Improved Construction of Generalized Quantum Tanner Codes

We propose a generalization of the recently proposed quantum Tanner codes by Leverrier and Zemor. These codes can be constructed equivalently from groups, Cayley graphs, or square complexes constructed from groups. In a recent work, we enlarged this to group actions on finite sets, Schreier graphs, and a family of square complexes. We extend the class of quantum Tanner codes further by replacing the tensor product code in the construction with a Tanner code on any bipartite graph. A stricter property on the other underlying graphs is required, and we show that a common variation of the construction can always be taken to satisfy this condition. This results in improved codes compared to the ones constructed based on Schreier graphs.