Variational Circuits for Quantum Solitons

We use quantum neural networks in the phase space as a Gaussian variational ansatz for the ground state of many-body Hamiltonians. Specifically, we consider a Bose-Hubbard model or quantum discrete nonlinear Schrodinger equation. In specific regimes, the model supports localized states and collections of localized states determined by the particle number and interaction strength. We study entanglement in the trained quantum network and perform boson sampling to outline the generation of particle pairs.