  Encoding the electronic structure of molecules using 2-electron reduced
density matrices (2RDMs) as opposed to many-body wave functions has been a
decades-long quest as the 2RDM contains sufficient information to compute the
exact molecular energy but requires only polynomial storage. We focus on linear
polymers with varying conformations and numbers of monomers and show that we
can use machine learning to predict both the 1-electron and the 2-electron
reduced density matrices. Moreover, by applying the Hamiltonian operator to the
predicted reduced density matrices we show that we can recover the molecular
energy. Thus, we demonstrate the feasibility of a machine learning approach to
predicting electronic structure that is generalizable both to new conformations
as well as new molecules. At the same time our work circumvents the
N-representability problem that has stymied the adaption of 2RDM methods, by
directly machine-learning valid Reduced Density Matrices.
