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I don't have any specific task or algorithm in mind, so depending on how they were tested – Is there any research which shows just how the D-Wave Two computer was faster (in terms of computation performance) than its predecessor (D-Wave One)?

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    $\begingroup$ What do you mean by "computation performance"? Using which benchmarks (e.g. algorithms, tasks, etc)? $\endgroup$ – nbro Mar 12 '18 at 20:26
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    $\begingroup$ Whatever tasks/algorithms they were tested against. $\endgroup$ – kenorb Mar 12 '18 at 20:27
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    $\begingroup$ You may specify that in your question. Even better, you may do a little research regarding the topic and include a few details in your question. $\endgroup$ – nbro Mar 12 '18 at 20:29
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    $\begingroup$ Personally, I feel this would be a much better question if, instead of talking about 'computational performance' (which isn't well defined, although there are certainly numerous good possible questions in this area), you either just ask about speed of qubit initialisation, a single anneal, followed by a measurement or find a much more specific question about computational performance $\endgroup$ – Mithrandir24601 Mar 12 '18 at 21:03
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    $\begingroup$ I think this question should be edited to describe what precise comparison is desired. It is just too broad right now to give a real answer. $\endgroup$ – user1271772 Oct 23 '18 at 21:28
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As Troyer and Lidar saw no speed increase with the D-Wave 1 compared to classical computers, the D-Wave 2 benchmark figure reported in 2013 of 3600 times as fast as CPLEX (the best algorithm on a conventional machine) suggests the D-Wave 2 is 3600 times as fast as the D-Wave 1.

However:

  • the results are in a pretty restricted set of parameters, so this may not be relevant for other parameters. (as an example, the benchmark figures for the D-Wave 2000Q only take constant factor performance gains into account)
  • the configuration of the CPLEX may not compare directly to the classical computers used to benchmark the D-Wave 1
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  • $\begingroup$ Where did Troyer and Lidar see no speed increase with D-One compared to classical computers? Also their paper "Defining and Detecting Speed-up" shows D-Wave Two being several orders of magnitude faster than classical computers. $\endgroup$ – user1271772 Oct 23 '18 at 21:30
  • $\begingroup$ Follow the link in my answer: "A research team led by Matthias Troyer and Daniel Lidar found that, while there is evidence of quantum annealing in D-Wave One, they saw no speed increase compared to classical computers" $\endgroup$ – Rory Alsop Oct 24 '18 at 11:14
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As far as I know the closest answer to your question for applications is given in the recent (still unpublished) work presented at the March meeting by Bibek Pokharel, where he compares graph 3-coloring instances on D-Wave Two, D-Wave 2X and D-Wave 2000Q, all other things staying reasonably equal. The short answer is that all the performance increase is essentially due to the possibility to run single anneals at shorter anneal-time. (e.g. 1$\mu$s instead of 5$\mu$s gives indeed about 5X of performance increase, in terms of time-to-solution (TTS) metric. With respect to 20$\mu$s of D-Wave Two the scaling is different).

I can also spoil that from D-Wave Two and D-Wave 2000Q on Sherrington-Kirkpatrick instances we observed no substantial improvement as well. Results will be published soon in collaborations with Stanford.

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