This is irrelevant. First, quantum programs don't "get" anything just by virtue of being quantum code, any more than classical computers "get" the foundations of electricity and magnetism because they use electrons. Second, classical computers absolutely can simulate quantum systems. They're inefficient, but they can do it. Third, determining whether an agent is stuck in an infinite loop has nothing to do with the physical world. They're just binary code running on a Turing machine. Fourth, the halting problem is provably unsolvable in both classical and quantum systems, so there's not even a relationship here. Fifth, what do you mean by quantum systems are physical? Does this mean classical systems aren't? Are physical systems only those that use every aspect of physics? Then quantum systems aren't physical either because they can't account for gravity. So do we need quantum gravitational computers? Sixth, what does "getting" quantum mechanics that have to do with AI agents? Do I need to understand quantum physics before I can have a conversation with someone? Can I not read an email without an appeal to hilbert space? Just, none of this is related to quantum computing. It's like having a bug in a deployment and saying string theory would've prevented that.

I see intermixing of the terms quantum computer and quantum system. These are different concepts, and I think that's the source of the confusion. A quantum computer is a well defined thing. It's just like a classical computer but instead of just binary bits, it can work with qubits that support superposition. But it still needs programs just like a classical computer, and the results that we can actually read are binary in both cases.

Both of them are quantum "systems", in that both require quantum physics to work, if we're considering modern CPU gate sizes. Just, classical computers expose binary bits, and quantum computers expose qubits.

What I think you're picturing is a quantum "system", like a blob of quantum goo, that you can toss some "state" into and...something. But, that's not what a quantum computer is, any more than a classical computer is something you could throw into a blob of electrical goop and expect it to do anything.