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The D-Wave team put out a few papers (like this one and this one) in the last few years describing how their methods can find ground states of certain spin-glass Hamiltonians faster than classical methods for an equivalent accuracy (more or less). As described in a previous post, there is still a way to go before this translates to a quantum advantage in a "real-world"/industry use-case. However I was curious to know, does the D-Wave show any advantage for use-cases that academics, e.g. condensed matter physicists, would care about? Or even for these use-cases, does more work need to be done before the D-Wave can be more useful than classical machines for studying complex and interesting enough Hamiltonians currently studied in academic fields?

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Interest in academia

In the past, only a small number of academic institutions, with a small number of professors, existed. Now there's about 30,000 universities and who knows how many colleges, research institutes, and companies engaged in academic research, and with so much "borrowed money", these institutions are able to employ far more academic researchers than ever before.

I've recently been reading a book by Eugene Wigner from 1930, and the papers cited in it, such as a 1929 paper by Hans Bethe, and it occurred to me that the very few people who managed to obtain academic positions back then, published a small number of papers but they were usually thorough, extremely high in quality, and very pertinent. These days many of the most famous researchers are publishing several hundred papers and often they don't even know those papers (I can give many examples in detail, including a recent one in which a Max Planck Director told me that he promised himself that he'll never publish a paper on the chromium dimer, and I told him "you did publish a paper on the chromium dimer last month" and he didn't know it). Many big-name academics will go their entire career having published perhaps 500 papers, but not one of them as meaningful as the top 5 papers by the analogously big-name physicists of Wigner and Bethe's time (I don't think this is an exaggeration, and we can choose specific researchers and study the matter closely and fairly if that's interesting enough to people here).

My point is that what is interesting to an "academic" can be almost anything these days.

The question is therefore quite open-ended, and that is probably why it already got a close vote for being "opinion-based", but I think it's still very doable to write an objective answer, so I doubt it will get 5 close votes.

Quantum advantage

This part is easy to answer objectively. Let's focus on the half of your question that I've put in bold font below:

"Does the D-Wave show any advantage for academic/condensed matter physics use-cases?"

The D-Wave machines are studying things like 3D Ising models with 5000+ spins. That is simply not possible to do on classical computers except with analytic methods (which are limited to approximations such as "all spin-spin couplings are given by $J$, rather than allowing spin-1 and spin-7 to be coupled by $J_{1,7}$ which is different from $J_{1,8}$) or with numerical methods that have been shown in many papers (for example the one provided in the hyperlink in the previous sentence here) to be significantly slower (7 orders of magnitude at about 900 spins) than doing quantum annealing.

If you want to solve the Schroedinger equation for the He atom, you can do it with with about 10-50 atomic units of precision on computers from about 20 years ago, but for the H2 molecule, even 10 years later we can see that 18 digits of accuracy is the best we can get. For the carbon atom (6 electrons), it's unlikely that we can even get 10-5 accuracy right now and you can imagine how bad things get if we want to study neon (10 electrons) or krypton (36 electrons) or uranium (92 electrons)!

However, we can easily do experiments on uranium to determine the ionization energy of uranium without ever solving the Schroedinger equation. In this way, doing experiments provide us a clear advantage over attempting to use classical computers to determine the same thing.

The D-Wave hardware is essentially a group of 5000+ spins that are coupled to each other, and we can experimentally study what the nature of the ground state, or the temperature at which phase transitions occur, or whatever is possible, and this will simply have an advantage over trying to simulate 5000 spins and their 25000-dimensional Hilbert space on a classical computer. Sometimes such devices are called "quantum simulators", and D-Wave is not the only organization that has been doing this in recent decades.

Interesting quantum advantage

I'm pretty sure it was this talk by Andrew King at AQC 2017 (you can see my head in front of the screen during much of the video) after which Ed Farhi (perhaps the one most credited for first coining the term "adiabatic quantum computing") said at the end extremely enthusiastically: "You have finally fulfilled Feynman's dream which was to use quantum mechanics to simulate a physical system!"

