I’m surely no expert—and would welcome hearing from someone who is—but isn’t it true that the phrase “average-case NP-hard” needs very careful definition?

Or do both D-Wave and MIT both know something?

Yes, the many-worlds interpretation makes definite predictions as to how the process of quantum decoherence actually occurs. The major issue is that empirically indistinguishable and empirically undistinguished are two rather different statements.

Importantly, this is intended to be no different from what ordinary quantum mechanics would predict if measurement was removed as a preferred process. The ‘many worlds interpretation’ part comes in when we note that in the wavefunction after a ‘measurement’, each type of eigenstate in the measured system is crossed with a particular state in the measuring system. Hence the interpretation of a ‘relative collapse’.

I should state that I’m not a proponent of the many-worlds interpretation. I have a copy of Everett’s thesis here, and by binary search I think I’ve found exactly the point at which he made a mistake and our thoughts diverge. I should write a proper article on this rather than expound in the comment page of a blog. But here is the main gist of the thing:

In the typical interpretation mixed-states aren’t ‘real’ states, they’re just tools to help us when we’re talking about ensembles. If we actually did know which pure state the measuring device was in then there would be no wave-function split. The conclusion is that the split is a fallacious notion based on a mixing of quantum and classical probabilities, when there shouldn’t be.

I appreciate your point, but doesn’t the MWI contemplate a similar “process” (e.g., branches of the universal wavefunction split when different components of a quantum superposition “decohere” from each other as a result of environmental interference effects). I believe tests have been proposed to distinguish the interpretations (and IMO the ability to conduct such tests is “merely” an “engineering” issue), but it’s difficult to draw any conclusions absent such experimental results.

On the other hand, its quite unclear to me that putting yourself “in superposition” distinguishes anything at al. It certainly dosen’t distinguish Everett & Bohm, and well in the Copenhagen interpretation you shouldnt be in a superposition at all. The fact that everything looks more or less the same when youre “in superposition” is what led Everett to propose his theory.

Unless by “put yourself in superposition”, you meant put yourself in a situation where Copenhagen demands a collapse and then interfere the waves in the way that distinguishes collapsed from uncollapsed WFs. At which point I’m both pedantic and sorry.