Before asking how to simulate the whole universe, one should first ask how to simulate 3 particles (google 3 body problems), and if he finds a way, then maybe an N body problem. One should in principle be able to, but think about it again, in a cup of water you got 10^26 atoms, each with multiple elementary particles. To simulate a cup of water is one thing, now imagine can you simulate an ocean? What about the "fluid" plasma in the sun a.k.a. the sun. You see even if you could, in an infinite number of steps it's quite a mess, even for a freaking cup of water.
Now before bursting your bubble, I will make 2 claims:
We in physics have some weird principle called Heisenberg Uncertainty Principle.
In Mathematics, they have something similar, as the guy above me pointed out, they have Godel's incompleteness theorem that can easily understand if one makes a new mathematics let's say with numbers from 1 to 5, and gives those numbers some meaning like logical operators and could in principle recreate all the mathematics with only 1,2,3,4,5. Then if one asks the question: you can do all those wonderful things with only those 5 symbols, but can 5 explain himself? And it is quite obvious that it can't since you took them and their meaning for granted in the first place.
Now you see, physics is based on math, so we are kinda ...screwed, on both sides, from 1 side from nature, with Heisenberg strangeness, and from the other side by math and it's an impossibility to be complete.
Now one if is curious, could go to this link and search deeper: http://www.hawking.org.uk/godel-and-the-end-of-physics.html, but the answer is the same and is: No, No you can't.
TLDR: no