What is the proof that quantum computers can efficiently simulate arbitrary quantum mechanical systems?
Why do you think simulating quantum physics means that you have to efficiently implement arbitrary quantum $n$-way interactions? If that's your requirement, quantum computers cannot do it efficiently.

You can write down an $n$-way unitary gate which implements an arbitrary $n$-bit-input $n$-bit-output function. This would let us solve an arbitrary problem on $n$ bits in one step. It is common sense that we can't find quantum systems in "real life" that will let us do this. 

Of course, in actual quantum physics, quantum dynamics is Hamiltonian and not just unitary, but there are still roughly $2^n$ parameters in an arbitrary $n$-way Hamiltonian, and doing this using 2-qubit gates (which have a constant number of parameters each) will require an exponential number of gates. Furthermore, I am fairly sure that the ability to implement arbitrary $n$-way Hamiltonians would still let you construct arbitrary binary functions on $O(n)$ bits.

So the requirement you pose for quantum computers to efficiently simulate arbitrary $n$-way interactions is much too strict. What you need is that quantum computers can efficiently simulate the $n$-way interactions that actually arise in quantum physics. Quantum computers are able to efficiently simulate $k$-local Hamiltonian dynamics for constant $k$, which may be enough to simulate interactions that arise in real quantum physics.

If you can suggest any $n$-way interactions that arise in quantum physics that  appear difficult for a quantum computer to simulate efficiently, this would be a truly exciting development. However, I don't know of any current suggestions for such interactions.

Whether quantum computers can efficiently simulate quantum field theory is still an open question, but progress is currently being made on it.