Do you mean what if the time dimension were compact, (so the spacetime would be R^n x T^1) or that space is anti-de Sitter (which includes closed timelike curves)? In either case you seem to be asking does time travel cause classical systems to behave like quantum systems. At the very least you...
It's widely believed that BQP (including the simulation of general quantum systems) requires exponential time and classical physics simulations only take polynomial time. If this is true (and it may very well not be), then doesn't the gap between the complexity of quantum and classical systems...
https://arxiv.org/abs/1905.10074
The paper finds that one can reduce the number of qubits to a constant (just one works) used in the last, modular exponential register of the variants of Shor's algorithm, used to factor integers and find discrete logarithms, by applying a universal hash...