantum CSS code. In previous work, we proposed lifting a CSS code by constructing covering spaces over its 2D simplicial complex representation, known as the Tanner cone-complex. This idea was inspired by the work of Freedman and Hastings, which associates CSS codes with handlebodies. In this paper, we show how the handlebody realization of a code can also be used to perform code lifting, and we provide a more detailed discussion of why this is essentially equivalent to the Tanner cone-complex approach. As an application, we classify lifts of hypergraph-product codes via their handlebody realization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_14327 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lifting a CSS code via its handlebody realization Guemard, Virgile Quantum Physics Information Theory We present a topological approach to lifting a quantum CSS code. In previous work, we proposed lifting a CSS code by constructing covering spaces over its 2D simplicial complex representation, known as the Tanner cone-complex. This idea was inspired by the work of Freedman and Hastings, which associates CSS codes with handlebodies. In this paper, we show how the handlebody realization of a code can also be used to perform code lifting, and we provide a more detailed discussion of why this is essentially equivalent to the Tanner cone-complex approach. As an application, we classify lifts of hypergraph-product codes via their handlebody realization. |
| title | Lifting a CSS code via its handlebody realization |
| topic | Quantum Physics Information Theory |
| url | https://arxiv.org/abs/2505.14327 |