A classical algorithm inspired by quantum neural network for solving a Bose-Hubbard-like system in phase-space representation

We investigate the implementation of a classical algorithm inspired by the quantum neural networks to solve a Bose-Hubbard-like system within the epistemically-restricted phase-space representation. The quantum states are expressed with the continuous variable model that intuitively represents the wavelike properties of a quantum system. We use the first quantization formalism to describe bosons in a double well potential. We utilize a fully-connected feedforward neural network that enacts several layers of Gaussian transformations and nonlinear activation functions to find the minimum energy of the system. A stochastic Monte Carlo method with Metropolis sampling generates a set of phase-space variables transformed iteratively by the neural network to reach the lowest possible energy. A gradient descent algorithm attempts to optimize the parameters of the Gaussian gates to reach the ground state energy of the system.