Lifting a CSS code via its handlebody realization

• URL: http://arxiv.org/abs/2505.14327v1
• Date: Tue, 20 May 2025 13:11:53 GMT
• Title: Lifting a CSS code via its handlebody realization
• Authors: Virgile Guemard,
• Abstract summary: We present a topological approach to lifting a quantum CSS code.<n>We show how the handlebody realization of a code can also be used to perform code lifting.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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