Fitness landscape for quantum state tomography from neutron scattering

TL;DR

This paper explores the potential of using neutron scattering data to perform quantum state tomography by analyzing the relationship between structure factors and quantum states, revealing a well-behaved fitness landscape.

Contribution

It provides a numerical investigation demonstrating a linear relationship between structure factors and state overlaps, and suggests generalizations to thermal states and finite clusters.

Findings

Linear relationship between structure factors and state overlaps

Well-behaved fitness landscape identified

Potential generalization to thermal equilibrium states

Abstract

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.