I'd like to claim that I've done a rigorous analysis of this, but
the truth is that the idea came from "Dragon's Egg", by Robert L.
Forward. It's a neat science fiction book about life on the
surface of a neutron star.
The question, of course, is whether
or not neutronium can exist in the form of collapsed atoms.
If so, some sort of chemistry should be possible, and therefore
nonotech may be possible. Otherwise, neutronium may end up
being either a "neutron soup" or a "neutron crystal." If
"soup", there may not be enough structure to support
computation. If "crystal" there may be enough structure,
but a completely new technical approach may be required.
If an atomic phase is possible at some pressure, but the
"soup" phase arises at a higher pressure, the engineering
will be very interesting. We'll need to maximize the computing
capacity by finding the appropriate configuration of matter to
mazimize the atomic-neutronium regime. This may require new
physics. Of course, the instant you start depending on new
physics the entire speculation becomes unconstrained.