In your 35 second blurb, and the New York Times article, it seems like the point you're making is that interference is the main way that quantum computers work. But what makes quantum interference special over other kinds? You can get interference in sound waves, light waves, radio waves, etc. You also mention that magnitudes can be complex, but the same is true of other kinds of waves; complex numbers are used for discussing impedance in electronics.

These are even relatively simple to work with; back in high school, I set up my basement as a darkroom, set up a sandbox for isolation, borrowed a laser from my physics teacher, bought a kit online with a beam splitter, mirrors, lenses, and film, and made some holograms of various objects utilizing light interference.

You could set up an apparatus in which light goes through a beam splitter, reflects off mirrors to travel via different paths, and is recombined and interferes in the end to produce an interference pattern. You could probably encode a lot of information in the exact length of the different paths, perhaps in an array of mirrors which could be actuated to produce slightly different path lengths in different parts of the beam (after the beam is expanded), and use the interference to make calculations.

Other than the smaller scale, and greater difficulty of working with it, what is special about quantum interference that would make it more amenable to solving problems that are NP complete than some apparatus producing similar kinds of interference with light?

Also, has it been proven (or argued sufficiently convincingly) that quantum computation at scale is actually possible? I'm wondering if there could be an issue where it requires more computation to construct a quantum computer than the computation you get out, or require a non-constant number of quantum computers (with respect to the size of the problem) to actually get reliable enough results out, or something of the sort.

I think this is somewhat like the questions of whether certain automata are Turing-complete (https://en.wikipedia.org/wiki/Wolfram%27s_2-state_3-symbol_T...), when a sufficiently complex process is needed to encode the problem into the automata that it could be argued that the computation was not actually carried out by the automata itself (I don't actually know if that question was answered; Wikipedia references a mailing list thread that has a lot of discussion, but I haven't seen any authoritative conclusion).

Given that empirically, only extremely simple quantum computers have been able to be constructed, what makes us think that there isn't some kind of tricky scaling issue like this were the additional complexity of building, running, or verifying the results of quantum computers will negate the benefits?