Notes: The Repeat in step 3 is for a number of steps depending on the quality of the current configuration. The time taken to construct each qubo instance generating random numbers, or reading from a file was not included in the timings, on the grounds that the task is to solve the problem, not construct and solve the problem. The far left tail of the D-Wave plots, on the other hand, may be underestimating its speed slightly, partly because the really easy problems morally require only a fraction of an anneal, but this is not represented here. These interpretations are just a bit of fun, really. Interestingly, the Prog-QUBO-m5 finds Set 2 size weightmode5 instances a lot harder than Set 3, even though it is the other way around for the heuristic solvers. Name required.
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That is surely the interesting question and it would indicate whether something along these lines could eventually be made computationally useful and much more.
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Trying to imagine how this conclusion could be untrue: i it could be that there is some class of problem, hitherto untested, on which the D-Wave does much better than software and that this class of problem is usefulii it could be that the test set used here is not in fact similar to the test set used in  which is easily checkableiii it could be that there is a new D-Wave device that is much better than the ones for which the test results were published.
On the other hand, we can fix the difficulty and look at the scaling as n increases, and arrive at just the opposite conclusion. To this end, we define the Time-to-Solve TTS for a heuristic solver operating on a given instance to be the average time taken to find the optimum value. The fastest TTS was 0.
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|A maximal induced tree used for strategy 3.
In particular, all heuristic results have been verified by two independent exact search programs. However, these two comparisons give apparently opposite answers. Of course proving optimality is much harder than finding a solution, but CPLEX may have a way of just going for a solution.
On the other hand, this would also make it more difficult for the software heuristic solver. The TTS can be rather small, e.
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Apologies that this renders comments below including my own that are prior to 29 June, out of date.
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Table of timings for proving runs. The TTS is taken to be the running time divided byand is used as the performance measure. It is assumed that the solver may be using a random algorithm, and the average is meant to be over this space of randomness. I am sure that you can improve a lot on these programs, but the point was to see if a simple idea would be enough.
From the point of view of what the V6 device can actually do, it is reasonable to include the constant setup time, but from the point of view of following trends, the setup time acts as a distortion.
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|In this case I believe any algorithm, specialised or not, is fair game for the purposes of deciding whether D-Wave is currently a useful computational device.
Each heuristic qubo run consists of finding optimal solutions which makes it possible to measure the CPU time to reasonable accuracy with the operating system CPU clock whose resolution is 1 centisecond. The idea is to do an equal-quality-compare-time comparison between this and the various solvers reported in which is carried out approximately by varying the running time of Prog-QAP until the overall quality of all solutions is similar to that of the best solvers in .
We can go further and look at the effect of completely eliminating the D-Wave setup time the constant component of the query timethough this is not currently possible as far as I am aware. The fastest TTS was 0.
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If it keeps doing random runs until the lowest value it has obtained has occurred times, then for the problems here it is highly likely that this value is the true optimum.
Prog-QUBO was run in heuristic mode, single-threaded on a single core of a standard desktop processor on random test instances available in the github repositorysplit as instances of three different types of problem run with two different strategies. Peter Shor says:. The fastest TTS was 0. See, e. Prog-QUBO is the main focus of this discussion.
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|This time the important information is contained in Fig.
Further details are given in AppendixB. In fact the setup component may be a slight overestimate because the figures reported in  were upper bounds estimated from the maximum of several example values. This set of instances forms the basis of most of the QUBO discussion in the above writeup. The operating system was Ubuntu The far left tail of the D-Wave plots, on the other hand, may be underestimating its speed slightly, partly because the really easy problems morally require only a fraction of an anneal, but this is not represented here.
So the actual procedure used was this:.