String theory based computations
No, as far as I know, there are no models that use string theory.

Given that quantum field theories seem to be simulatable in polynomial time by a quantum computer (Jordan, Lee, and Preskill, 2012), the only possible more powerful physical system would be quantum gravity. This is because physicists generally believe that quantum field theory gives an excellent approximate description of the universe if gravity is neglected; however, general relativity seems incompatible with quantum mechanics. Thus, to get a full description of the universe, we need a theory of quantum gravity.  Many physicists believe this theory is given by string theory; however, physicists currently don't understand string theory well enough to use it as a basis for a model of computation.