§ Reversible computation as groups on programs

If we consider a language like Janus where every program is reversible, we can then get a group structure on programs with the identity program not computing anything at all, the inverse performing the reverse operation. Alternatively, one can use the trick from quantum mechanics of using anciliary qubits to build reversible classical gates. The question is, do either of these approaches allow for better-than-STOKE exploration of the program space? Ie, can we somehow exploit the discrete group structure (in the case of Janus) or the Lie group structure of the unitary group (as in the QM case) to find programs in far quicker ways?