  The recent debate on hyper-computation has raised new questions both on the
computational abilities of quantum systems and the Church-Turing Thesis role in
Physics. We propose here the idea of geometry of effective physical process as
the essentially physical notion of computation. In Quantum mechanics we cannot
use the traditional Euclidean geometry but we introduce more sophisticate non
Euclidean geometry which include a new kind of information diffuse in the
entire universe and that we can represent as Fisher information or active
information. We remark that from the Fisher information we can obtain the Bohm
and Hiley quantum potential and the classical Schrodinger equation. We can see
the quantum phenomena do not affect a limited region of the space but is
reflected in a change of the geometry of all the universe. In conclusion any
local physical change or physical process is reflected in all the universe by
the change of its geometry, This is the deepest meaning of the entanglement in
Quantum mechanics and quantum computing. We stress the connection between
metric and information as measure of change. Because computation is not
restricted to calculus but is the environment changing via physical processes,
super-Turing potentialities derive from an incomputable information source
embedded into the geometry of the universe in accordance with Bell's
constraints. In the general relativity we define the geometry of the space
time. In our approach quantum phenomena define the geometry of the parameters
of the probability distribution that include also the space time parameters. To
study this new approach to the computation we use the new theory of Morphogenic
systems.
