I\'m going to start programming a 2D tile-based game in Qt and read about the QGraphicsScene and QGraphicsView classes which are intended for displaying and handling lots of 2D
You should use QGraphicsView.
The 40,000 Chips int the Qt Documentation is your best example to closely examine. It deals with the complexity of large numbers of elements, drawing them at multiple scales and a lot more.
Play with the example and you will see that all the chips actually make up a large photo if you zoom out and that you can select, and drag and drop multiple chips at any view, or you can zoom in enough to see some text on an individual chip. It will take time to understand each part, but this is a very thorough example to look into.
In the chips.cpp source, it shows how it can still run quickly by using a "LevelOfDetail" or lod variable switch statement based off of the transformation stored in a style option.
Qt Graphics View has been optimized to do a lot of the things you have talked about in your question, but it takes a while to understand how to approach it.
If you are still having issues with the size of the map you want to use, I would store tile layouts on the harddrive and load the ones you need when you need them, and remove the ones you don't need off of the scene as necessary.