Quantum computers can’t solve impossible problems — they can solve some instances of very high complexity computation in less time compared to classical computing.

Like I said — a missile doesn’t have a hard time figuring things out quickly enough, it has a hard time gathering accurate information (flare countermeasures), or determining where the craft will be in X time (unknowable since it is piloted) and then getting to the correct position at the right time because it is a physical aircraft bound by physical laws.

Kinematics are not complex problems compared to computational techniques on a classical computer

If you were talking about some type of quantum camera that (insert made up helpful feature here), sure, maybe; but the inputs to your quantum computer are the same as the classical one. And after the quantum computer does its job, even, somehow, let’s pretend it does it instantaneously, are still limited by response time of the missile and Physical laws. Which are the real crux of the difficulties anyways