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?
What? The Schrodinger equation is just a linear differential equation. I can solve it here right now by hand if the Hamiltonian is time-independent, even for millions of dimensions.
|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).
Calculating the mean field of a thousand electrons is easy for a classical computer. Calculating the exchange and correlation energies of a thousand interacting electrons is not. Quantum computers would have an enormous advantage there.
There of course may be advantages to specific calculations on quantum computers but that isn't because the Schroedinger equation itself is somehow "a quantum equation"
The example they try it on is a quantum harmonic oscillator, i.e. the potential V(x) is just the squared norm of x. That's analytically solvable. Also,
> 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.
