Discrete particles vs. continuous wave functions is a red herring, I think. It’s true that in a simulation of QM one would have to approximate amplitudes up to some finite precision (and approximate infinite dimensional Hilbert spaces using finite dimensional Hilbert spaces). But this is not a problem that is unique to QM. Simulating classical mechanics also requires approximating the positions and momenta of particles to finite precision.
You are right, though, that computing quantum mechanics is harder than computing classical mechanics. This is true even if we completely discretize both theories. The length of a vector representing the state of a classical system is linear in the size of the system, but the length of a vector representing the state of a quantum system is exponential in the size of the system.
Discrete particles vs. continuous wave functions is a red herring, I think. It’s true that in a simulation of QM one would have to approximate amplitudes up to some finite precision (and approximate infinite dimensional Hilbert spaces using finite dimensional Hilbert spaces). But this is not a problem that is unique to QM. Simulating classical mechanics also requires approximating the positions and momenta of particles to finite precision.
You are right, though, that computing quantum mechanics is harder than computing classical mechanics. This is true even if we completely discretize both theories. The length of a vector representing the state of a classical system is linear in the size of the system, but the length of a vector representing the state of a quantum system is exponential in the size of the system.