I don't really understand the leftist varieties of anarchism--I mean, I think anarcho-capitalism is unworkable in reality, but how on earth could you have some form of communism without a massive government, or an entity with the same powers of government?
Technically communism by definition lacks a state. They normally advocate for a complete abolition of state along with money, markets, taxation and other such stuff. It's easier to think of anarchism as absence of a state, rather than absence of governance.