Generalizing Quantum Tanner Codes

In this work, we present a generalization of the recently proposed quantum Tanner codes by Leverrier and Zémor, which contains a construction of asymptotically good quantum low-density parity-check codes. Quantum Tanner codes have so far been constructed equivalently from groups, Cayley graphs, or square complexes constructed from groups. We show how to enlarge this to group actions on finite sets, Schreier graphs, and a family of square complexes, which is the largest possible in a certain sense. Furthermore, we discuss how the proposed generalization opens up the possibility of finding other families of asymptotically good quantum codes.