A study on coherent Ising machines with Gaussian entanglement

In this Master's thesis, we study the optical coherent Ising machines by describing the quantum optical dynamics in the Gaussian approximation. After reviewing the essential theoretical formalism, namely the Lindblad master equation and quantum trajectories, we introduce the main concepts regarding coherent Ising machines, which are based on two-photon nonlinearities and inter-mode coupling. We then show that the action of a Spatial Light Modulator can be represented by a non-local Lindblad dissipator . We study the dynamics of Gaussian entanglement in a multi-mode system realizing the coherent Ising machine. We find that the efficiency of the quantum machine can be enhanced by the presence of quantum correlations. Indeed, we observe better performances when compared to the mean-field dynamics. A maximal value for the entanglement of the system was found at threshold. We also discuss future perspectives.