The reality of the wave function or quantum fields

I have argued before that not all ontological entities are equally real.  If what is real in the world is what has explanatory usefulness then not everything is equally real.  Not all concepts/entities have equal usefulness.  Deutsch and then Wallace (The Emergent Multiverse, Oxford Univ. Press, 2012, page 389) argue that there are not enough atoms in the universe to account for how Shor's quantum algorithm can factorize a number. The required machinery must be seen to be in the form of quantum fields, not matter. This argues strongly for the reality of the high dimensionality quantum realm. (But I would not necessarily say this has to be in the form of a set of emergent, non interacting,  nearly classical, Everettian worlds.)