Control and optimisation is a key research area, especially in the context of quantum technologies where it is an enabler of core functionalities. Due to the recent advances in GPU processing capabilities it is important to investigate how far one can take advantage of the speedups available for existing algorithms. The Limited-Memory Broyden-Fletcher-Goldfarb-Shanno is an iterative, non-linear optimisation algorithm, used to find local minima and maxima of functions. When applied to quantum control it may allow to improve the performance of current methods to provide more accurate results in less time, and thus a more accurate controls. By parallelising the L-BFGS algorithm, it allows for faster computation of these values, the challenge comes from developing a parallel optimisation from a iterative method. The aim of this project is to parallelise the L-BFGS algorithm on GPUs specifically looking at quantum control and compare results to existing methods.