Ryan Peterman

And it's rich in many, many ways that are not, the influence of the algorithmic thinking on physical theories, including today theories in quantum gravity, black holes, is immense.

And we have new sources of problems and new models and new complexity classes, et cetera, et cetera.

And there's a fantastic, fantastic interaction.

It's also a rich complexity theory in that it turns out that you can discover quantum algorithms and maybe then de-quantize them in special cases, like I mentioned factoring before, de-randomizing.

Sometimes it's a way, it's a road to discover new algorithms.

It reveals connections between problems.

It's extremely rich.

But one of the maybe most amazing consequences is that people, I mean, we being what we are, we make up models and study them.

The interactive proofs I mentioned before, it turns out that even before quantum, they were generalized to interactive proofs, not with one prover, but with many provers, which seemed to be weird, but turns out to be very important in itself because it led to this PCP theorem.

Then people said, okay, let's allow quantum verifiers, quantum provers, and see what they can do.

So one amazing result, which is about five years ago, is the acronyms.

Of course, we have acronyms for all these complexity classes.

It's MIP star equal RE.

You may have seen it.

Maybe you didn't.

And it looks weird, but I'll tell you what it says, really.

It says that there is a really weird proof system with quantum provers

that are trying to convince verifiers, an efficient verifier, and it turns out you ask for which problems can they do it, forget the own knowledge, just convince.

It turns out they can do it for the halting problem, for problems that are not computable.

Things that are not computable are