  We are interested in how quantum data can allow for practical solutions to
otherwise difficult computational problems. A notoriously difficult phenomenon
from quantum many-body physics is the emergence of many-body localization
(MBL). So far, is has evaded a comprehensive analysis. In particular, numerical
studies are challenged by the exponential growth of the Hilbert space
dimension. As many of these studies rely on exact diagonalization of the
system's Hamiltonian, only small system sizes are accessible. In this work, we
propose a highly flexible neural network based learning approach that, once
given training data, circumvents any computationally expensive step. In this
way, we can efficiently estimate common indicators of MBL such as the adjacent
gap ratio or entropic quantities. Our estimator can be trained on data from
various system sizes at once which grants the ability to extrapolate from
smaller to larger ones. Moreover, using transfer learning we show that already
a two-dimensional feature vector is sufficient to obtain several different
indicators at various energy densities at once. We hope that our approach can
be applied to large-scale quantum experiments to provide new insights into
quantum many-body physics.
