The idea that sparked my paper on efficient structural combination came from the question "can we see a solution to a problem" by layering many sub solutions on top of each other?

I was looking for something that can be displayed graphically. One of my favorite problems, the problem of finding a convex hull for a given set of vertices, was examined for that property. What do we see when layering solutions for some vertex combinations from the whole set of vertices?

The answer is surprisingly simple. Going over solutions for every combination of four vertices, the edges that are also part of the global solution appear most often in comparison to any other edge in those sub solutions. Visually those edges are the most bold edges when drawing each sub solution into one graph with all vertices. How to build a homemade quantum computer that gives us those visual solutions?

All we need is very thin layers of dark lacquered transparent film, where each layer can be scraped to let light shine trough. Every layer will represent a sub solution and get scraped along the three or four edges of the convex hull. After we scraped each layer, they will be aligned and stacked on top of each other. To visually solve the convex hull of all vertices, we need to backlit the film with strong light. The edges of our solution will shine the brightest.

I didn't build this quantum computer with film (yet), because it would need a lot of layers if we only have 50 vertices for example. To still give you a visual impression, below you'll see a graph of 50 vertices and the edges of each sub solution rendered by the browser. I did choose to give edges that appear more often to be drawn with exponentially stronger color than edges that appear less often, as visual enhancement.