[bicubic]

This is a very interesting question. What if the universe is stateless and any state at time T can be calculated in O(1)

What if we just lack the expressiveness or the initial conditions to model a stateless universe?

A fun consequence of stateless universe would be that you can rewind, fast forward, loop, speed up, slow down time at no extra cost.

[comicjk]

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