I'll elaborate and be more specific. I understand that this is almost a metaphysical question but nonetheless I want to give it a try.
Could an external being outside our Universe create 10 simulations of our Universe and get always the same results when the same initial conditions are applied?
Or would quantum mechanics behave unpredictably even in this situation?
At first this may look entirely arbitrary, since we could postulate any kind of powers to the being. But the issue is not the laws for the being, but what the laws of this universe are: are there physical events that lack causes within the physics of the universe?
If there isn't, then we can trivially postulate that the being can simulate them. But if there is, then there is no way to perform a deterministic simulation to get the right result. A random simulation may of course get it by chance.
So, are there "uncaused events"?
There are quantum events that are random relative to the postulates of quantum theory. Quantum indeterminacy suggests that there is no hidden reason for the outcomes of a measurement and hence it is essentially ``uncaused'' (at least by hidden variables). In a sense it is logically independent of other states. So if quantum mechanics as we know it is the metaphysically correct description of what is going on, then there are fundamentally uncaused events.
The problem, and what makes the question somewhat hopeless, is that you can never prove that your physical theory is metaphysically correct since it could just be simulated by a different, more powerful physical theory. We may have great experimental, theoretical and philosophical reasons to believe in a theory but a naughty philosopher will always be able to postulate some contrived theory that fakes it (using absurd resources in a much bigger universe).
The hypothetical being could create whatever simulation they like, but presumably they want it to be an accurate simulation. To check its accuracy they will have to observe our universe - which means they will have to interact with our universe. Now they are no longer external - they are connected with our universe (in QM terms they are “entangled”) so their simulation must include themselves and a simulation of their simulation ... So we have reached an infinite regress, which seems to rule out this scenario.
Your question is like asking can an experimenter predict the state of Schrödinger’s cat by creating a detailed simulation of the cat, the box, the radioactive source etc. The difficulty is they cannot know that their simulation is accurate unless they open the box.
The point is that "all the information about the universe" could well comprise knowledge about states of the universe in the future as well as knowledge about yet unknown laws of physics. Since to my knowledge nobody knows the future, and the unknown is, by definition, unknown, your question is impossible to answer. But at least if knowledge about the (infinite) future is required to describe the universe, the notion of prediction becomes meaningless.
What you probably meant instead is, that the external being knows everything about the current state of the universe and some time in the past (represented for example by time derivatives of measurable quantities), plus our current knowledge about the laws of physics. If this knowledge would allow a simulation to compute the future, we would live in a deterministic universe.
From what we know, the universe is not deterministic. The path integral formalism of quantum field theory allows a pretty intuitive understanding what the probabilistic nature of the universe means: we can only determine the probability, that the state of the universe evolves over a series of given intermediate states that we provide for testing. In other words, we can conjecture that something that was arbitrarily chosen by us happens in the universe, and after we have made this conjecture, we can compute the probability that this evolution is compatible with what we know about physics. But we will never know for sure. We can only repeat experiments and see if the computed probability matches the experimental histograms.
There is even a very tiny probability that someone who looks like Captain Kirk suddenly materializes next to you. This does not mean that "beaming" is a regular part of physics, but only that the lottery of the universe might throw the dices so that even the weirdest things might actually happen. But again, only with a minute probability that practically means "never".
Whether the laws of physics can be completed to be deterministic again, is an open question in my opinion, although many people try/claim to prove that it cannot.
Let's first discuss what happens when a human experimenter performs a quantum mechanical experiment. They will prepare some quantum state and make a measurement whose outcome will be probabilistic (not deterministic). That is, while the measurement probabilities might be predictable, the actual single measurements can not be predicted. I would make the argument that quantum mechanics is actually what allows us to predict what happens in such an experiment in a probabilistic way.
Now about the external being to our universe. The reason a human experimenter is able to learn any information about a quantum experiment is by creating a physical experimental apparatus to interact with the quantum system and measure the properties of the created quantum state. It's unclear whether the external being that you describe performs measurements in a similar way, or whether there is a different mechanism that allows them to see the full state, or whether they are even able to learn anything about the state at all. Without more information about the setup, there is not much more to say.
