  We introduce a new graphical framework for designing quantum error correction
codes based on classical principles. A key feature of this graphical language,
over previous approaches, is that it is closely related to that of factor
graphs or graphical models in classical information theory and machine
learning. It enables us to formulate the description of the recently-introduced
`coherent parity check' quantum error correction codes entirely within the
language of classical information theory. This makes our construction
accessible without requiring background in quantum error correction or even
quantum mechanics in general. More importantly, this allows for a collaborative
interplay where one can design new quantum error correction codes derived from
classical codes.
