John Martinis' group is planning to do that within the next two years [1][2]. Ten years might be realistic for solving useful problems faster and cheaper, but the esoteric speedups are right around the corner.
1: https://arxiv.org/abs/1608.00263 2: https://www.youtube.com/watch?v=kgMWommXxU8
One question I'd have is whether quantum simulation is indeed the fastest way to solve the quantum speckle problem on a classical computer. The other related thing to think about is whether the output of a quantum speckle computer can only be explained by the large state space and quantum mechanics or whether there are alternative explanations.
So definitely an interesting direction but even if they're successful we're still not quite there. When we have a quantum computer doing useful work with exponential speedup over classical computers that would be something and even then we only have a very limited set of algorithms at the moment.
They give arguments for this in the paper. Intuitively, if there's some fast way to classically sample a random quantum circuit then that means most quantum circuits should be easy to simulate classically. But that doesn't seem to be the case: we don't have algorithms that go fast on most circuits but go slow in highly specialized cases. It's the other way around.
> whether the output of a quantum speckle computer can only be explained by the large state space and quantum mechanics or whether there are alternative explanations.
Given that all the engineering was based on quantum mechanics, it would be very surprising if the machine worked based on something else. It's quite difficult to make things accidentally work like that. It'd be like trying to build a car, confirming it can take you from place to place, then realizing that actually you made a hang-glider by accident.
The mentioning of quantum computers is very interesting in the following sense: If one were able to build a sufficiently large quantum computer, this would provide strong evidence that the (at the moment rather hypothetical) theory whether quantum mechanics is rather an emergent phenomen by a deterministic process (cellular automaton)
> https://arxiv.org/abs/1405.1548
which the Nobel laureate Gerard 't Hooft worked on for the last years is probably wrong. To quote p. 79-80:
"Such scaled classical computers can of course not be built, so that this quantum computer will still be allowed to perform computational miracles, but factoring a number with millions of digits into its prime factors will not be possible – unless fundamentally improved classical algorithms turn out to exist. If engineers ever succeed in making such quantum computers, it seems to me that the CAT is falsified; no classical theory can explain quantum mechanics."
On the other hand, if we seriously get into trouble building a sufficiently large quantum computer (despite our best efforts), this would at least to me provide evidence that 't Hooft is on something - since that this is a prediction that his Cellular Automaton Interpretation of Quantum Mechanics provides.
The Hooft thing is that there are limits on computation due to the process of the universe and that if a classical computer that was at the plank scale, runs at plankian speed (help help I am using terms I can't understand!!!) and covered the whole of the universe couldn't do it from the beginning of time to heat death... then nor can an arbitrary QC. Shores algorithm does factors in (log n)^3 maybe we'll find that there are physical limits on the scale of QC which hold it below hundreds of millions of qbits where a plankian computer could be synthesised, and/or it may be that such a computer can't run at high clock speeds, and because of this BQP algorithms can't be run on problems that are not allowed in the sense that they somehow solve the universe.
I don't think anyone has any reason to believe this is true in an engineering sense but there is every reason to believe that large QC will be very, very difficult in an engineering sense and I think that the people building one do expect to run into problems of this sort eventually, but at the moment they are delighted to find that they are able to do things at the lower end that will create devices that are going to be transformational for reasoning about some components of the physical universe - for example simulation of the interactions of very large molecules - maybe mapping seconds of a virus interacting with a cell membrane using months of QC ?
The problem with fusion is commercial viability. Building something for billions of dollars that can barely put out more energy than you put in isn't commercially viable. At any rate, fusion seems more like a very tough engineering problem, the physics has been there for a long while.
With quantum computing there are also no real signs that a quantum computer will beat a "classical" computer at anything any time soon. It always was and still is very difficult to get quantum systems to scale and you need a large enough system to make a difference and it may be impossible to do so. Again a lot of this is more of an engineering problem though admittedly the line between physics and engineering can be blurry since it's not always clear whether something can't be done because you've reached a fundamental limitation vs. having a clever enough design.
It's possible someone will eventually solve the problems in these areas (assuming there aren't fundamental reasons we're just not aware of yet why it's impossible) but IMO the odds are low and you need some sort of breakthrough.