Variational quantum algorithm for Gaussian discrete solitons and their boson sampling

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. A soliton is a non-perturbative solution of a classical nonlinear wave-equation; it may describe mean-field states of atoms (as in Bose-Einstein condensation) or photons (as in nonlinear optics) [1]. From a quantum mechanical perspective, a soliton may correspond to a coherent state; however, the nonlinearity may induce squeezing or non-Gaussianity [2]. The quantum properties of solitons inspired experimental investigations, as quantum non-demolition, squeezing [3-6] and photon bound states [7]. Authors reported on theoretical studies on the soliton quantum features, as evaporation and breathing [8-13].