Fitness landscape for quantum state tomography from neutron scattering

Recently, a direct connection between static structure factors and quantum ground states for two-spin interaction Hamiltonians was proven. This suggests the possibility of quantum state tomography from neutron scattering. Here, we investigate the associated fitness landscape numerically. We find a linear relationship between the mean square distances of the structure factors and the associated state overlaps, implying a well-behaved fitness landscape. Furthermore, we find evidence suggesting that the approach can be generalized to thermal equilibrium states. We also extend the arguments to the cases of applied magnetic fields and finite clusters.