Willow quantum chip demonstrates verifiable quantum advantage on hardware

It is not very clear from the text and from what I can say there is no "verifiability" concept in the papers they link.

I think what they are trying to do is to contrast these to previous quantum advantage experiments in the following sense.

The previous experiments involve sampling from some distribution, which is believed to be classically hard. However, it is a non-trivial question whether you succeed or fail in this task. Having perfect sampler from the same distribution won't allow you to easily verify the samples.

On the other hand these experiments involve measuring some observable, i.e., the output is just a number and you could compare it to the value obtained in a different way (one a different or same computer or even some analog experimental system).

Note that these observables are expectation values of the samples, but in the previous experiments since the circuits are random, all the expectation values are very close to zero and it is impossible to actually resolve them from the experiment.

Disclaimer: this is my speculation about what they mean because they didn't explain it anywhere from what I can see.

Sounds like N, not 2

I’ve only skimmed the paper but it seems like the “information not usually available” from NMR is the Jacobian and Hessian of the Hamiltonian of the system.

So basically you’re able to go directly from running the quantum experiment to being able to simulate the dynamics of the underlying system, because the Jacobian and Hessian are the first and second partial derivatives of the system with respect to all of its parameters in matrix form.

This is quite different from their previous random circuit sampling (RCS) experiments that have made headlines a few times in the past. The key difference from an applied standpoint is that the output of RCS is a random bitstring which is different every time you run the algorithm. These bitstrings are not reproducible, and also not particularly interesting, except for the fact that only a quantum computer can generate them efficiently.

The new experiment generates the same result every time you run it (after a small amount of averaging). It also involves running a much more structured circuit (as opposed to a random circuit), so all-in-all, the result is much more 'under control.'

As a cherry on top, the output has some connection to molecular spectroscopy. It still isn't that useful at this scale, but it is much more like the kind of thing you would hope to use a quantum computer for someday (and certainly more useful than generating random bitstrings).

This is not the RCS problem or indeed anything from number theory.

The announcement is about an algorithm which they are calling Quantum Echoes, where you set up the experiment, perturb one of the qbits and observe the “echoes” through the rest of the system.

They use it to replicate a classical experiment in chemistry done using nuclear magnetic resonance imaging. They say they are able to reproduce the results of that conventional experiment and gather additional data which is unavailable via conventional means.

My understanding is that this one is "verifiable" which means you get a reproducible result (i.e. consistent result comes out of a computation that would take much longer to do classically).

Non-verifiable computations include things like pulling from a hard-to-compute probability distribution (i.e. random number generator) where it is faster, but the result is inherently not the same each time.

I'd classify this one as different as it accompanies a publication in Nature - https://www.nature.com/articles/s41586-025-09526-6

It's the third one I am seeing from Google specifically.

It's what happens when companies are driven by profit rather than making accurate scientific statements that reputation is built by and further research funding is predicated on.

Hyperbolic claims like this are for shareholders who aren't qualified to judge for themselves because they're interested in future money and not actual understanding. This is what happens when you delegate science to corporations.

The article states: “...13,000 times faster on Willow than the best classical algorithm on one of the world’s fastest supercomputers...”

I agree it's not very precise without knowing which of the world's fastest supercomputers they're talking about, but there was no need to leave out this tidbit.

but much like AI hype quantum hype is also way over played, yeah modern asymmetric encryption will be less secure, but even after you have quantum computers that can do Shor's algorithm it might be a while before there are quantum computers affordable enough for it to be an actual threat (i.e. it's not cheaper to just buy a zero day for the target's phone or something).

But since we already have post quantum algorithms, the end state of cheap quantum computers is just a new equilibrium where people use the new algorithms and they can't be directly cracked and it's basically the same except maybe you can decrypt historical stuff but who knows if it's worth it.