  Modern quantum optical systems such as photonic quantum computers and quantum
imaging devices require great precision in their designs and implementations in
the hope to realistically exploit entanglement and reach a real quantum
advantage. The theoretical and experimental explorations and validations of
these systems are greatly dependent on the precision of our classical
simulations. However, as Hilbert spaces increases, traditional computational
methods used to design and optimize these systems encounter hard limitations
due to the quantum curse of dimensionally. To address this challenge, we
propose an approach based on neural and tensor networks to approximate the
exact unitary evolution of closed entangled systems in a precise, efficient and
quantum consistent manner. By training the networks with a reasonably small
number of examples of quantum dynamics, we enable efficient parameter
estimation in larger Hilbert spaces, offering an interesting solution for a
great deal of quantum metrology problems.
