Iiii do not think you should be able to solve the Schrodinger equation with thousands of dimensions in general on a non-quantum computer, what with that being a quantum-mechanical equation some of whose solutions would reflect quantum-hard problems?
|psi(t)> = exp(-iHt/hbar) |psi(t=0)>
No offence but this sounds like you've never actually studied any quantum mechanics. The difficulty of solving such equations is purely just the difficulty of solving any complex set of PDEs, as the article talks about. There is nothing about the Schrodinger equation that means it's not computable on a classical computer (EDIT nor would it be easier on a quantum computer).
> in the case of the Schro ̈dinger equation, due to the separable nature of its network structure, we employ a separate neural network for each dimension.
which doesn't sound very general. Admittedly in my quick skim of this paper I didn't follow much.