Lifting a CSS code via its handlebody realization

Fuente: arXiv
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Main Author: Guemard, Virgile
Format: Preprint
Published: 2025
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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