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arXiv · 2505.14327

Lifting a CSS code via its handlebody realization

Virgile Guemard
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Abstract

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.

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Virgile Guemard. 2025-05-20. Lifting a CSS code via its handlebody realization. https://arxiv.org/abs/2505.14327

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