  Homological quantum error correction uses tools of algebraic topology and
homological algebra to derive Calderbank-Shor-Steane quantum error correcting
codes from cellulations of topological spaces. This work is an exploration of
the relevant topics, a journey from classical error correction, through
homology theory, to CSS codes acting on qudit systems. Qudit codes have torsion
in their logical spaces. This is interesting to study because it gives us extra
logical qudits, of possibly different dimension.
  Apart from examples and comments on the topic, we prove an original result,
the Structure Theorem for the Qudit Logical Space, an application of the
Universal Coefficient Theorem from homological algebra, which gives us
information about the logical space when torsion is involved, and that improves
on a previous result in the literature. Furthermore, this work introduces our
own abstracted and restricted version of the general notion of a cell complex,
suited exactly to our needs.
