The efficient numerical simulation of nonequilibrium real-time evolution in is a key challenge for current computational methods, due to dimensionality. This refers in particular in the regime of two spatial dimensions, whose experimental exploration is currently pursued with strong
efforts in quantum simulations. An efficient machine learning inspired approach based on artificial neural network encodings of quantum many-body wave functions is used to describe the time dynamics. In this thesis, neural-network quantum states are used to approximate the implicit midpoint rule method for solving the time-dependent Schrödinger equation. The proposed neural-network architecture is the restricted Boltzmann machine, which has been shown to represent the ground state of various Hamiltonians with high accuracy. To deal with the dimensionality of a two-dimensional Ising model on a lattice with periodic boundary conditions, the use of the GPU is employed in delivering results for larger lattices. Afterwards, a time-wise comparison between the CPU-based and GPU-based method is done, regarding the improvements.

Keyword: Quantum dynamics, Simulation, GPU, Neural Networks, Wave function