In that sense, at least one academic, was found the talk (and probably the subsequent papers) to be fascinating.

However, to me the papers after this one were just getting overly repetitive (in my answer to your previous question, I listed several papers by D-Wave that were published in Nature or Science journals, that seemed to just be a repeat of the same thing over and over again when many of us (likely including the investors and customers who give them all their money) would have preferred for them to work on doing something actually useful (such as working on their "universal" quantum computer and such as increasing the connectivity between the qubits). To be fair, they probably can't improve their hardware much right now, which would be why there seems to have been zero progress on the universal quantum computer, and even their highly delayed Zephyr architecture won't have much more (from a practical standpoint) qubit-connectivity compared to Pegasus and Chimera.

How interesting?

My (biased) opinion

Personally I don't find the behavior of the Ising model, or even the Heisenberg model, or Hubbard model (both which would be far to complex for D-Wave's overly simplistic hardware) to be any more interesting at 5000 spins than at more modest numbers of spins, at which most of the valuable science is already known.

Even though I'm an academic, things need to have clear value and meaning for them to interest me, and my threshold for that in terms of matter modeling is probably higher than it is for anyone that finds this series of D-Wave papers (after the first one) fascinating. I spend a lot of time modeling matter, but one of the things that I do is calculate eigenvalues of the Schroedinger equation for real atoms and molecules, such that their differences can be compared to real experiments, or my predictions can be used to help experimentalists make the molecules that they want. Another thing that I would do is molecular dynamics calculations on COVID-19 spike proteins and possible drugs, to see which drugs are most likely to bind to them. Another thing that I would do is to see how well certain nanomaterials can bind to heavy metals for the purpose of cleaning our water from dangerous elements like lead, nickel and cadmium. I also like to fit potential energy surfaces to reproduce spectroscopic data of real molecules, so that we can better understand the composition of the atmosphere of Earth and exoplanets in space (hopefully assisting with finding life on other planets).

When a Hamiltonian (like the Ising model) is no longer modeling a real system, I am much less interested in using it or knowing where it's solution undergoes phase transitions or whatever else D-Wave is studying. Some people use Hubbard models to study superconductivity, so I'm sure these model Hamiltonians are interesting to some condensed matter physicists, but most of us know that these models will not be good enough for real-world applications, and therefore are not interesting to most academics outside of certain areas of condensed matter physics. Even the Jackeli-Khaluillin Hamiltonian which garnered 2000+ citations, was shown by my friend Steve Winter to be far too simple in that they lead to the predictions of three potential Kitaev spin liquids, that all turned out not to behave how the original model hoped, once more accurate models were used.

Condensed matter physicists

There's a lot of condensed matter physicists who do love to study model Hamiltonians, and papers in that area often get more citations than work that studies real systems, so there are people who might "care about" (to use your words) the D-Wave work, but we will have to eagerly wait for one of them to tell us what they think (perhaps they don't care about the specific models being studied by D-Wave, or the way that they're studying them, or the fact that they have 5000+ spins rather than 150 or whatever people can already study without their hardware).

In the Andrew King talk for which I provided a link earlier in this answer, he says something like "D-Wave is solving a real-world problem, as long as by "real-world" you mean condensed matter physics." Everyone laughed, and the joke was basically that condensed matter physics is not the real world, but it is indeed an area of academic interest, and you are wondering whether there's academic interest in what D-Wave is doing.

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    $\begingroup$ Thanks for the very full answer! I would also be interested to the get opinions of condensed matter physicists studying model Hamiltonians, so if you are such a person I would be really grateful for your perspective! $\endgroup$ Commented Sep 4, 2023 at 5:41
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    $\begingroup$ I have already sent this to two people who work in the model Hamiltonian field, and who are active on StackExchange (at least they were in the past), with hopes that we'll get some other perspectives here. $\endgroup$ Commented Sep 4, 2023 at 10:45

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