We don't know of anything that is provably not computation. There's not a single proof that "process X is not reproducible computationally, yet it is implemented in the universe". All the statements like the one in the subject line are desires (conscious or unconscious) for special privilege for humans.
You can of course simulate quantum randomness using an RNG or some such but the essential inherent unpredictability can't be simulated like that.
To be clear, I'm not trying to argue that quantum randomness is a component of consciousness!
Regards consciousness and computation, though, it's always seemed suspicious to me that we can't reliably specify 'qualia' like "what it's like to feel wet" or "what it's like to hear a trumpet" except either in terms of a physical description (e.g. the waveform of the trumpet note) that misses out the experiential component or in terms of "samples" - i.e. references to other 'qualia': "sounds like a french horn but less round" or whatever.
I'd have thought being able to adequately specify something was a necessary step in reducing it to computation. We've been using language for thousands of years though, and as far as I'm aware precisely specifying experiences in this way is still an unsolved problem.