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In this plot:

enter image description here

taken from here, IonQ is claiming to have a potential application in machine learning by 2023. What applications could they have in mind?

From what I understand, modern error correction prevents obtaining speedup from any quadratic algorithms, so the only realistic speedup could be done with algorithms faster than polynomial. From this chart: enter image description here

It seems like there aren't any ML applications that are faster than quadratic without "the fine-print" that they might not be do-able in a real-life situation.

Is there something I'm missing here?

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    $\begingroup$ @user1271772, I mean I think it's more of a qualitative evaluation saying that after a certain number of qubits certain applications become feasible. I think it's somewhat reasonable for a quantum computing company to have an idea of what applications will be feasible at certain qubit numbers. Seems like they think that machine learning will come first, then quantum chemistry much later. Since there are chemistry problems that can be reduced to finding eigenvalues, I would've thought that this would be the first thing ready. $\endgroup$
    – Steven Sagona
    Commented Mar 10, 2021 at 5:29
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    $\begingroup$ I agree that they are likely exaggerating, but I think it's likely there is some substance to their claims. $\endgroup$
    – Steven Sagona
    Commented Mar 10, 2021 at 5:31
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    $\begingroup$ @StevenSagona you're right to be skeptical, there certainly aren't going to be any serious applications (e.g. in ML or quantum simulation, etc) without error correction, and certainly not by 2023. it's exaggeration to the point of being dishonest, and ionQ has received a lot of criticism recently for claims like this (see e.g. this thread) $\endgroup$
    – 4xion
    Commented Mar 10, 2021 at 19:38
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    $\begingroup$ @4xion, I'm not sure a single person's rant (who seems to work for Amazon with competing technology) classifies as "receiving a lot of criticism." (Seems like he's claiming that error correction is impossible for Ion qubits even though it appears as though they have papers that show they can at least correct a single qubit) While I'm skeptical, I have some hope that they have some kind of argument for this. (And trusting other competitors criticisms might be just as, if not more, inaccurate) $\endgroup$
    – Steven Sagona
    Commented Mar 10, 2021 at 20:07
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    $\begingroup$ @StevenSagona In term of why the chemistry application is later than ML, it might has to do with the fact that achieving "chemical accuracy", or whatever you want to call it, is really hard with noisy devices. I guess they are betting on having robust enough device to achieve really accurate solution... I do feel like the graph has more than a bit of exaggeration than one would like... but again, it's a business so I understand. I do hope they will be successful in reach their goal though. And same goes for all the quantum computing companies out there. $\endgroup$
    – KAJ226
    Commented Mar 11, 2021 at 4:40

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"IonQ is claiming to have a potential application in machine learning by 2023. What applications could they have in mind?"

None.

  • The plot you showed has no units on the y-axis. It doesn't even have numbers.
  • The choice of 2023, 2025, and 2027 for "inflection points" (which they didn't define, and based on their graph has nothing to do with the standard calculus definition of the term) was arbitrary.
  • The choice of topics listed (Machine Learning, Materials, Chemistry) is arbitrary, and the order is even more arbitrary. In fact it would make more sense to switch chemistry and materials, since materials involve far more atoms than molecules, and are often significantly harder to model using the techniques for which quantum computers provide an advantage (QCs are very unlikely to speed up DFT, but could possibly speed up FCI, but FCI for materials is objectively orders of magnitude harder than molecules).
  • This last point is funny: they predicted "faster optimization" in 2025, but "better optimization" will have to wait until 2027 (just hilarious!).

If you are just wondering what applications of machine learning are possible in the future, please see this question: Is there any potential application of quantum computers in machine learning or AI?.

If you are wondering what applications IonQ has in mind for the year 2023, the answer is most certainly zero. I wish I could also underline "most certainly zero" to put more emphasis on it. Let me say it again: quantum computing will not be outperforming classical computers for any machine learning applications in 2023.

You may also find useful a similar answer about applications of quantum computes in drug design.

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