Connecting the concepts of quantum state tomography and molecular representations for machine learning

Quantum state tomography has been widely used to reconstruct the quantum state of a system from a set of informationally-complete measurements. Obtaining enough information about, e.g., the wavefunction of a molecule allows its complete characterization. On the other hand, deep learning models have proven useful to perform molecular property prediction (forward design) and inverse design subject to property constraints within the approximate bounds of the data manifold, suggesting that their learned representations are reliable within the region of chemical compound space spanned by their training data. In this work, from the tomographic perspective, we argue that enforcing faithful prediction of an increasing number of diverse molecular descriptors from a shared learned representation progressively constrains the space of admissible internal explanations, driving the inter-alignment of models as they converge towards representation that can explain all observed properties. In the limit where the set of descriptors approaches information-completeness, this alignment drives the learned representations to states that can act, locally, as informationally-equivalent to the molecule's reduced quantum density matrix – a deep tomography. Under this lens, the generalization capabilities of a deep learning model, and the alignment among successful models, arise from unphysical or shortcut solutions becoming progressively incompatible as supervision approaches informational completeness.