I use multi-colored post-it notes to remind myself things.
After the task is complete I don't want to tear the notes.
How do I covert these post-it notes into a quilt?
Here are examples of quilts
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The "post-it" notes, if on standard sticky notes paper, cannot be made into a quilt directly. If you want to do this in future, you should look into coloured and starched squares of high thread-count cotton or linen to write on, use fabric markers to write the notes with, then just use them as normal quilting squares afterward.
If you want a quilt using your old paper sticky notes as a design, you will have to copy/print them onto fabric. The printers that can do this directly don't use very permanent ink, so great for T-shirts that only need to last a couple of years, not so good for quilts. You can also do it yourself by making the notes into collages, copying the collage squares using a colour laser printer and transferring the image to fabric using gel medium. Again, not extremely long lasting/colour fast. You can also use photos and other elements. One explanation of how to do this is given at Cloth, Paper, Scissors, see also the image below:
You can sew the cloth like ordinary patchwork/quilting until you have the desired size for your quilt, then use plain cloth for the "back" of the quilt or make enough to have your post-it design on front and back and then complete using batting, etc. Just remember the quilt will lose its colour with frequent washing, so will not last that long if you use it often.
Wall Hanging / Art
If what you really want is a wall hanging or poster that just looks like a sticky note quilt/collage, you can use the method above or just stick the notes onto whatever backing you want to use (paper/canvas/board) with a suitable glue stick in the collage design you want, then apply a good matte acrylic varnish once you are satisfied with your design. If you use a canvas or fabric as the backing and use a really good quality varnish that dries "flexibly" you can even use decorative stitching on it and hem the edges to make it look more like a quilt.
Remember to stretch the canvas/fabric on/over a suitable frame or board before starting to glue the paper squares on. Also apply varnish to both sides when finished if you want the paper to look textured like the canvas/cloth. This works better with coarser thread (more textured surface) such as rough linen or canvas, or even old burlap/sisal bags.