I devised a formalism for describing all computational
universes, including quantum and classical, as well as
extending it with other extremeties.
A computational universe, U, is a four-tuple $(\; U$_{P}, U_{Q}, U_{F}, U_{G}
) where $U$_{P} is a set of
preparable and observable states;
$U$_{P} is a subset of the
operable states $U$_{Q}. The
operations $U$_{F} is a set of functions
from $U$_{Q} U_{Q} forming a
group under the operation of
composition. $U$_{G} is a function
taking $(X\; x\; U$_{Q}) to (X x
U_{P}) where X is an list (ordered set) of
probabilities.