Quantum consistent neural/tensor networks for photonic circuits with strongly/weakly entangled states

Abstract: 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.