Anarchist communism is one of the oldest anarchist ideologies, and the most successful. Communism doesn't require a state, it only requires revolution, and the swift action of the masses to expropriate and reclaim private property for the working class. The role of the state is to uphold the inequalities and injustices of capitalism, to maintain class rule. In the post-capitalist classless society that communism proposes, there is no longer need for that institution.
"If, indeed, anyone should think that, in the communistic society, man must still remain under some form of compulsion in order to, do what is right, and leave off what is wrong, he had better give up communism at once and abandon all hope for the human race." - Johann Most, once the most famous anarchist (communist) in America
Take this from an anarcho-communist (me).