  Human experts cannot efficiently access the physical information of quantum
many-body states by simply "reading" the coefficients, but have to reply on the
previous knowledge such as order parameters and quantum measurements. In this
work, we demonstrate that convolutional neural network (CNN) can learn from the
coefficients of local reduced density matrices to estimate the physical
parameters of the many-body Hamiltonians, such as coupling strengths and
magnetic fields, provided the states as the ground states. We propose QubismNet
that consists of two main parts: the Qubism map that visualizes the ground
states (or the purified reduced density matrices) as images, and a CNN that
maps the images to the target physical parameters. By assuming certain
constraints on the training set for the sake of balance, QubismNet exhibits
impressive powers of learning and generalization on several quantum spin
models. While the training samples are restricted to the states from certain
ranges of the parameters, QubismNet can accurately estimate the parameters of
the states beyond such training regions. For instance, our results show that
QubismNet can estimate the magnetic fields near the critical point by learning
from the states away from the critical vicinity. Our work illuminates a
data-driven way to infer the Hamiltonians that give the designed ground states,
and therefore would benefit the existing and future generalizations of quantum
technologies such as Hamiltonian-based quantum simulations and state
tomography.
