I'm assuming you are referring to quantum computing for it's speed computations? That wouldn't make a different here. They have only X amount of tries before the phone locks them out. It is the number of tries that is the issue here.
No, what I am assuming is the company will be compelled to provide the data on the phone without the potential for lock=out or erasure during brute-force. Then, in all likelihood state-of-the-art methods in brute-forcing AES (with the best theoretical speed-up up to and including quadratic due to Grover's algorithm on a quantum computer, or some unknown state-of-the-art slower than that on a classical computer) will be employed until the data is ultimately decrypted.
From my understanding, if you had for example a 128-qbit quantum computer, it would be able to crack any 16 character password in a single operation.
It's not really a single operation though. How would that quantum computer test against an iPhone when each test is a mark against the 10 max test count? An iPhone is still based in standard silicon using bits; you can't exactly pop a process that uses qubits into it and expect it to work.
Nope. For general search operations (modeling your 128-bit cipher as a black box) the best we know how to do is Grover's algorithm, which gives you a quadratic speed up. Your 128 bit problem is now a 64 bit problem (which is of course still quite good).