That's exactly the kind of argument that's used to proclaim the security of various encryption systems: If a long enough key is used, the time it would take to try all decryption combinations is many times longer than the life of the universe, or would require more computers than there are electrons in the universe, etc. [with various assumptions about computer power and algorithmic efficiency thrown into the mix].
Then along comes the still-infant technology of quantum computing, and suddenly all those estimates of impossibly long times and impossibly large numbers are called into question. Quantum computers can simultaneous examine all possible output states, and so (in theory) are not subject to the same exponential limitations as conventional computers. What were previously infinitesmally small probabilites are now substantial.
Quantum mechanics is real, and it is fundamental to the nature of this universe (and maybe an infinity or near-infinity of other universes). Even aside from the many valid points that other posters on this thread have made about the non-random, iterative nature of evolution, it is not impossible that quantum mechanical "random" processes could have produced a universe in which intelligent life evolved. No matter how "unlikely" that might seem to some people, our observation of that fact would be the consequence of our being an instance of that "unlikely" event.
Oh...you mean intellegent design!
...and the only reason that this computing can happen is because intellegent humans have created a machine that can calculate faster than the human brain is able to calculate. All of which points to intellegent design, with purpose. But the experiment is intentionally set up to factor out intellegence, so your observation is not applicable to this scenario.
BTW, please show us one instance of natural quantum computations happening in the natural world, without intellegent intervention. Computers don't count, as they are programmed by intellegent men.