Could chess puzzles change with the introduction of stronger engines? Something I've noticed is even older chess puzzles never seem to age, somehow they even seem more masterful and demanding then the puzzles created today, but what if the solution for a puzzle is refuted by a program such as AlphaZero, or when quantum super computers are made, stronger engines, different engines?Will there be any shift with established puzzles, or do we just get to enjoy new theory and different puzzles?
Our modern chess engines are already perfect for solving tactical puzzles. @Bad_Bishop's example is an easy problem for Stockfish.

If you're talking about artificial deep chess problems (not puzzles), even AlphaZero might have problems. Some chess engines (e.g. Houdini) has a "tactic" mode for those problems.

No. Nothing much will change with stronger engines.