Unlike conventional approaches that treat the quantum processor as a black box simply producing results after receiving instructions, we leverage the ability to manipulate a coherent quantum state dynamically.

We generate and store high-fidelity and computationally complex quantum states and remotely manipulate and probe such states with instructions sent in real-time.

We examined the possibility of utilizing certified randomness for cryptography, non-interactive zero-knowledge proofs, blockchains, and more.

scirate.com/arxiv/2503.1... for some potential applications

Exactly what X is doesn't really matter. But if you write a paper claiming a computational task is hard (if you don't claim it's hard, why build a quantum computer?), you have to provide the number. I need to see a ridiculously large enough number, whether it has 10 or 100 zeros is less important.

I am just eager to see the biclique case studied and you guys are the most prepared to do it justice. I do think the results as is is already significant, because infinite dimensional lattice is less physically motivated compared to two and three dimensional lattices.

I'm trying to push you guys to study the biclique lattice because I am eager to see it! I do think your results are highly significant as is because it's hard to imagine infinite dimensional lattices being physically practical for useful things.

I agree if they do another experiment and try to claim supremacy, they have the burden of proof and need to rule out your method. Here, however, your results are the more recent one.

And I think it's an important question to have a good answer for, since it relates to the fundamental feasibility for quantum annealers to be useful.

I strongly advocate for this to be tested to have a definitive answer. I think one cannot make a claim that D-wave's experiment has no quantum advantage if this case is not reproduced with comparable error, especially when it is highly plausible that this case might be harder.

The biclique lattice also remains hard under both classical simulation techniques, hence they only simulate two and three dimensional lattices.

Scaling up perhaps requires a supercomputer, which are hard to acquire and requires significant engineering effort. These folks are scientists and are not interested in writing high performance software. The message of the papers are the techniques and the theory.

Congratulations on the nice results! Is it possible to run the method on the biclique lattice?

I do highly recommend a read. The authors came from different specialization with different perspectives on tensor networks, and I think I can safely say everyone learned things they didn't know about tensor networks when writing it.

Is it the case that the infinite dimensional case of D-wave's paper is still hard?