Assuming that the universe is run with a fixed time step (23*10^-42 units per second) and discounting any relativity effects, and assuming that there are 2.7 * 10^83 particles in the universe to calculate, and assuming these particles can be simulated with an n log n run time, I compute the power of a computer capable of simulating the universe at 10^125 FLOPS.

Given that a supercomputer now days is 280.6 * 10^12 FLOPS, and using Moore's law that computing power roughly doubles every 24 months (and assuming this growth rate is constant into the foreseeable future, which I doubt it is) we will have a supercomputer 741.16 years from now capable of simulating the entire universe in real time.