I have now made a first attempt to make a parent-child hierarchy implementation.
I am doing something like this:

Qt Code: 
  1. Field = new QGraphicsRectItem(outRect);
  2. .
  3. .
  4. SubField = new QGraphicsRectItem(outRect, Field);
  5. .
  6. .
  7. XRect = new QGraphicsRectItem(outRect, SubField);
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The result is using a remarkably small amount of memory, but the drawing performance is extremely poor, both compared to the "flat" item strategy. Why?
Another observation is that I used exactly the same placement calculations as for the "flat" version, and I expected that it all should turn out a mess since the child item should use the origin of its parent, not the global chip origin. Yet it worked the first time, which tell me I don't really understand how this works.
I will now make QGraphicItem subclasses for the Field, SubField and shape objects to see if it improves performance.