  Nanomolecular assemblies of C$_{60}$ can be synthesized to enclose dipolar
molecules. The low-temperature states of such endofullerenes are described by
quantum mechanical rotors, which are candidates for quantum information devices
with higher-dimensional local Hilbert spaces. The experimental exploration of
endofullerene arrays comes at a time when machine learning techniques are
rapidly being adopted to characterize, verify, and reconstruct quantum states
from measurement data. In this paper, we develop a strategy for reconstructing
the ground state of chains of dipolar rotors using restricted Boltzmann
machines (RBMs) adapted to train on data from higher-dimensional Hilbert
spaces. We demonstrate accurate generation of energy expectation values from an
RBM trained on data in the free-rotor eigenstate basis, and explore the
learning resources required for various chain lengths and dipolar interaction
strengths. Finally, we show evidence for fundamental limitations in the
accuracy achievable by RBMs due to the difficulty in imposing symmetries in the
sampling procedure. We discuss possible avenues to overcome this limitation in
the future, including the further development of autoregressive models such as
recurrent neural networks for the purposes of quantum state reconstruction.
