Anything. Everything. In domains where the search space is small enough to physically enumerate and store or evaluate every option, search is commonly understood as a process solved by simple algorithms. In domains where the search space is too large to physically realize or index, search becomes "intelligence."

E.g. winning at Chess or Go (traditional AI domains) is searching through the space of possible game states to find a most-likely-to-win path.

E.g. an LLM chat application is searching through possible responses to find one which best correlates with expected answer to the prompt.

With Grover's algorithm, quantum computers let you find an answer in any disordered search space with O(sqrt(N)) operations instead of O(N). That's potentially applicable to many AI domains.

But if you're so narrow minded as to only consider connectionist / neural network algorithms as "AI", then you may be interested to know that quantum linear algebra is a thing too: https://en.wikipedia.org/wiki/HHL_algorithm