My understanding is that the magnetic fields needed to hold the ions in place in ion trap quantum computers are very complex, and for that reason, currently, only 1-D computers are possible, therefore reducing the ease of communication between qubits. There does seem to be a proposition for a 2-d system using a Paul trap in this preprint but I can't seem to find if this has actually been tested.

Does the scalability of ion trap quantum computers depend upon this alone (whether or not the ions can be arranged in configurations other than a straight line) or are other factors entailed? If the former, what progress has been made? If the latter, what are the other factors?