According to the website Beginner Gardening, ants are a problem when you see them on patio stones because they can damage or even destroy the stone foundation. You can quickly kill the ants you see on your patio stones, but in order to completely get rid of the ants for good, you have to get to the queen. Otherwise, the queen will continue to mate and produce more ants that will crawl back up on your patio stones.
Boil a pot of water and add 2 tbsp of dish soap. Pour this mixture over the ants on your patio stones. Not only will your stones be nice and clean when you are done, but the ants will be dead.
Mix 1 cup of sugar and 1 cup of borax and sprinkle on several small paper plates.
Set the plates up against the sides of your patio stones. The new ants that will be making their way to your patio stones will smell the sugar and begin to carry pieces of the mixture back to their nest. There, the queen and other ants will eat the mixture and die. This is how you kill the colony.
Sprinkle food grade diatomaceous earth in between your patio stones and along the side of your patio stones. This will keep any future colonies from coming and settling near your patio stones. Any ants that step on this powder will dehydrate and die because the powder is coarse and will pierce the exoskeleton of the ant.
If you are interested in using a chemical ant killer to get rid of the ants on your patio stones, the University of Minnesota recommends using permethrin, carbaryl or bifenthrin.