Hopefully none, if it's anything close to the kind of anarchy I want.
Classical liberalism is a 19th? Century ideology derived from the works of Adam Smith -The Wealth of Nations etc.-, involving lots of philosophical ideas from the time like utilitarianism *shudder*. It fits pretty nicely onto the traditional political spectrum firm to the right.
Anarchy is... ummmm... well... hard to pin down. Frequently it's hard-left libertarian-communism, anarcho-communists, syndacalists, social anarchists etc. Not much similarity with classical liberalism there. To (too) many people it means something to do with 'free-market, bitcoin, non-agression principle, recreational nukes, my right to destroy my property even if it's food and there's a famine what are you a fucking fascist-commie'. I try not to get to involved with them.
To me anarchy is about living honestly, openly in the moment, removing all abstractions, and limiting my contact with the 'economy'. It's about joy and play and exploration and discovery and experience. And it's tricky to define, and tricky to realise, but it can be a hell of a lot of fun to try. My anarchy takes a strong egoist/nihilist slant, and tells a whole lot of shit to fuck off.
So hopefully not a lot in common between the two, but who knows what politicians will be identifying as next?