I’ve only skimmed the paper but it seems like the “information not usually available” from NMR is the Jacobian and Hessian of the Hamiltonian of the system. So

I’ve only skimmed the paper but it seems like the “information not usually available” from NMR is the Jacobian and Hessian of the Hamiltonian of the system. So basically you’re able to go directly from running the quantum experiment to being able to simulate the dynamics of the underlying system, because the Jacobian and Hessian are the first and second partial derivatives of the system with respect to all of its parameters in matrix form.