  In the context of quantum information, highly nonlinear regimes, such as
those supporting solitons, are marginally investigated. We miss general methods
for quantum solitons, although they can act as entanglement generators or as
self-organized quantum processors. We develop a computational approach that
uses a neural network as a variational ansatz for quantum solitons in an array
of waveguides. By training the resulting phase-space quantum machine learning
model, we find different soliton solutions varying the number of particles and
interaction strength. We consider Gaussian states that enable measuring the
degree of entanglement and sampling the probability distribution of
many-particle events. We also determine the probability of generating particle
pairs and unveil that soliton bound states emit correlated pairs. These results
may have a role in boson sampling with nonlinear systems and in quantum
processors for entangled nonlinear waves.
