Lifting a CSS code via its handlebody realization
Quantum Physics
2025-05-21 v1 Information Theory
math.IT
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.
Cite
@article{arxiv.2505.14327,
title = {Lifting a CSS code via its handlebody realization},
author = {Virgile Guemard},
journal= {arXiv preprint arXiv:2505.14327},
year = {2025}
}