This claim makes little sense. There are many problems that are much easier to verify than to solve. Why isn't that approach ever used to validate these quantum computing claims?
(1) They're picking problems domains that are maximally close to the substrate of the computation device, so they can hit maximum problem sizes (like 10^25). For many (all?) fast-verifiable problems they can't currently handle impressively large problem sizes. In the same way that GPUs are only really good at "embarrassingly parallel" algorithms like computer graphics and linear algebra, these quantum chips are only really good at certain classes of algorithms that don't require too much coherence.
(2) A lot of potential use cases are NOT easy to validate, but are still very useful and interesting. Weather and climate prediction, for example. Quantum chemistry simulations is another. Nuclear simulations for the department of energy. Cryptography is kinda exceptional in that it provides easily verifiable results.
(0) For a quantum algorithm/simulation to be classically verifiable, it needs additional structure; something that leads to a structured, verifiable output despite the intermediate steps being intractable to simulate classically. That additional structure necessarily adds complexity beyond what can be run on current devices.
To pick an arbitrary example I'm familiar with, this paper (https://arxiv.org/abs/2104.00687) relies on the quantum computer implementing a certain cryptographic hash function. This alone makes the computation way more complex than what can be run on current hardware.
And they’re not actually solving weather problems right now, I think. That was just an example. What they are actually solving are toy mathematical challenges.
Also I doubt that a quantum algorithm is possible that provably solves the Navier-Stokes equations with known boundary and initial conditions. At least you need some discretization, and maybe you can get a quantum algorithm that provably converges to the real solution (which alone would be a breakthrough, I believe). Then you need some experimental lab setup with well controlled boundary and initial conditions that you can measure against.
In any case the validation would be at a very different standard compared to verifying prime factorization. At most you can gain confidence in the correctness of the simulation, but never absolute certainty.
For example: "Calculate whether we'll have El Niño this year"
The validation will not need to be run on a machine, but on the real world. Either we have el niño or we don't.
Hossenfelder’s linked tweet addresses this head on [1]. We need four orders of magnitude more qubits before a QC can simulate anything real.
In the meantime, we’re stuck with toy problems (absent the sort of intermediate test algorithms Aaronson mentions, though the existence of such algorithms would undermine the feat’s PR value, as it would afford cheap takedowns about the QC lacking supremacy).
For example, isolate two molecules in a vacuum and predict its future state. Now make it 5, now 100, etc...
I suggested simulating the experiment of n molecules in a vacuum, another experiment might be a chaotic system like a double pendulum. Although there would need to be a high level of precision in setting up the physical parameters of the experiment.
Well, really it can't run them at all, but a more-general computer this size which could, still wouldn't be large enough.
Try "I don't understand this claim"?