  Quantum error avoiding codes are constructed by exploiting a geometric
interpretation of the algebra of measurements of an open quantum system. The
notion of a generalized Dirac operator is introduced and used to naturally
construct families of decoherence free subspaces for the encoding of quantum
information. The members of the family are connected to each other by the
discrete Morita equivalences of the algebra of observables, which render
possible several choices of noiseless code in which to perform quantum
computation. The construction is applied to various examples of discrete and
continuous quantum systems.
