QMA

So there's a bunch of technical problems in quantum computing theory that I have cared about that have fallen to AI this summer, or to humans collaborating with AI in many cases.

These include properties of quantum complexity classes, like one that's called QMA, or Quantum Merlin-Arthur, It would take me some time to explain these problems.

I don't know if you want me to.

No, no, go ahead.

But there was a question about is QMA equal to a variant called QMA1? So basically like can you take a quantum proof protocol and can you make it so that a valid proof will always be accepted rather than merely accepted with a high probability? And a lot of us suspected that that was the case.

I had results about this question in 2009.

Okay.

But – That was solved this summer.

One class includes all problems with quantum proofs and is known as QMA.

The other, called QCMA, includes problems with classical proofs that a quantum computer can check.

The unwieldy acronyms stand for Quantum Merlin Arthur and Quantum Classical Merlin Arthur, respectively, in reference to a fanciful thought experiment featuring the two characters from medieval legend.

The caveat is that the team's result is an oracle separation between QMA and QCMA.

This means it relies on certain assumptions that restrict the space of possibilities one needs to consider.