"What is computation?" was the subject of a 2010 ACM symposium and "what is the nature of reality?", the universe, is an open question in philosophy. In my blog of 28 Aug. 2012 I suggested that a computer might best be described as a reconfigurable causal network. In the classical physics clockwork view of reality the universe certainly is a causal network. The problem is its not all that reconfigurable. The big bang did the configuring and that's hard to change. Perhaps equate a multiverse with a computer then. Provided there are a variety of initial conditions.
If you mean by "the universe" only that portion of reality which is external to yourself then your actions might do a tiny bit of reconfiguring, but not much. You plus the universe would be a coupled pair of computers/Turing machines. I run some Asa H simulations in this way. (See my blog of 10 March 2016.)
One can generalize these notions to a quantum computer and a quantum mechanical reality/universe.