Very simply, Hume posits we cannot know causality. This is similar to Parmenides' "what is, is" aka "you can't get from now, A, to some A that is not now but will be."
Quantum physics has an uncertainty principle, and discrete values for given quantities in a system. These two are similar to Hume's "we can't prove causality" and Parmenides' "what is, is." However, quantum physics also has wave-particle duality, which is close-up spooky action, which moves past "we can't know causality" and "what is, is, and what isn't, isn't" by a kind of Oneness that decoheres into two-ness (simply, decoherence describes the wave-function moving to a particle "here or there," and from "now to future").
So, Parmenides' notion of "no change" is more clearly demonstrated to be false at that quantum energy level, while Hume's notion of "no causality" (wave function to particle) is less clearly refuted.