Before I continue, it's obvious looking at any graph that war has been declining since prehistory.
Right now antimatter is only produced a few particles at a time in particle accelerators. But it's almost certain we'll learn how to produce lots of it in the future, to power spacecraft and possibly as a weapon. Annihilating 0.7 grams of antimatter with 0.7 grams of normal matter would release the energy of Little Boy, the bomb dropped on Hiroshima: 15,000 tons of TNT.
The 5.56x45 mm NATO bullet commonly fired by assault rifles weighs about 4 grams. You could hollow out the bullet and line the inside with tiny magnets. Half a milligram of antimatter could float between the magnets without touching the walls. When the bullet hits something, the magnets will break and the antimatter will annihilate. This tiny rifle bullet could explode with the energy of over 10 tons of TNT. How would this change war? It seems like war would have to change hugely, and between developed nations might be too costly to ever happen. Though in the hands of terrorists a crate of rifle magazines could rival the destructive power of a nuclear weapon.
This all depends on two things, an factories producing antimatter on an industrial scale and much more advanced magnets. These things won't happen in my lifetime but they will eventually happen. Of course, war might have been almost eliminated by then.