Even without quantum effects, determinism doesn't enable us to do much with it, except statistical ensemble predictions. We can never know the initial state of a system to infinite precision, as is needed to predict its trajectory. [0]
[0] Light-ish reading on nonlinear dynamics: James Gleick - Chaos: Making a New Science
[0] Light-ish reading on nonlinear dynamics: James Gleick - Chaos: Making a New Science