  Schemes for topological quantum computation are usually based on the
assumption that the system is initially prepared in a specific state. In
practice, this state preparation is expected to be challenging as it involves
non-topological operations which heavily depend on the experimental realization
and are not naturally robust against noise. Here we show that this assumption
can be relaxed by using composite anyons: starting from an unknown state with
reasonable physical properties, it is possible to efficiently distill suitable
initial states for computation purely by braiding. This is achieved by encoding
logical information in a subsystem code with gauge system corresponding to the
internal degrees of freedom of composite objects.
