Ryan Peterman

verifiable by efficient verifiers if the provers are quantum and they are entangled and whatever.

But it's a weird proof system, very weird, but it does something that looks totally ridiculous.

Things that are uncomputable by any class of computer are verifiable in this interactive probabilistic sense by efficient verifier.

So what I like to say in talking about this is that it seems that the best reaction, the best hypothetical reaction of anybody who hears this

Okay, you complexity theorists, you play in your sandbox and you build all these sand casters and make up all these models that have nothing to do with anything just because you can.

And once you're weird enough, you get weird enough consequences.

So one message, which I think is very powerful,

is that this result has absolutely fundamental impact on math and physics.

It turns out that it implies, and this was already done in the initial paper,

It implies resolution of well-known conjectures in math and physics.

It turns out that, you know, weird as it is, it's a new mathematical technique to solve problems that nobody had any idea.

Famous problems, important problems that fields were dedicated to are resolved by this result, by the techniques of this result.

So you ask the impact of quantum... You see, the impact is...

many generations over for different motivations and developments, but all of them following the methodology of complexity theory, of understanding the power of computational models, proof systems, and so on, has magically led to such a consequence.

And this is just, we are in the beginning of this.

This type of proof technique is now being explored and used, and there are more results using this type of techniques to learn long-standing problems.

Pretty amazing.

It's a 200-page paper.

It builds on 10 years of understanding, which is both a lot of development in the quantum algorithms and quantum proof systems sphere, but also relying on techniques from classical proof systems, which have to do with coding theory and various algebraic stuff that is used to prove, for example, the PCP theorem that I mentioned.

It's, you know, it's a huge body of work.