Ants do not eat aphids.
More Info: Though ants do not eat aphids, they do share a symbiotic relationship with them, that is, both parties receive some benefit from the relationship. Aphids provide an important food source for certain species of ants. The ants farm the aphids much like cows milking them for the honeydew that aphids secrete.
The relationship is symbiotic in that the ant will remove natural enemies from their aphid colony.
How Do Ants Protect Aphids from Natural Enemies?
Ants protect aphids from natural enemies by either destroying the eggs of predators like the ladybug, or in some cases directly attacking the predator in a herd. This is done because aphids provide a necessary food source for the ants, and are farmed and raised by the ants much like humans raise cattle.
What Eats Aphids?
The most commonly known insect that eats aphids is the Hippodamia convergens, more widely known as the ladybug beetle. However, there is another predator that is so efficient at consuming aphids that it is called Aphidoletes aphidimyza and has a common name that is simply aphid predator. Other creatures that eat aphids include but are not limited to the green lacewing, hoverfly larvae, some species of birds, praying mantises and most arachnids.