This report presents a review of a paper written by ( Citation: Apers & Wolf, 2019 Apers, S. & Wolf, R. (2019). Quantum Speedup for Graph Sparsification, Cut Approximation and Laplacian Solving. https://doi.org/10.48550/ARXIV.1911.07306 ) in which a new quantum algorithm for graph sparsification relying on nearly linear classical algorithms is introduced, leading to quantum speedups for several problems such as extremal cuts and Laplacian solving. Introduction $$\textit{" Graphs are nice […], but sparse graphs are nicer.

Foreword: In this short report, I will make a quick review of L-systems, relying on the book The algorithmic beauty of plants [@TheAB], without talking about the code implementation. The theoretical tools have not changed since the release of the book, it fully covers the state-of-the-art. I will simply explain part of its content. Finally, I have carefully chosen to explain only the parts that are the most interesting to me.