Quasicrystal product codes

We construct and study a class of geometrically local quantum LDPC codes without translation invariance. These codes are obtained via a protocol similar to the lifted product, but which generates stabilizer models supported on quasicrystal lattices. Although the models obtained in this scheme are CSS codes, their homological description does not correspond to that of the underlying manifold. They therefore generalize existing topological and fracton constructions, and exhibit novel dynamical and thermodynamic properties.