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The C10k Problem is a classical computing problem whose name (C10k) is a numeronym for concurrently handling ten thousand connections.

How could a quantum network be constructed to handle 10,000 clients concurrently?

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    $\begingroup$ Aside from being a problem currently being researched (which is a perfectly good and interesting thing to ask about), this is going to depend very much on the type of hardware/implementation used (at least, I'm assuming that you're asking about how this could work on the hardware level) - 10k superconducting qubits would be done in a different way to 10k ion trap qubits, so do you have a specific implementation of quantum computer in mind for this question? $\endgroup$ – Mithrandir24601 Jun 17 '18 at 17:55
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    $\begingroup$ I am most intetested in realizing a virtualized system. My current research is focused on the viability of distributed quantum computer architectures at scale. Also, NGINX was designed to solve C10k. I am thinking about a quantum version (ie a quantum webserver). I will update my question once I am able to formulate it more succinctly. $\endgroup$ – meowzz Jun 17 '18 at 18:48
  • $\begingroup$ The connection may indeed be superficial. I suppose while there are many ways the C10k problem can be applied (the primary focus of responses so far seem to be on hardware; which is understandable given how I presented the question), it is clear me now that my primary interest is it's application to quantum networks. Will update question soon. $\endgroup$ – meowzz Jun 18 '18 at 0:39
  • $\begingroup$ @meowzz: Perhaps you can ask a new question if you are going to change it in a way that makes me have to re-write my answer. I wrote my answer based on this question, and I did that before some of the comments here, it just didn't show up online until much later because I'm traveling at the moment to a conference and have had spotty Wi-Fi connection. $\endgroup$ – user1271772 Jun 18 '18 at 1:16
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    $\begingroup$ I changed your question title back to your question. The big issue's that a question's title should tell users what's being asked; simply stating the question is a great way to do that. By contrast, most folks won't know what "The Q10K problem" refers to without having first read this question. $\endgroup$ – Nat Jun 22 '18 at 6:45
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In the comments to my answer the OP has written:

In the universal gate case you stated the largest systems are <100. How could it reach 10k?

Well I have good news for you. Four days ago D-Wave announced at the AQC conference that they can now do YY coupling:

enter image description here

Here you can see the superconducting circuit that gives you ZZ and YY coupling at the same time:

enter image description here

I cannot show you more of their "preview" presentation, but expect for them to publish something very soon.

Why is YY coupling significant? It is because in 2007, Jacob Biamonte and Peter Love from D-Wave proved that XX + ZZ is enough for universal quantum computation. XX and YY are equivalent up to a rotation, so they could easily have instead said that YY + ZZ is universal.

Now that D-Wave has engineered a universal set of couplers, it should be possible to have a 10,000 qubit universal quantum computer when they extend to 1250 units cells (since 8 x 1250 = 10,000, see my first answer).

I'm sorry that there's no literature references for this yet, but the picture tells the whole story, and I'm afraid that until D-Wave publishes something, this is the "source" for the information. This is how you can cite this answer.

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Enabling network sockets to handle 10k clients at the same time with over 1 gigabit per second Ethernet (the C10k problem), is different from making a quantum computer that can handle 10k qubits concurrently. Remember 10k bits is only 1.25kB which is not even enough to store a typical operating system.

If you want to consider each qubit as a "client" in some generalization of the C10k problem, then the answer to your question depends on whether or not you need a universal gate set to be applicable between each of the 10,000 qubit connections. If so, the largest quantum computers with a universal gate set are the 50-qubit machine by IBM and the 72-qubit machine by Google (which has been announced but not shown to the public yet).

You mention D-Wave, which makes non-universal quantum annealers. If each qubit is considered a "client", it is true that the D-Wave 2000Q has 2048 qubits, but not all of them can be connected to any other qubit. This is the connectivity graph for a typical D-Wave machine. Notice that each qubit can only be connected to at most 6 other qubits. To get 10,000 qubits in this arrangement, you just need to create more of these "unit cells" of 8 qubits each. What's pictured here is the D-Wave One which has 16 units cells of 8 qubits each (8 x 16 = 128 total qubits). The D-Wave Two had 64 units cells of 8 qubits each (8 x 64 = 512 qubits). The D-Wave 2X had 132 unit cells (8 x 144 = 1152 total qubits), and the D-Wave 2000Q has 256 unit cells (8 x 256 = 2048 total qubits).

For 10,000 qubits you just need 1250 units cells (8 x 1250 = 10,000). After that point D-Wave says that a re-design would need to be required, perhaps in the size of the unit cells, or in going from 2D to 3D, or in the physics itself.

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    $\begingroup$ I have edited 1000 to 10,000. It was a typo since I was writing that on a low spec public computer while waiting for an airport shuttle. To extend the IBM machine from 50 qubits to 10,000 qubits would involve surpassing obstacles which are not going to be clear to anyone but the IBM engineers who will not likely tell you anything (just like Intel doesn't publicize their ideas for how to surpass any obstacles in making classical chips). Same goes for extending the Google quantum computer from 72 qubits to 10,000. The best answer you will probably get is on how to extend D-Wave to 10,000. $\endgroup$ – user1271772 Jun 18 '18 at 1:51
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    $\begingroup$ I appreciate your breakdown of D-Wave technologies (especially the connectivity graph). "After that point D-Wave says that a re-design would need to be required, perhaps in the size of the unit cells, or in going from 2D to 3D, or in the physics itself." What the redesign would consist of is of interest to me. I have been considering a 100x100 matrix (10,00 cells) which could then be moved into 3d (100x100x100=1,000,000 cells). $\endgroup$ – meowzz Jun 18 '18 at 1:52
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    $\begingroup$ Except that the current D-Wave architecture has unit cells of 8-qubits each. See the picture I linked in my answer. So it makes more sense to talk about having 1250 unit cells of 8 qubits each, to get 10,000. The 1250 unit cells can be arranged in a 25x50 2D rectangle, or maybe 2 layers (in 3D, so one on top of the other) with each layer being a 25x25 lattice, or any other possible combination that leads to 1250 unit cells of 8 qubits each. $\endgroup$ – user1271772 Jun 18 '18 at 2:07
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    $\begingroup$ @meowzz: The only architecture for which there is knowledge of how to scale up to 10,000 is the D-Wave architecture and I explained exactly how that would happen. If you want to know the specifics of what the re-design would require, unfortunately that is something only D-Wave would know and you are asking them to reveal information that they don't want their competitors to know. $\endgroup$ – user1271772 Jun 19 '18 at 17:16
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    $\begingroup$ Same goes for the universal quantum computers. IBM, Google, and D-Wave are commercial quantum companies, not universities. I don't think you can expect users to explain things that these companies treat as "trade secrets". I have already given 3 examples of my own thoughts on what a route to overcoming the challenges will be. But that is for going BEYOND 10,000, not for going only to 10,000 ! $\endgroup$ – user1271772 Jun 19 '18 at 17:19

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