How to port to GPU (Dual Contouring)

Hello!
I want to port the Dual Contouring Algorithm to the GPU. Can someone get me started on how to do this?
The algorithm does this:
Generate a voxel octree from a noise function.
For octree leafs, a vertex is generated.
The vertices are triangulated.
Is the only way a compute shader? Or is there a better way?
Thanks in advance!

learn the algorithm first