Classical determinism says that, given the full state of the universe at one moment and the laws governing it, the future is fixed. Complexity may prevent us from calculating that future, but it does not make the future open. What is difficult in practice remains pre-determined in principle.
Quantum physics changes this picture by replacing classical determinism with a quantum form of chaos. The quantum state still evolves according to precise laws, but what evolves is no longer one definite classical configuration leading to one definite later configuration. Instead, even a relatively simple initial state can evolve into a branching structure of later possibilities.
This matters already at the level of the early universe. The quantum state of nearly homogeneous cosmic soup evolved, through the fundamental laws governing particle interactions, into a richer state containing many later alternatives together with their probabilities. In that sense, the weakest deterministic statement one can make is still a strong one:
The quantum state of the universe at any given moment fixes the probabilities of every later outcome of every later event.
What is no longer fixed is one unique future in the old classical sense. What is pre-determined is the full probabilistic structure of the later tree of possibilities. From a certain stage onward, however, the situation may become simpler again. Once the universe becomes dominated by localized, classicalized objects, the later evolution may be well approximated by effectively classical equations along each branch. In that case, one may say that after a certain point the universe is no longer exploring the full quantum structure in any practically relevant way, but is instead following one classical-looking branch whose internal evolution is again close to deterministic.
A useful image is that of a play in which the lines are not written in advance as one fixed script, but are instead drawn live from a giant raffle drum. What makes this different from genuine improvisation is that the contents of the drum, together with the probability of drawing each line, were themselves fixed much earlier. The future is not one unique sequence written in advance, but neither is it authored anew at each moment. It is a weighted branching of possibilities inherited from the earlier state of the world.
This is why quantum physics does not rescue free will. At best, it replaces one fixed classical future with a tree of possibilities with probabilities already determined by the earlier state of the universe. That is not freedom. It is only a softer version of inevitability. The future may no longer be fixed as one unique chain of events, but the range of possible outcomes and their weights are still inherited from the past through lawful evolution.
In neither case is there room for free will within our current understanding of the laws of nature.
See also:
Did quantum physics end determinism?
Why the quantum world looks classical