  A method for the implementation of a universal set of fault-tolerant logical
gates is presented using homological product codes. In particular, it is shown
that one can fault-tolerantly map between different encoded representations of
a given logical state, enabling the application of different classes of
transversal gates belonging to the underlying quantum codes. This allows for
the circumvention of no-go results pertaining to universal sets of transversal
gates and provides a general scheme for fault-tolerant computation while
keeping the stabilizer generators of the code sparse.
