Commenter Michael J. Biercuk asks about D-wave’s machine:
What is the fundamental experimental test which would demonstrate the system is not simply undergoing a classical, incoherent process?
Of course there are answers to this question which involve some technically fairly challenging experiments (proving that a quantum computer is quantum computing is something which many experimentalists have struggled over, for far smaller systems than D-wave’s system.) But there is a much simpler experiment which I haven’t seen answered in any of the press on D-wave, and which, for the life of me, I don’t understand why it hasn’t been done and publicized.
This question is simply, does your system show any speedup over a classically equivalent procedure? The experimental running of D-wave’s system is something like the following: set the couplings so that an easily achievable ground state is achievable. Cool the system down. Drag the couplings of the system from the easily achievable ground state to the setup which is the ground state of the instance of computational problem one wishes to solve. This procedure takes a certain amount of time and succeeds with a certain probability. Actually there are probably three times here: cooling time, adiabatic evolution time, and measurement time. Let’s throw out that last time and just talk about the cooling time and adiabatic evolution time. One should be able to easily produce a plot of probability of successfully solving the problem as a function of those times.
Now if you want to say that the above procedure has any advantage over classical systems, then you might think you want to compare this to the best classical algorithms operating on our best classical computers. But what I’m interested in is something even more basic. If you carry out a procedure where you start the system hot, and the couplings such that the ground state is the solution to the instance of the computational problem you are trying to solve, and then you cool the system down, what does the probability of successfully solving the problem look like as a function of this cooling down time. And, of course, the most interesting question is whether there is any sum of times for the first experiment versus the second “classical” experiment for which the probability of succeeding is greater for the possibly quantum setup?
I mean, it seems like this is a rather simple setup, and I can’t see how pretty much any information about their system can leak out to us poor academics (who would of course steal it and use it to build our own quantum computer) in performing this experiment, so why hasn’t it been done? Or maybe it has been done, but the results aren’t so flattering…