That's not what quantum mechanics really does. The wavefunction, which is the core of a quantum calculation, "runs" all the time whether any part of it is observed or not. A given observable property of the wavefunction may not be predictable without looking, but that doesn't make the wavefunction any easier to simulate. And without the wavefunction running, we wouldn't observe the probabilities which we observe in experiments.
> The wavefunction, which is the core of a quantum calculation, "runs" all the time whether any part of it is observed or not.
The wave function doesn't really have to "run" to exist though... a wave doesn't actually have any influence on anything until it is collapsed. If nothing observes the wave, it won't have any affect at all. It will just be there, in some cosmic register, waiting for some dust cloud to inquire about it.
Consider a polygon in a game engine, which started at 0,0 and has a known velocity. You are at tick 4762, and that polygon is represented by a position function, but it doesn't actually "run" until you declare a tick, and do the math.
I dispute whether a wavefunction can influence things without collapsing, but putting that aside...
Your example of a polygon with a constant velocity is carefully chosen: that equation has an analytical solution, so you can calculate x(t) and "skip" forward in time. This is not possible in general, even in classical mechanics. If it were a system of more than two interacting particles, you wouldn't be able to fast-forward; you would have to calculate all the intermediate timesteps even if you only wanted the last one.
If the universe simulator can solve iterative problems in O(1), then I question whether our concept of optimization is meaningful enough to it for this discussion to make sense.
There are some physical systems (mathematically, "Hamiltonians") which have this "stateless" property. However, if the time/energy uncertainty principle is true, simulating time T in O(1) cannot be possible in general unless BQP=PSPACE (the unlikely idea that quantum computers can efficiently solve any problem that can be stored in polynomial amounts of memory). See this paper: https://arxiv.org/abs/1610.09619
See the last sentence of my comment: it's not consistent with experiments. The success of quantum mechanics as a predictive tool comes from acting as if the wavefunction is always present, no matter what aspect of it is measured.
There may be a whole different theory of physics which can replace quantum mechanics and doesn't have wavefunctions, and has completely different simulation requirements, but at that point you could postulate anything.
