The difference between QC and all those other examples of interference is that, in the case of QC, the interference happens in configuration space rather than ordinary 3-dimensional space. And configuration space is enormous; it has a dimension that grows exponentially with the number of particles. The number of paths that could interfere with each other to produce a given amplitude is likewise exponential (in that case, in the number of computational steps).
No, of course no one has proven that it can work: presumably, the only proof that will convince everyone will be the actual construction of the machines! But in the 1990s, the theory of quantum error-correction convinced almost everyone that, as far as current physics can say, the difficulties (though staggering) seem to be ""merely"" difficulties of engineering. As I discussed in another answer, a deep reason why QC could never be scaled would be MUCH more interesting scientifically than a mere success in scaling it (which would "merely" confirm what physicists already believe). And of course, with the ongoing efforts of Google and others to demonstrate "quantum supremacy" with 50-70 qubits, we're likely to get experimental results that are relevant to your questions within the next few years.
Out of all your replies, I THINK that this is the one that helped me grok why QC is different than somehow simulating quantum math in a classical computer. The idea of being able to tap into more than 3 dimensions sounds like something very fundamental, kind of like relativity, and a key aspect of how our universe works that at least I was never aware of (and probably a lot of other people!)
Would you consider writing an in-depth article on configuration space and how it applies to QC (and possibly other research) and sharing it here on HN someday?
Pretty much any intro to QC (and in particular, any of the intros I've written, and linked to elsewhere on this thread) will make the point about Hilbert space (that's what it's called) having a dimension that grows exponentially with the number of particles in your system. This is because every possible classical configuration of the system is its own orthogonal "direction" in Hilbert space, and the full state can be an arbitrary superposition (i.e., complex linear combination) of those directions.
No, of course no one has proven that it can work: presumably, the only proof that will convince everyone will be the actual construction of the machines! But in the 1990s, the theory of quantum error-correction convinced almost everyone that, as far as current physics can say, the difficulties (though staggering) seem to be ""merely"" difficulties of engineering. As I discussed in another answer, a deep reason why QC could never be scaled would be MUCH more interesting scientifically than a mere success in scaling it (which would "merely" confirm what physicists already believe). And of course, with the ongoing efforts of Google and others to demonstrate "quantum supremacy" with 50-70 qubits, we're likely to get experimental results that are relevant to your questions within the next few years.