Dear Tommaso,
Thank you for your understanding. Unlike some others posting here I am writing merely as an avocation, not a vocation.
It is very possible that with increased intelligence will come increased knowledge and potentially new paradigms defining intelligence, and perhaps even new physics. It is not even clear that we humans are Turing machines, and if that is the case then it will provide an interesting scenario. On the one hand it may make some approaches to brain emulation impossible (e.g. by modelling neurons in Turing machines (blue brain project, synapse, etc) it also provides an existence proof for a much more powerful class of non-Turing machines.j
As for "computing beyond matter", it is precisely these sorts of scenarios that would need to occur, the ones based on new physics, that would enable the machines to gain access to resources that did not require unbounded matter and energy acquisition in normal 3+1d spacetime. Regardless of how this occurs, it will be a necessary development to escape the possibility of resource competition with machines because it gives the machines unlimited room to grow.
Assuming that there are no new physics developments that occur, there are still large upper bounds on the amount of computation (see Seth Lloyd's paper on the limits of computation). While these limits are not infinite, they are large compared to our current state of the art (approx 40 orders of magnitude larger).
As for the creation of the Omega Point, being the state before a big crunch singularity where infinite computations are performed in an apparently infinite time (to a co-moving observer), this would depend on several factors, one of which being the ability to reverse the apparent acceleration of spacetime. Chardin's first waypoint on the way to timelike infinity was the creation of the Noosphere (lit. thought sphere), where the entire globe became suffused in consciousness. I think we'll need to work on fixing the Earth and ourselves first before we can work on the universe.
