[bermanoid]

Taking this down to an even more basic level that doesn't require much knowledge of this stuff - the basic strategy of this program is to find a quantum system that they can prove (rigorously) has energy levels that map directly to the Riemann zeta zeros (well, the non-trivial ones) under a simple shift/rotation in the complex plane.

Since energy levels of these systems are always real (and in a straight line on the complex plane), this would establish that the zeros are all in a straight line as well, namely the one where Re(z) = 1/2.

The tough bit is finding that system. These researchers seem to think they've made headway; I'm withholding judgment for now, since by my reading the whole motivation for reaching for a physical system (real eigenvalues) is exactly what they still need to establish about their proposed system. They might have just succeeded in recasting the Riemann hypothesis in a different but no more tractable form, we'll have to see.