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We use neural networks to represent the characteristic function of many-bodyGaussian states in the quantum phase space. By a pullback mechanism, we modeltransformations due to unitary operators as linear layers that can be cascadedto simulate complex multi-particle processes. We use the layered neuralnetworks for non-classical light propagation in random interferometers, andcompute boson pattern probabilities by automatic differentiation. We alsodemonstrate that multi-particle events in Gaussian boson sampling can beoptimized by a proper design and training of the neural network weights. Theresults are potentially useful to the creation of new sources and complexcircuits for quantum technologies.

Gaussian boson sampling and multi-particle event optimization by machine learning in the quantum phase space